WO2018019073A1 - 编码方法、设备和装置 - Google Patents

编码方法、设备和装置 Download PDF

Info

Publication number
WO2018019073A1
WO2018019073A1 PCT/CN2017/090359 CN2017090359W WO2018019073A1 WO 2018019073 A1 WO2018019073 A1 WO 2018019073A1 CN 2017090359 W CN2017090359 W CN 2017090359W WO 2018019073 A1 WO2018019073 A1 WO 2018019073A1
Authority
WO
WIPO (PCT)
Prior art keywords
polarization
weight vector
polarization weight
channel
bits
Prior art date
Application number
PCT/CN2017/090359
Other languages
English (en)
French (fr)
Inventor
刘小成
陈莹
李榕
Original Assignee
华为技术有限公司
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 华为技术有限公司 filed Critical 华为技术有限公司
Priority to BR112019001775-5A priority Critical patent/BR112019001775A2/pt
Priority to JP2019504681A priority patent/JP6797281B2/ja
Priority to EP21152711.4A priority patent/EP3879729A1/en
Priority to EP17833376.1A priority patent/EP3474472B1/en
Publication of WO2018019073A1 publication Critical patent/WO2018019073A1/zh
Priority to US16/261,220 priority patent/US10879932B2/en
Priority to US17/135,061 priority patent/US11444640B2/en

Links

Images

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13—Linear codes
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/033—Theoretical methods to calculate these checking codes
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/29—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
    • H03M13/2906—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes using block codes
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/61—Aspects and characteristics of methods and arrangements for error correction or error detection, not provided for otherwise
    • H03M13/615—Use of computational or mathematical techniques
    • H03M13/616—Matrix operations, especially for generator matrices or check matrices, e.g. column or row permutations
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0057—Block codes
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/63—Joint error correction and other techniques
    • H03M13/635—Error control coding in combination with rate matching
    • H03M13/6362—Error control coding in combination with rate matching by puncturing
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
    • H04L1/0009—Systems modifying transmission characteristics according to link quality, e.g. power backoff by adapting the channel coding

Definitions

  • the present application relates to the field of codec technologies, and in particular, to an encoding method and device.
  • Polar (polarization) code is a coding method that theoretically proves that it can reach the Shannon limit and has low coding and decoding complexity.
  • the Polar code is a linear block code whose generating matrix is G N and its encoding process is For the encoded bits, For the bits to be encoded, where Is a binary line vector of length N (ie code length); G N is an N ⁇ N matrix, and among them B N is an N ⁇ N transposed matrix, such as a Bit Reversal matrix; Defined as the Kronecker product of log 2 N matrices F 2 .
  • the polarization channel reliability corresponding to each input bit can be estimated in different manners, and the polarization channel placement information bits with high reliability are preferentially selected.
  • the position of the information bits needs to be indicated by a sequence, and the position of the information bits can be unified by online calculation or offline storage.
  • the DE method and the GA method depend on the parameter rate matching method of the actual channel, the code rate and the modulation method when calculating the reliability.
  • the reliability estimation result of the changed polarization channel of any one of the above parameters also changes, and the position of the corresponding information bit also changes, which eventually leads to excessive storage overhead.
  • the present application provides an encoding method and apparatus to reduce computational complexity and storage complexity of Polar code encoding.
  • the application provides an encoding method, including:
  • N is a positive integer according to the target code length M of the Polar code
  • the polarization weight is the basis for selecting the information bits, then determining the information bits according to the first polarization weight vector, and finally performing Polar coding on the N to-be-coded bits to obtain the Polar coded bits. Therefore, the calculation of the polarization weight of the Polar code polarized channel is performed to determine the position of the information bit and the fixed bit, and has nothing to do with the channel parameter and the code rate, thereby reducing the computational complexity of the Polar code encoding, and, for different code lengths.
  • the polarization weight corresponding to the bit rate Polar code has the same part, which greatly reduces the storage space, thereby reducing the storage complexity of the Polar code encoding.
  • the target code length M of the Polar code is equal to a positive integer power of 2, M is a positive integer, and N bits to be encoded are determined, including: N is equal to M, and the target code length of the Polar code is a Polar code.
  • calculating the polarization weights of the N polarized channels to obtain the first polarization weight vector includes: calculating the polarization weights W i of the N polarized channels according to the following formula to obtain the first polarization Weight vector:
  • i is the channel index
  • calculating the polarization weights of the N polarized channels to obtain the first polarization weight vector includes: obtaining the first polarization weight vector W 0 N-1 by recursive calculation according to the following formula:
  • ⁇ i (2 i-1 + ⁇ ) ⁇ ;
  • ⁇ i is an intermediate variable related to the channel index i
  • ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code
  • W 0 is Any constant.
  • the target code length M of the Polar code is equal to a positive integer power of 2
  • the first polarization weight vector including the polarization weights of the N polarized channels is obtained, including: the second stored from the pre-stored Obtaining a first polarization weight vector in the polarization weight vector, the second polarization weight vector includes a polarization weight of the N max polarization channels, and N max is a mother code code corresponding to a maximum code length supported by the preset communication system. Long, the mother code length is 2 positive integer power.
  • the second polarization After receiving the input information bits, determining the number N of bits to be encoded according to the target code length M of the Polar code, and then acquiring the first polarization weight vector from the pre-stored second polarization weight vector, the second polarization
  • the weight vector includes the polarization weight of the mother code length N max polarization channels corresponding to the maximum code length supported by the communication system, and then the information bits are determined according to the first polarization weight vector, and finally the N bits to be coded are performed.
  • Polar encoding obtaining the Polar encoded bits. Therefore, the polarization weight of the Polar code polarized channel is obtained by offline storage to determine the position of the information bit and the fixed bit.
  • the polarization weight vector in the short code length is The element set is a subset of the set of elements in the long code length weight vector, and the polarization weights of the same polarized channel with the same index (sequence number) are the same, thereby reducing the storage space and reducing the storage complexity of the Polar code encoding.
  • offline storage can reduce the latency caused by online calculations when storage space allows.
  • the set of elements in the first polarization weight vector is a subset of the set of elements in the second polarization weight vector
  • the polarization weight is equal to the polarization weight of the polarized channel whose corresponding channel index is less than or equal to N max plus the weight increment
  • ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code.
  • the second polarization After receiving the input information bits, determining the number N of bits to be encoded according to the target code length M of the Polar code, and then acquiring the first polarization weight vector from the pre-stored second polarization weight vector, the second polarization
  • the weight vector includes the polarization weight of the maximum code length N max polarization channels supported by the communication system, and then the information bits are determined according to the first polarization weight vector, and finally the N code to be coded bits are Polar coded to obtain the Polar code. Bits. Therefore, the polarization weight of the Polar code polarized channel is obtained by semi-online calculation of the semi-offline storage to determine the position of the information bit and the fixed bit.
  • the Polar is smaller than the pre-stored N max .
  • the set of elements in the code polarization weight vector is a subset of the set of elements in the N max weight vector, and the polarization weights of the same polarized channel with the same index (sequence number) are the same, and the Polar code polarization weight is greater than the pre-stored N max .
  • the polarization weight of the polarization channel whose channel index is less than or equal to N max is one-to-one corresponding to the polarization weight in the second polarization weight vector, and the polarization weight of the polarization channel whose channel index is greater than N max is equal to the corresponding Polarization weight of a polarized channel whose channel index is less than or equal to N max plus weight increment Therefore, the storage space can be reduced, and the storage complexity of the Polar code encoding can be reduced. This method can reduce the delay caused by online calculation and reduce the storage complexity.
  • the target code length M of the Polar code is not equal to the positive integer power of 2, and the N bits to be encoded are determined, including: symbol Indicates rounding down.
  • the method before acquiring the first polarization weight vector including the polarization weights of the N polarization channels, the method further includes: determining a position of the NM bits to be deleted among the N to-be-coded bits, and determining according to the determining As a result, a correction coefficient set including polarization weights corresponding to the N bits to be encoded is calculated, the correction coefficient is used to represent the correction amount of the deleted bits for each polarization weight; and the first polarization density including the N polarization channels is obtained.
  • the polarization weight vector includes: calculating polarization weights of the N polarization channels according to the correction coefficient set to obtain a first polarization weight vector.
  • determining the location of the NM bits to be deleted among the N bits includes: determining a channel index sequence of the N polarized channels For each index in the channel index sequence, the following operations are performed: the binary numbers corresponding to each index are reverse-ordered and converted into decimal numbers to obtain a new channel index sequence. New channel index sequence Index sorting in ; select channel index sequence in ascending order The NM indexes in the index are the bit indexes to be deleted.
  • the step is not limited to performing bit reverse order operation on each index.
  • the binary number corresponding to each index may be interleaved or scrambled, or the like, or each index may not be processed.
  • a correction coefficient set including a correction coefficient of N bits is calculated according to the determination result, including:
  • p i is a polarized channel with channel index i
  • the polarization weights of the N polarized channels are calculated according to the set of correction coefficients, and the first polarization weight vector is obtained, including: calculating the polarization weights W i of the N polarized channels according to the following formula, First polarization weight vector:
  • i is the channel index
  • g (i,j) is the i-th row of the correction coefficient set g
  • the elements of the column, ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code.
  • the polarization weights of the N polarized channels are calculated according to the set of correction coefficients, and the first polarization weight vector is obtained, including: obtaining the first polarization weight vector W 0 N- by recursive calculation according to the following formula: 1 :
  • ⁇ i (2 i-1 + ⁇ ) ⁇ ;
  • ⁇ i is an intermediate variable related to the channel index i
  • ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code
  • g (i , j) is an element of the i-th row and the j-th column in the correction coefficient set g
  • W 0 is an arbitrary constant.
  • the position of the information bit and the fixed bit is determined by the calculation of the polarization weight of the Polar code polarized channel, which has no relationship with the channel parameter and the code rate, and can reduce the calculation of the Polar code encoding. And implementation complexity.
  • determining the position of the information bit according to the first polarization weight vector includes: sorting the polarization weights in the first polarization weight vector from large to small, and selecting the first K polarization weights.
  • the bits are used as information bits.
  • the encoding method is performed by a base station or terminal.
  • the application provides an encoding device, including:
  • a first determining module configured to determine N bits to be encoded, where N bits to be encoded include information bits and fixed bits, N is a positive integer, and an acquiring module is configured to acquire a polarization weight of the N polarized channels a polarization weight vector, the polarization weight is the basis for selecting the information bits, the N to be coded bits correspond to the N polarization channels, and the second determining module is configured to determine the position of the information bits according to the first polarization weight vector, and the coding module For performing Polar coding on the N to-be-coded bits to obtain the Polar-coded bits.
  • the target code length M of the Polar code is equal to a positive integer power of 2, and M is a positive integer.
  • the first determining module is specifically configured to: determine that N is equal to M, and the target code length of the Polar code is a Polar code.
  • the obtaining module is specifically configured to: calculate a polarization weight W i of the N polarized channels according to the following formula, and obtain a first polarization weight vector:
  • i is the channel index
  • the obtaining module is specifically configured to: obtain the first polarization weight vector W 0 N-1 by recursive calculation according to the following formula:
  • ⁇ i (2 i-1 + ⁇ ) ⁇ ;
  • ⁇ i is an intermediate variable related to the channel index i
  • ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code
  • W 0 is Any constant.
  • the target code length M of the Polar code is equal to a positive integer power of 2
  • the obtaining module is specifically configured to: obtain a first polarization weight vector from a pre-stored second polarization weight vector, and second The polarization weight vector includes polarization weights of N max polarization channels, Nmax is the mother code length corresponding to the maximum code length supported by the preset communication system, and the mother code code length is a positive integer power of 2.
  • the set of elements in the first polarization weight vector is a subset of the set of elements in the second polarization weight vector
  • the polarization weight is equal to the polarization weight of the polarized channel whose corresponding channel index is less than or equal to N max plus the weight increment
  • ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code.
  • the target code length M of the Polar code is not equal to the positive integer power of 2
  • the first determining module is specifically configured to: determine symbol Indicates rounding down.
  • the method further includes: a third determining module, configured to determine, before the acquiring module acquires the first polarization weight vector that includes the polarization weights of the N polarized channels, to delete the N to-be-coded bits a position of the NM bits; a calculation module, configured to calculate, according to a result determined by the third determining module, a set of correction coefficients including polarization weights corresponding to the N bits to be encoded, the correction coefficient used to represent the deleted bit pair for each polarization
  • the correction amount of the weight is specifically configured to: calculate polarization weights of the N polarized channels according to the set of correction coefficients, to obtain a first polarization weight vector.
  • the third determining module is specifically configured to: determine a channel index sequence of the N polarized channels For each index in the channel index sequence, the following operations are performed: the binary numbers corresponding to each index are reverse-ordered and converted into decimal numbers to obtain a new channel index sequence. New channel index sequence Index sorting in ; select channel index sequence in ascending order The NM in the middle is the bit index to be deleted.
  • the set of correction factors The calculation module is specifically used to calculate each term g (i, j) in the correction coefficient set g according to the following formula:
  • p i is a polarized channel with channel index i
  • the obtaining module is specifically configured to: calculate a polarization weight W i of the N polarized channels according to the following formula, and obtain a first polarization weight vector:
  • i is the channel index
  • g (i,j) is the i-th row of the correction coefficient set g
  • the elements of the column, ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code.
  • the obtaining module is specifically configured to: obtain the first polarization weight vector W 0 N-1 by recursive calculation according to the following formula:
  • ⁇ i (2 i-1 + ⁇ ) ⁇ ;
  • ⁇ i is an intermediate variable related to the channel index i
  • ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code
  • g (i , j) is an element of the i-th row and the j-th column in the correction coefficient set g
  • W 0 is an arbitrary constant.
  • the second determining module is specifically configured to: sort the polarization weights in the first polarization weight vector from large to small, and select the bits corresponding to the first K polarization weights as information bits.
  • the encoding device is a base station or a terminal.
  • the application provides a communication device, including:
  • a memory for storing instructions for performing an operation
  • a processor coupled to the memory, configured to: determine N bits to be encoded according to the instruction, where the N bits to be encoded include information bits and fixed bits, N is a positive integer; and acquires N polarized channels a polarization weighted first polarization weight vector, the polarization weight being a basis for selecting information bits, the N to-be-coded bits corresponding to the N polarization channels; determining according to the first polarization weight vector a position of the information bit; performing Polar coding on the N to-be-coded bits to obtain a Polar-coded bit.
  • the communication device is a base station or terminal.
  • the present application provides a communication device, the computer storage medium storing computer executable instructions that, when invoked by a computer, cause the computer to perform the method as described in the foregoing embodiments .
  • 1 is a schematic diagram of an encoding process of an existing Polar code
  • FIG. 2 is a block diagram of a coding structure of Embodiment 1 of an encoding method of the present application;
  • Embodiment 3 is a flowchart of Embodiment 1 of an encoding method of the present application.
  • Embodiment 4 is a flowchart of Embodiment 2 of an encoding method of the present application.
  • FIG. 8 is a schematic structural diagram of Embodiment 1 of an encoding apparatus according to the present application.
  • Embodiment 9 is a schematic structural diagram of Embodiment 2 of an encoding device of the present application.
  • FIG. 10 is a schematic structural diagram of an embodiment of a communication device according to the present application.
  • FIG. 1 is a schematic diagram of an encoding process of an existing Polar code.
  • the encoding of a Polar code is performed by a transmitting end.
  • the encoding process of the Polar code includes three processes of construction, encoding, and rate matching.
  • the encoding process Polar encoding the bits to be encoded to obtain the Polar encoded bits.
  • the rate matching process since the code length of the code code after the Polar code is 2 is the positive integer power, and the actual implementation needs to flexibly configure the code length, it is necessary to perform rate matching to obtain the code of any code length. A portion of the NM bits in the code length of a positive integer power of 2 is obtained, and the target code length is obtained. Where N, M, N 1 , and N 2 are all positive integers.
  • the encoding method provided by the present application mainly relates to the encoding process of the Polar code shown in FIG. 1 , and most relates to the construction process.
  • the reliability of the channel is estimated based on the actual parameters and the code rate of all the polarized channels to determine the position of the information bits, and the remaining positions are fixed bit positions.
  • the position of the information bits needs to be indicated by a sequence, and the position of the information bits can be unified by online calculation or offline storage.
  • offline storage a very large table is needed to store the sequence, and different channel parameters are considered.
  • the code rate and the different code lengths, the number of sequences to be stored will be millions, so the existing way of determining the information bit position has higher complexity for online computing and offline storage.
  • the present application provides an encoding method for determining the position of information bits and fixed bits by calculating the polarization weight of the Polar code polarized channel, which has no relationship with the channel parameters and the code rate, and can reduce the calculation of the Polar code encoding. Complexity and storage complexity.
  • the coding method and apparatus provided by the present application are described in detail below with reference to the accompanying drawings.
  • the present application is mainly applied to various wireless communication systems, and acts on a digital signal processing unit in the system to improve the reliability of wireless communication.
  • the network element involved in the present application is mainly a base station and a terminal, and the base station implements communication with the terminal.
  • FIG. 2 is a block diagram of a coding structure according to Embodiment 1 of the coding method of the present application.
  • information bits (number N 1 ) and target code length M of the Polar code are input as follows, and then Polar code construction is performed, first according to Polar.
  • FIG. 3 is a flowchart of Embodiment 1 of the encoding method of the present application. As shown in FIG. 3, the method in this embodiment may include:
  • N bits to be encoded where the N bits to be encoded include information bits and fixed bits.
  • the code length of the code encoded by the Polar code is a positive integer power of 2
  • the code length needs to be flexibly configured, that is, to obtain a Polar code of an arbitrary code length, and thus the input information bit is received.
  • the number N of bits to be encoded is determined according to the target code length M of the Polar code.
  • the N bits to be encoded include information bits and fixed bits
  • the target code length of the Polar code is the output code length of the Polar code.
  • the target code length M of the Polar code is equal to the positive integer power of 2, that is, the rate matching is not required
  • the number N of bits to be encoded determined at this time is equal to M.
  • the target code length M of the Polar code is not equal to the positive integer power of 2, that is, the rate matching is required, and the number of bits to be encoded determined at this time is determined. symbol Indicates rounding down.
  • S102 Acquire a first polarization weight vector that includes polarization weights of N polarization channels.
  • the polarization weight is the basis for selecting information bits, and the N to-be-coded bits correspond to N polarization channels.
  • one bit corresponds to one polarization channel
  • the polarization weight of the polarization channel is the basis for selecting information bits, and the polarization weight is different from the reliability of the channel in the prior art, and whether the target code length M of the Polar code is satisfied.
  • the acquisition of the positive integer power polarization weights of 2 is different.
  • the following describes in detail how to obtain the first polarization weight vector when the number N of bits to be encoded is equal to the target code length M of the Polar code, specifically, the first pole
  • the polarization weights W i of the N polarized channels in the weight vector are calculated according to the following formula:
  • i is the channel index
  • ⁇ and ⁇ are preset according to the target code length and code rate of the Polar code For the Polar code of different code length and code rate, the parameters ⁇ and ⁇ can be adjusted to obtain a better performance Polar code information bit indication sequence.
  • the calculation formula is:
  • Polar matrix does not contain F N B N bits in reverse operation, if the bits in reverse order with the encoding matrix B N, needs to be calculated is extremely The weights are performed in the corresponding bit reverse order operations.
  • the first polarization weight vector W 0 N-1 is obtained by recursive calculation according to the following formula:
  • ⁇ i (2 i-1 + ⁇ ) ⁇ ;
  • ⁇ i is an intermediate variable related to the channel index i
  • ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code
  • W 0 is Any constant.
  • a is a constant value, which can usually be set to zero.
  • the polarization weights in the first polarization weight vector may be sorted from large to small, and the bits corresponding to the first K polarization weights are selected as information bits, that is, the position of the information bits is selected, and the remaining positions are set. For fixed bits, a complete bit to be encoded of length N is obtained.
  • the encoding process of the bits to be encoded is completed using the encoding matrix F N of the Polar code.
  • the encoding method provided in this embodiment determines the number N of bits to be encoded according to the target code length M of the Polar code after receiving the input information bits, and then acquires the first pole of the polarization weight including the N polarized channels.
  • the weight vector is determined, and then the information bits are determined according to the first polarization weight vector, and finally the N bits to be encoded are Polar coded to obtain the Polar coded bits. Therefore, the calculation of the polarization weight of the Polar code polarized channel is performed to determine the position of the information bit and the fixed bit, and has nothing to do with the channel parameter and the code rate, thereby reducing the computational complexity of the Polar code encoding, and, for different code lengths.
  • the polarization weight corresponding to the bit rate Polar code has the same part, which greatly reduces the storage space, thereby reducing the storage complexity of the Polar code encoding.
  • the difference between the polarization weights of the adjacent two-order polarization codes and the weight increment ⁇ i can be obtained , and the S102 in the first embodiment
  • a specific implementation manner is to obtain the first polarization weight vector by online calculation, as another implementable manner, and can also be obtained by offline storage, compared with online calculation, and offline storage if the storage space permits. The way to reduce the latency caused by online computing.
  • the mode of offline storage is described in detail below with reference to FIG. 4. It should be noted that the offline storage mode is applicable to a scenario in which the target code length M of the Polar code satisfies the positive integer power of 2.
  • FIG. 4 is a flowchart of Embodiment 2 of the encoding method of the present application. As shown in FIG. 4, the method in this embodiment may include:
  • N bits to be encoded where the N bits to be encoded include information bits and fixed bits.
  • N max is a preset communication system supports a maximum code length corresponding to the length of the mother code, mother code length is a positive integer power of two.
  • the mother code length N max corresponding to the maximum code length supported by the communication system may be set in advance according to the actual communication scenario, and the mother code code length is a positive integer power of 2, which is preceded by the first embodiment.
  • the calculation formula shown calculates the second polarization weight vector and stores it offline.
  • the first polarization weight vector is obtained directly from the pre-stored second polarization weight vector. It can be known from the calculation formula shown in the first embodiment that when the positive integer power code length of 2, the element set in the polarization weight vector under the short code length is a subset of the element set in the long code length weight vector.
  • the polarization weights of the same polarized channel with the same index (sequence number) are the same.
  • the polarization weights in the first polarization weight vector may be sorted from large to small, and the bits corresponding to the first K polarization weights are selected as information bits. That is, the position of the information bit is selected, and the remaining positions are set as fixed bits, and a complete bit to be encoded of length N is obtained.
  • S204 Perform Polar coding on the N to-be-coded bits to obtain a Polar-coded bit.
  • the encoding process of the bits to be encoded is completed using the encoding matrix F N of the Polar code.
  • the encoding method provided in this embodiment determines the number N of bits to be encoded according to the target code length M of the Polar code after receiving the input information bits, and then obtains the first pole from the pre-stored second polarization weight vector.
  • the weight vector, the second polarization weight vector includes the polarization weight of the mother code length N max polarization channels corresponding to the maximum code length supported by the communication system, and then determines the information bits according to the first polarization weight vector.
  • the L coded bits are Polar coded to obtain the Polar coded bits. Therefore, the polarization weight of the Polar code polarized channel is obtained by offline storage to determine the position of the information bit and the fixed bit.
  • the polarization weight vector in the short code length is The element set is a subset of the set of elements in the long code length weight vector, and the polarization weights of the same polarized channel with the same index (sequence number) are the same, thereby reducing the storage space and reducing the storage complexity of the Polar code encoding.
  • offline storage can reduce the latency caused by online calculations when storage space allows.
  • a specific implementation manner that is different from the S202 in the foregoing Embodiment 2 is obtained by using offline storage.
  • the method may also be obtained by semi-online calculation of semi-offline storage.
  • the method for semi-online calculation of semi-offline storage is described in detail in the third embodiment of the present application. It should be noted that the method is applicable to a scenario in which the target code length M of the Polar code satisfies the positive integer power of 2.
  • the first polarization weight vector is obtained from the second polarization weight vector stored in advance in S202.
  • the element set in the first polarization weight vector is the first a subset of the set of elements in the dual polarization weight vector;
  • the polarization weights correspond one-to-one, and the polarization weight of the polarization channel whose channel index is greater than N max is equal to the polarization weight of the polarization channel whose corresponding channel index is less than or equal to N max plus the weight increment
  • ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code.
  • the polarization weight to 15 is obtained by increasing the polarization weight from the index from 0 to 7 by the weight increment (8 + ⁇ ) ⁇ .
  • the encoding method provided in this embodiment determines the number N of bits to be encoded according to the target code length M of the Polar code after receiving the input information bits, and then obtains the first pole from the pre-stored second polarization weight vector.
  • the weight vector, the second polarization weight vector includes the polarization weight of the maximum code length N max polarization channels supported by the communication system, and then determines the information bits according to the first polarization weight vector, and finally the N bits to be coded.
  • Perform Polar coding to obtain the Polar encoded bits. Therefore, the polarization weight of the Polar code polarized channel is obtained by semi-online calculation of the semi-offline storage to determine the position of the information bit and the fixed bit.
  • the Polar is smaller than the pre-stored N max .
  • the set of elements in the code polarization weight vector is a subset of the set of elements in the N max weight vector, and the polarization weights of the same polarized channel with the same index (sequence number) are the same, and the Polar code polarization weight is greater than the pre-stored N max .
  • the polarization weight of the polarization channel whose channel index is less than or equal to N max is one-to-one corresponding to the polarization weight in the second polarization weight vector, and the polarization weight of the polarization channel whose channel index is greater than N max is equal to the corresponding Polarization weight of a polarized channel whose channel index is less than or equal to N max plus weight increment Therefore, the storage space can be reduced, and the storage complexity of the Polar code encoding can be reduced. This method can reduce the delay caused by online calculation and reduce the storage complexity.
  • FIG. 7 is a flowchart of Embodiment 4 of the encoding method of the present application.
  • the weight vector is as shown in FIG. 7.
  • the method in this embodiment may include:
  • N bits to be encoded where the N bits to be encoded include information bits and fixed bits.
  • the code length of the code encoded by the Polar code is a positive integer power of 2
  • the code length needs to be flexibly configured, that is, to obtain a Polar code of an arbitrary code length, and thus the input information bit is received.
  • the number N of bits to be encoded is determined according to the target code length M of the Polar code, and the N bits to be encoded include information bits and fixed bits.
  • the target code length M of the Polar code is not equal to the positive integer power of 2, that is, rate matching is required, the number of bits to be encoded determined at this time is determined. symbol Indicates rounding down.
  • determining a location of the N-M bits to be deleted among the N to-be-coded bits includes:
  • the step is not limited to performing bit reverse order operation on each index.
  • the binary number corresponding to each index may be interleaved or scrambled, or the like, or each index may not be processed.
  • the original channel index sequence For one of the indexes, the corresponding binary number After the bit is reversed, Correct All the elements in the block are processed in reverse order. ,will After all indexes in the reordering, the channel index sequence is taken from small to large in order The bit corresponding to the NM index in the middle is the bit to be deleted.
  • the coefficients of the polarization weights need to be corrected, and the corresponding correction coefficient set g is in one-to-one correspondence with each computing node in the butterfly decoding tree, and thus is a vector of N ⁇ n, according to the determination result.
  • p i is a polarized channel with channel index i
  • the initial g is calculated using the following formula
  • the remaining g (i, j) are calculated according to the same rules.
  • the polarization weights W i of the N polarized channels are calculated according to the following formula to obtain a first polarization weight vector:
  • i is the channel index
  • g (i,j) is the i-th row of the correction coefficient set g
  • the elements of the column, ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code.
  • the first polarization weight vector W 0 N-1 is obtained by recursive calculation according to the following formula:
  • ⁇ i (2 i-1 + ⁇ ) ⁇ ;
  • ⁇ i is an intermediate variable related to the channel index i
  • ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code
  • g (i , j) is an element of the i-th row and the j-th column in the correction coefficient set g
  • W 0 is an arbitrary constant.
  • the polarization weights in the first polarization weight vector may be sorted from large to small, and the bits corresponding to the first K polarization weights are selected as information bits. That is, the position of the information bit is selected, and the remaining positions are set as fixed bits, and a complete bit to be encoded of length N is obtained.
  • the encoding process of the bits to be encoded is completed using the encoding matrix F N of the Polar code.
  • the encoding method provided in this embodiment determines the number N of bits to be encoded according to the target code length M of the Polar code after receiving the input information bits, and then determines the position of the NM bits to be deleted among the N to-be-coded bits. And calculating a correction coefficient set including the correction coefficients of the N bits to be coded according to the determination result, and then calculating polarization weights of the N polarization channels according to the correction coefficient set to obtain a first polarization weight vector, and finally according to the first polarization The weight vector determines the information bits, and performs Polar coding on the N to-be-coded bits to obtain the Polar-coded bits.
  • the position of the information bit and the fixed bit is determined by the calculation of the polarization weight of the Polar code polarized channel, which has no relationship with the channel parameter and the code rate, and can reduce the calculation of the Polar code encoding. And implementation complexity.
  • FIG. 8 is a schematic structural diagram of Embodiment 1 of an encoding apparatus of the present application.
  • the encoding apparatus 100 of this embodiment may include: a first determining module 11, an obtaining module 12, a second determining module 13, and an encoding module 14.
  • the first determining module 11 is configured to determine N bits to be encoded, where the N bits to be encoded include information bits and fixed bits
  • the acquiring module 12 is configured to acquire a first polarization that includes polarization weights of the N polarized channels.
  • the weighting vector, the polarization weight is the basis for selecting the information bits, and the N bits to be encoded correspond to the N polarization channels;
  • the second determining module 13 is configured to determine the position of the information bits according to the first polarization weight vector;
  • the encoding module 14 is configured to: Polar coding is performed on the N bits to be encoded to obtain the Polar coded bits.
  • the target code length M of the Polar code is equal to a positive integer power of 2
  • the first determining module 11 is specifically configured to: determine that N is equal to M
  • the target code length of the Polar code is the output code length of the Polar code.
  • the obtaining module 12 is specifically configured to: calculate polarization weights of the N polarized channels to obtain a first polarization weight vector.
  • the obtaining module 12 is specifically configured to: calculate a polarization weight W i of the N polarized channels according to the following formula, and obtain a first polarization weight vector:
  • i is the channel index
  • the obtaining module 12 is specifically configured to: obtain the first polarization weight vector W 0 N-1 by recursively calculating according to the following formula:
  • ⁇ i (2 i-1 + ⁇ ) ⁇ ;
  • ⁇ i is an intermediate variable related to the channel index i
  • ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code
  • W 0 is Any constant.
  • the coding device of this embodiment may be used to implement the technical solution of the method embodiment shown in FIG. 3, and the implementation principle is similar, and details are not described herein again.
  • the encoding device in this application may be a base station or a terminal.
  • the encoding device in this embodiment determines the number N of bits to be encoded according to the target code length M of the Polar code, and then acquires the first polarization including the polarization weights of the N polarized channels.
  • the weight vector, the polarization weight is the basis for selecting the information bits, and then the information bits are determined according to the first polarization weight vector, and finally the N bits to be coded are Polar coded to obtain the Polar coded bits. Therefore, the calculation of the polarization weight of the Polar code polarized channel is performed to determine the position of the information bit and the fixed bit, and has nothing to do with the channel parameter and the code rate, thereby reducing the computational complexity of the Polar code encoding, and, for different code lengths.
  • the polarization weight corresponding to the bit rate Polar code has the same part, which greatly reduces the storage space, thereby reducing the storage complexity of the Polar code encoding.
  • the target code length M of the Polar code is equal to a positive integer power of 2
  • the obtaining module 12 is specifically configured to: obtain the first polarization weight vector from the pre-stored second polarization weight vector, and the second polarization weight
  • the vector includes polarization weights of N max polarized channels, N max is the mother code length corresponding to the maximum code length supported by the preset communication system, and the mother code code length is a positive integer power of 2.
  • the polarization weight is obtained by using the offline storage method.
  • the offline storage method can reduce the delay caused by the online calculation.
  • the set of elements in the first polarization weight vector is a subset of the set of elements in the second polarization weight vector
  • the target code length of the Polar code is M>
  • N max the polarization weight of the polarization channel whose channel index is less than or equal to N max corresponds to the polarization weight in the second polarization weight vector
  • the polarization weight of the polarization channel whose channel index is greater than N max is equal to The polarization weight of the polarized channel whose corresponding channel index is less than or equal to N max plus the weight increment
  • ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code.
  • the method of semi-offline storage is calculated by semi-online, which can reduce the delay caused by online calculation and reduce the storage complexity.
  • the target code length M of the Polar code is not equal to the positive integer power of 2
  • the first determining module 11 is specifically configured to: determine symbol Indicates rounding down.
  • FIG. 9 is a schematic structural diagram of Embodiment 2 of the encoding apparatus of the present application.
  • the encoding apparatus 200 of the present embodiment further includes: a third determining module, based on the structure of the encoding apparatus shown in FIG. And a computing module 16, the third determining module 15 is configured to determine NM bits to be deleted among the N to-be-coded bits before the obtaining module 12 acquires the first polarization weight vector of the polarization weights of the N polarized channels s position.
  • the calculation module 16 is configured to calculate, according to the result determined by the third determining module 15, a set of correction coefficients including polarization weights corresponding to the N bits to be encoded, where the correction coefficients are used to represent the correction amount of the deleted bits for each polarization weight;
  • the module 12 is specifically configured to: calculate polarization weights of the N polarized channels according to the set of correction coefficients, to obtain a first polarization weight vector.
  • the third determining module 15 is specifically configured to: determine a channel index sequence of the N polarized channels For each index in the channel index sequence, the following operations are performed: the binary numbers corresponding to each index are reverse-ordered and converted into decimal numbers to obtain a new channel index sequence. New channel index sequence Index sorting in the selection of channel index sequences in ascending order The NM in the middle is the bit index to be deleted.
  • the calculation module 16 is specifically configured to calculate each item in the correction coefficient set g according to the following formula
  • p i is a polarized channel with channel index i
  • the obtaining module 12 is specifically configured to: calculate a polarization weight W i of the N polarized channels according to the following formula, and obtain a first polarization weight vector:
  • i is the channel index
  • g (i,j) is the i-th row of the correction coefficient set g
  • the elements of the column, ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code.
  • the obtaining module 12 is specifically configured to: obtain the first polarization weight vector W 0 N-1 by recursively calculating according to the following formula:
  • ⁇ i (2 i-1 + ⁇ ) ⁇ ;
  • ⁇ i is an intermediate variable related to the channel index i
  • ⁇ and ⁇ are parameters preset according to the target code length and code rate of the Polar code
  • g (i , j) is an element of the i-th row and the j-th column in the correction coefficient set g
  • W 0 is an arbitrary constant.
  • the second determining module 13 is specifically configured to: sort the polarization weights in the first polarization weight vector from large to small, and select the bits corresponding to the first K polarization weights as information bits.
  • the coding device of this embodiment may be used to implement the technical solution of the method embodiment shown in FIG. 7.
  • the implementation principle is similar, and details are not described herein again.
  • the encoding device determines the number N of bits to be encoded according to the target code length M of the Polar code after receiving the input information bits, and then determines the position of the NM bits to be deleted among the N to-be-coded bits. And calculating a correction coefficient set including the correction coefficients of the N bits to be coded according to the determination result, and then calculating polarization weights of the N polarization channels according to the correction coefficient set to obtain a first polarization weight vector, and finally according to the first polarization Weight vector
  • the information bits are determined, and the N bits to be encoded are Polar coded to obtain the Polar coded bits.
  • the position of the information bit and the fixed bit is determined by the calculation of the polarization weight of the Polar code polarized channel, which has no relationship with the channel parameter and the code rate, and can reduce the calculation of the Polar code encoding. And implementation complexity.
  • the aforementioned program can be stored in a computer readable storage medium.
  • the program when executed, performs the steps including the foregoing method embodiments; and the foregoing storage medium includes various media that can store program codes, such as a ROM, a RAM, a magnetic disk, or an optical disk.
  • the polarization weight is calculated according to the formula or polynomial corresponding to the binary representation of the polarization channel number.
  • the polarization weight of one polarization channel is greater than the polarization weight of another polarization channel, then the position of the 'one polarization channel' in the first polarization weight vector must be before 'the other polarization channel' .
  • the first polarization weight vector is arranged from small to large according to the polarization weight, then if the polarization weight of one polarization channel is greater than the polarization weight of the other polarization channel, then this 'one polarization channel' is in the first The position in a polarization weight vector must be after 'another polarization channel'.
  • the position of each polarization channel in the first polarization weight vector can be regarded as the polarization weight multiplied by a factor.
  • first polarization weight vectors including the polarization weights of the N polarization channels and the corresponding device
  • first polarization weight vectors can be given, which can be based on the polarization weights.
  • serial numbers in these examples are all ranked from 1, that is, the sequence number has a minimum value of 1. This is equivalent to the sequence number starting from 0. If the sequence numbers are arranged from 0, then each sequence number in the corresponding sequence can be reduced by one.
  • the first polarization weight vector may be arranged according to the polarization weight from large to small, where the ordering sequence minimum value is 1, and accordingly, if the sequence number minimum value is 0, all the sorting numbers are decremented by one:
  • N 16
  • the first polarization weight vector is:
  • N 1024, the first polarization weight vector is:
  • the first polarization weight vector can also be arranged from small to large according to the polarization weight.
  • the sequence number has a minimum value of 1. Similarly, if the sequence number minimum value is 0, all the sequence numbers are decremented by one:
  • N 16
  • the first polarization weight vector is:
  • N 1024, the first polarization weight vector is:
  • any N or Nmax can be pre-stored.
  • FIG. 10 exemplarily shows a schematic structural diagram of a communication apparatus provided by the present application.
  • the communication device can be a base station or a terminal. Based on the same concept, the present application provides a communication apparatus for performing the above method flow.
  • the apparatus 1000 includes a processor 1001, a memory 1002, and a communication interface 1003.
  • the processor 1001, the memory 1002, and the communication interface 1003 are coupled to each other.
  • the memory 1002 may include a volatile memory such as a RAM; the memory may also include a non-volatile memory such as a flash memory, an HDD or an SSD; the memory 1002 may also include A combination of the above types of memories.
  • the communication interface 1003 can be a wired communication access port, a wireless communication interface, or a combination thereof, wherein the wired communication interface can be, for example, an Ethernet interface.
  • the Ethernet interface can be an optical interface, an electrical interface, or a combination thereof.
  • the wireless communication interface can be a WLAN interface.
  • the processor 1001 may be a CPU, an NP or a combination of a CPU and an NP.
  • the processor 1001 may further include a hardware chip.
  • the above hardware chip may be an ASIC, a PLD, or a combination thereof.
  • the above PLD may be a CPLD, an FPGA, a GAL, or any combination thereof.
  • the memory 1002 can also be combined with the processor 1001, such as by circuitry.
  • the memory 1002 is further configured to store instructions for performing various operations, and the processor 1001 invokes the instructions stored in the memory 1002, and may perform one or more steps in the foregoing embodiments, or an optional implementation manner thereof
  • the communication device 1000 implements the foregoing method, for example, calculating or storing at least one N corresponding first polarization weight vector sequentially arranged according to the polarization weight size, wherein the polarization weight of each polarization channel may be included but not limited to The method disclosed in each of the above embodiments is calculated.
  • Computer program package Includes one or more computer instructions.
  • the computer can be a general purpose computer, a special purpose computer, a computer network, or other programmable device.
  • the computer instructions can be stored in a computer readable storage medium or transferred from one computer readable storage medium to another computer readable storage medium, for example, computer instructions can be wired from a website site, computer, server or data center (eg Coax, fiber, digital subscriber line (DSL) or wireless (eg, infrared, wireless, microwave, etc.) is transmitted to another website, computer, server, or data center.
  • the computer readable storage medium can be any available media that can be accessed by a computer or a data storage device such as a server, data center, or the like that includes one or more available media.
  • Useful media can be magnetic media (eg, floppy disk, hard disk, magnetic tape), optical media (eg, DVD), or semiconductor media (eg, Solid State Disk (SSD)).
  • embodiments of the present invention can be provided as a method, or a computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or a combination of software and hardware. Moreover, the invention can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) including computer usable program code.
  • a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) including computer usable program code.
  • the computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture comprising the instruction device.
  • the apparatus implements the functions specified in one or more blocks of a flow or a flow and/or block diagram of the flowchart.
  • These computer program instructions can also be loaded onto a computer or other programmable data processing device such that a series of operational steps are performed on a computer or other programmable device to produce computer-implemented processing for execution on a computer or other programmable device.
  • the instructions provide steps for implementing the functions specified in one or more of the flow or in a block or blocks of a flow diagram.

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Probability & Statistics with Applications (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Computational Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Physics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Algebra (AREA)
  • Computing Systems (AREA)
  • Quality & Reliability (AREA)
  • Compression, Expansion, Code Conversion, And Decoders (AREA)
  • Optical Communication System (AREA)
  • Error Detection And Correction (AREA)
  • Image Processing (AREA)
  • Eye Examination Apparatus (AREA)
  • Prostheses (AREA)

Abstract

本申请提供一种编码方法、设备和装置。该方法包括：确定N个待编码比特，N个待编码比特中包含信息比特和固定比特，获取包含N个极化信道的极化权重的第一极化权重向量，N个待编码比特对应N个极化信道，根据第一极化权重向量确定信息比特的位置，对N个待编码比特进行Polar编码，获得Polar编码后的比特。

Description

编码方法、设备和装置 技术领域
本申请涉及编解码技术领域，尤其涉及一种编码方法和设备。
背景技术
信道编码是通信系统中用于提高数据传输的可靠性，保证通信质量的无线接入技术，Polar(极化)码是一种理论上证明可以达到香农极限且具有低编译码复杂度的编码方式。Polar码是一种线性块码，其生成矩阵为GN,其编码过程为
Figure PCTCN2017090359-appb-000001
为编码后比特，
Figure PCTCN2017090359-appb-000002
为待编码比特，其中
Figure PCTCN2017090359-appb-000003
是一个二进制的行矢量，长度为N(即码长)；GN是一个N×N的矩阵，且
Figure PCTCN2017090359-appb-000004
其中
Figure PCTCN2017090359-appb-000005
BN是一个N×N的转置矩阵，例如比特反转(Bit Reversal)矩阵；
Figure PCTCN2017090359-appb-000006
定义为log2N个矩阵F2的克罗内克(Kronecker)乘积。Polar码的编码过程中，首先需要确定
Figure PCTCN2017090359-appb-000007
中信息比特和固定比特的位置，用来携带信息的比特称为信息比特，剩下的比特置为收发端预先约定的固定值，称为固定比特，然后再根据
Figure PCTCN2017090359-appb-000008
进行编码。具体可通过不同的方式对每个输入比特对应的极化信道可靠度进行估计并优先选择可靠度高的极化信道放置信息比特。在实际应用当中，信息比特的位置需要用一个序列来指示，可以通过在线计算或者离线存储的方式来统一信息比特的位置。
现有技术中，有三种极化信道可靠度估计的方法，一种是计算每个极化信道的巴氏(Bhattacharyya)参数，该参数反应了极化信道的错误概率，然后选择K个最小的巴氏参数对应的极化信道放置信息比特，但是该方法只适用于二进制擦除信道，对于其他信道无法准确地进行可靠度估计，因此性能不高；另外两种分别是密度进化(Density evolution，DE)方法和高斯近似(Gaussion approximation，GA)法。DE方法和GA方法的计算复杂度相对较高，不适用于在线计算，对于离线存储，DE方法和GA方法在计算可靠度的时候依赖于实际信道的参数速率匹配方式，码率以及调制方式，上述参数中的任何一项发生变化极化信道的可靠度估计结果也会发生变化，对应的信息比特的位置也发生变化，最终导致存储的开销过大。
发明内容
本申请提供一种编码方法和设备，以降低Polar码编码的计算复杂度与存储复杂度。
第一方面，本申请提供一种编码方法，包括：
接收到输入的信息比特后，根据Polar码的目标码长M确定待编码比特的个数N，N为正整数，然后获取包含N个极化信道的极化权重的第一极化权重向量，极化权重是选择信息比特的依据，接着根据第一极化权重向量确定出信息比特，最后对N个待编码比特进行Polar编码，获得Polar编码后的比特。从而实现了通过Polar码极化信道的极化权重的计算来确定信息比特与固定比特的位置，与信道参数及码率没有关系，可以降低Polar码编码的计算复杂度，而且，对于不同码长和码率的Polar码对应的极化权重有相同的部分，大大降低存储空间，从而还可降低Polar码编码的存储复杂度。
在一种可能的设计中，Polar码的目标码长M等于2的正整数次幂，M为正整数，确定N个待编码比特，包括：N等于M，Polar码的目标码长为Polar码的输出码长；获取包含N个极化信道的极化权重的第一极化权重向量，包括：计算N个极化信道的极化权重，得到第一极化权重向量。
在一种可能的设计中，计算N个极化信道的极化权重，得到第一极化权重向量，包括：根据如下公式计算N个极化信道的极化权重Wi，得到第一极化权重向量：
Figure PCTCN2017090359-appb-000009
其中，
Figure PCTCN2017090359-appb-000010
i为信道索引，Bn-1Bn-2…B0为i的二进制表示，其中Bn-1为最高位，B0为最低位，Bj∈{0,1}，j∈{0,1,···,n-1}，i∈{0,1,···,N-1}，N＝2n，n为正整数，φ与α为根据Polar码的目标码长和码率预设的参数。
在一种可能的设计中，计算N个极化信道的极化权重，得到第一极化权重向量，包括：根据如下公式通过递归计算得到第一极化权重向量W0 N-1：
βi＝(2i-1+φ)α；
Figure PCTCN2017090359-appb-000011
Figure PCTCN2017090359-appb-000012
其中，
Figure PCTCN2017090359-appb-000013
其中，i∈{1,···,N-1}，βi为与信道索引i有关的中间变量，φ与α为根据Polar码的目标码长和码率预设的参数，W0为任意常数。
在一种可能的设计中，Polar码的目标码长M等于2的正整数次幂，获取包含N个极化信道的极化权重的第一极化权重向量，包括：从预先存储的第二极化权重向量中获取第一极化权重向量，第二极化权重向量包含Nmax个极化信道的极化权重，Nmax为预设的通信系统支持的最大码长所对应的母码码长，母码码长为2的正整数次幂。
通过接收到输入的信息比特后，根据Polar码的目标码长M确定待编码比特的个数N，然后从预先存储的第二极化权重向量中获取第一极化权重向量，第二极化权重向量包含通信系统所支持的最大码长所对应的母码码长Nmax个极化信道的极化权重，接着根据第一极化权重向量确定出信息比特，最后对N个待编码比特进行Polar编码，获得Polar编码后的比特。从而实现了通过离线存储的方式获得Polar码极化信道的极化权重来确定信息比特与固定比特的位置，对于不同码长和码率的Polar码，短码码长下极化权重向量中的元素集合为长码码长权重向量中的元素集合的子集，且索引(序号)相同的极化信道的极化权重值一样，因此可降低存储空间，降低Polar码编码的存储复杂度，相比较在线计算，在存储空间允许的情况下，离线存储的方式可降低在线计算带来的时延。
在一种可能的设计中，Polar码的目标码长M＜＝Nmax时，第一极化权重向量中的元素集合为第二极化权重向量中的元素集合的子集；Polar码的目标码长M＞＝Nmax时，信道索引小于或等于Nmax的极化信道的极化权重与第二极化权重向量中的极化权重一一对应，信道索引大于Nmax的极化信道的极化权重等于对应的信道索引小于或等于Nmax的极化信道的极化权重加上权重增量
Figure PCTCN2017090359-appb-000014
其中，φ与α为根据Polar码的目标码长和码率预设的参数。
通过接收到输入的信息比特后，根据Polar码的目标码长M确定待编码比特的个数N，然后从预先存储的第二极化权重向量中获取第一极化权重向量，第二极化权重 向量包含通信系统所支持的最大码长Nmax个极化信道的极化权重，接着根据第一极化权重向量确定出信息比特，最后对N个待编码比特进行Polar编码，获得Polar编码后的比特。从而实现了通过半在线计算半离线存储的方式获得Polar码极化信道的极化权重来确定信息比特与固定比特的位置，对于不同码长和码率的Polar码，小于预存的Nmax的Polar码极化权重向量中的元素集合为Nmax权重向量中的元素集合的子集，且索引(序号)相同的极化信道的极化权重值一样，大于预存的Nmax的Polar码极化权重向量中，信道索引小于或等于Nmax的极化信道的极化权重与第二极化权重向量中的极化权重一一对应，信道索引大于Nmax的极化信道的极化权重等于对应的信道索引小于或等于Nmax的极化信道的极化权重加上权重增量
Figure PCTCN2017090359-appb-000015
因此可降低存储空间，降低Polar码编码的存储复杂度，该方式既可降低在线计算带来的时延，还可降低存储复杂度。
在一种可能的设计中，φ＝0，α＝1/4。
在一种可能的设计中，Polar码的目标码长M不等于2的正整数次幂，确定N个待编码比特，包括：
Figure PCTCN2017090359-appb-000016
符号
Figure PCTCN2017090359-appb-000017
表示向下取整。
在一种可能的设计中，获取包含N个极化信道的极化权重的第一极化权重向量之前，还包括：确定N个待编码比特中要删除的N-M个比特的位置，并根据确定结果计算包含N个待编码比特对应的极化权重的修正系数集合，修正系数用于表征删除的比特对每一极化权重的修正量；获取包含N个极化信道的极化权重的第一极化权重向量，包括：根据修正系数集合计算N个极化信道的极化权重，得到第一极化权重向量。
在一种可能的设计中，确定N个比特中要删除的N-M个比特的位置，包括：确定N个极化信道的信道索引序列
Figure PCTCN2017090359-appb-000018
对信道索引序列中的每一个索引，进行如下操作：将每一索引对应的二进制数进行比特逆序，再转化为十进制数，得到新的信道索引序列
Figure PCTCN2017090359-appb-000019
对新的信道索引序列
Figure PCTCN2017090359-appb-000020
中的索引排序；按照从小到大的顺序选择信道索引序列
Figure PCTCN2017090359-appb-000021
中的N-M个索引为要删除的比特索引。
需要说明的，该步骤中不限于对每一索引做比特逆序操作，例如还可以是将每一索引对应的二进制数进行交织或扰码等等，或者不对每一索引做处理。
在一种可能的设计中，根据确定结果计算包含N个比特的修正系数的修正系数集合，包括：
修正系数集合
Figure PCTCN2017090359-appb-000022
修正系数集合g中的每一项g(i,j)按照如下公式计算：
Figure PCTCN2017090359-appb-000023
Figure PCTCN2017090359-appb-000024
其中，i∈{0,1,···,N-1}，j∈{0,1,···,n-1}，N＝2n，pi为信道索引为i的极化信道对应的比特是否要被删除的标识，pi∈{0,1}。
在一种可能的设计中，根据修正系数集合计算N个极化信道的极化权重，得到第 一极化权重向量，包括：根据如下公式计算N个极化信道的极化权重Wi，得到第一极化权重向量：
Figure PCTCN2017090359-appb-000025
其中，
Figure PCTCN2017090359-appb-000026
i为信道索引，Bn-1Bn-2…B0为i的二进制表示，其中Bn-1为最高位，B0为最低位，Bj∈{0,1}，j∈{0,1,···,n-1}，i∈{0,1,···,N-1}，N＝2n，g(i,j)为修正系数集合g中第i行第j列的元素,φ与α为根据Polar码的目标码长和码率预设的参数。
在一种可能的设计中，根据修正系数集合计算N个极化信道的极化权重，得到第一极化权重向量，包括：根据如下公式通过递归计算得到第一极化权重向量W0 N-1：
βi＝(2i-1+φ)α；
Figure PCTCN2017090359-appb-000027
Figure PCTCN2017090359-appb-000028
其中，
Figure PCTCN2017090359-appb-000029
其中，i∈{1,···,N-1}，βi为与信道索引i有关的中间变量，φ与α为根据Polar码的目标码长和码率预设的参数，g(i,j)为修正系数集合g中第i行第j列的元素，W0为任意常数。
上述可能的设计中，通过接收到输入的信息比特后，根据Polar码的目标码长M确定待编码比特的个数N，然后确定N个待编码比特中要删除的N-M个比特的位置，并根据确定结果计算包含N个待编码比特的修正系数的修正系数集合，接着根据修正系数集合计算N个极化信道的极化权重，得到第一极化权重向量，最后根据第一极化权重向量确定出信息比特，对N个待编码比特进行Polar编码，获得Polar编码后的比特。从而实现了对于任意目标码长的Polar码，通过Polar码极化信道的极化权重的计算来确定信息比特与固定比特的位置，与信道参数及码率没有关系，可以降低Polar码编码的计算与实现复杂度。
在一种可能的设计中，φ＝0，α＝1/4。
在一种可能的设计中，根据第一极化权重向量确定信息比特的位置，包括：将第一极化权重向量中的极化权重从大到小进行排序，选择前K个极化权重对应的比特作为信息比特。
在一种可能的设计中，所述编码方法由基站或终端执行。
第二方面，本申请提供一种编码设备，包括：
第一确定模块，用于确定N个待编码比特，N个待编码比特中包含信息比特和固定比特，N为正整数，获取模块，用于获取包含N个极化信道的极化权重的第一极化权重向量，极化权重是选择信息比特的依据，N个待编码比特对应N个极化信道，第二确定模块，用于根据第一极化权重向量确定信息比特的位置，编码模块，用于对N个待编码比特进行Polar编码，获得Polar编码后的比特。
在一种可能的设计中，Polar码的目标码长M等于2的正整数次幂，M为正整数，第一确定模块具体用于：确定N等于M，Polar码的目标码长为Polar码的输出码长；获取模块具体用于：计算N个极化信道的极化权重，得到第一极化权重向量。
在一种可能的设计中，获取模块具体用于：根据如下公式计算N个极化信道的极化权重Wi，得到第一极化权重向量：
Figure PCTCN2017090359-appb-000030
其中，
Figure PCTCN2017090359-appb-000031
i为信道索引，Bn-1Bn-2…B0为i的二进制表示，其中Bn-1 为最高位，B0为最低位，Bj∈{0,1}，j∈{0,1,···,n-1}，i∈{0,1,···,N-1}，N＝2n，n为正整数，φ与α为根据Polar码的目标码长和码率预设的参数。
在一种可能的设计中，获取模块具体用于：根据如下公式通过递归计算得到第一极化权重向量W0 N-1：
βi＝(2i-1+φ)α；
Figure PCTCN2017090359-appb-000032
Figure PCTCN2017090359-appb-000033
其中，
Figure PCTCN2017090359-appb-000034
其中，i∈{1,···,N-1}，βi为与信道索引i有关的中间变量，φ与α为根据Polar码的目标码长和码率预设的参数，W0为任意常数。
在一种可能的设计中，Polar码的目标码长M等于2的正整数次幂，获取模块具体用于：从预先存储的第二极化权重向量中获取第一极化权重向量，第二极化权重向量包含Nmax个极化信道的极化权重，Nmax为预设的通信系统支持的最大码长所对应的母码码长，母码码长为2的正整数次幂。
在一种可能的设计中，Polar码的目标码长M＜＝Nmax时，第一极化权重向量中的元素集合为第二极化权重向量中的元素集合的子集；Polar码的目标码长M＞＝Nmax时，信道索引小于或等于Nmax的极化信道的极化权重与第二极化权重向量中的极化权重一一对应，信道索引大于Nmax的极化信道的极化权重等于对应的信道索引小于或等于Nmax的极化信道的极化权重加上权重增量
Figure PCTCN2017090359-appb-000035
其中，φ与α为根据Polar码的目标码长和码率预设的参数。
在一种可能的设计中，φ＝0，α＝1/4。
在一种可能的设计中，Polar码的目标码长M不等于2的正整数次幂，第一确定模块具体用于：确定
Figure PCTCN2017090359-appb-000036
符号
Figure PCTCN2017090359-appb-000037
表示向下取整。
在一种可能的设计中，还包括：第三确定模块，用于在获取模块获取包含N个极化信道的极化权重的第一极化权重向量之前，确定N个待编码比特中要删除的N-M个比特的位置；计算模块，用于根据第三确定模块确定的结果计算包含N个待编码比特对应的极化权重的修正系数集合，修正系数用于表征删除的比特对每一极化权重的修正量；获取模块具体用于：根据修正系数集合计算N个极化信道的极化权重，得到第一极化权重向量。
在一种可能的设计中，第三确定模块具体用于：确定N个极化信道的信道索引序列
Figure PCTCN2017090359-appb-000038
对信道索引序列中的每一个索引，进行如下操作：将每一索引对应的二进制数进行比特逆序，再转化为十进制数，得到新的信道索引序列
Figure PCTCN2017090359-appb-000039
对新的信道索引序列
Figure PCTCN2017090359-appb-000040
中的索引排序；按照从小到大的顺序选择信道索引序列
Figure PCTCN2017090359-appb-000041
中的N-M个为要删除的比特索引。
在一种可能的设计中，修正系数集合
Figure PCTCN2017090359-appb-000042
计算模块 具体用于按照如下公式计算修正系数集合g中的每一项g(i,j)：
Figure PCTCN2017090359-appb-000043
Figure PCTCN2017090359-appb-000044
其中，i∈{0,1,···,N-1}，j∈{0,1,···,n-1}，N＝2n，pi为信道索引为i的极化信道对应的比特是否要被删除的标识，pi∈{0,1}。
在一种可能的设计中，获取模块具体用于：根据如下公式计算N个极化信道的极化权重Wi，得到第一极化权重向量：
Figure PCTCN2017090359-appb-000045
其中，
Figure PCTCN2017090359-appb-000046
i为信道索引，Bn-1Bn-2…B0为i的二进制表示，其中Bn-1为最高位，B0为最低位，Bj∈{0,1}，j∈{0,1,···,n-1}，i∈{0,1,···,N-1}，N＝2n，g(i,j)为修正系数集合g中第i行第j列的元素,φ与α为根据Polar码的目标码长和码率预设的参数。
在一种可能的设计中，获取模块具体用于：根据如下公式通过递归计算得到第一极化权重向量W0 N-1：
βi＝(2i-1+φ)α；
Figure PCTCN2017090359-appb-000047
Figure PCTCN2017090359-appb-000048
其中，
Figure PCTCN2017090359-appb-000049
其中，i∈{1,···,N-1}，βi为与信道索引i有关的中间变量，φ与α为根据Polar码的目标码长和码率预设的参数，g(i,j)为修正系数集合g中第i行第j列的元素，W0为任意常数。
在一种可能的设计中，φ＝0，α＝1/4。
在一种可能的设计中，第二确定模块具体用于：将第一极化权重向量中的极化权重从大到小进行排序，选择前K个极化权重对应的比特作为信息比特。
在一种可能的设计中，所述编码设备是基站或终端。
上述第二方面以及上述第二方面的各可能的设计所提供的编码设备，其有益效果可以参见上述第一方面和第一方面的各可能的设计所带来的有益效果，在此不再赘述。
第三方面，本申请提供一种通信装置，包括：
存储器，用于存储执行操作的指令；
处理器，与所述存储器耦合，根据所述指令用于：确定N个待编码比特，所述N个待编码比特中包含信息比特和固定比特，N为正整数；获取包含N个极化信道的极化权重的第一极化权重向量，所述极化权重是选择信息比特的依据，所述N个待编码比特对应所述N个极化信道；根据所述第一极化权重向量确定所述信息比特的位置；对所述N个待编码比特进行Polar编码，获得Polar编码后的比特。
在一种可能的设计中，所述通信装置是基站或终端。
第四方面，本申请提供一种通信装置，所述计算机存储介质存储有计算机可执行指令，所述计算机可执行指令在被计算机调用时，使所述计算机执行如前述各实施例所述的方法。
附图说明
图1为现有的Polar码的编码过程示意图；
图2为本申请编码方法实施例一的编码结构框图；
图3为本申请编码方法实施例一的流程图；
图4为本申请编码方法实施例二的流程图；
图5为本申请实施例二中N＝4，8，16的极化码分别对应的极化权重向量的示意图；
图6为本申请实施例三中N＝4，8，16的极化码分别对应的极化权重向量的示意图；
图7为本申请编码方法实施例四的流程图；
图8为本申请编码设备实施例一的结构示意图；
图9为本申请编码设备实施例二的结构示意图；
图10为本申请通信装置的一个实施例的结构示意图。
具体实施方式
图1为现有的Polar码的编码过程示意图，Polar码的编码由发送端执行，如图1所示，Polar码的编码过程包括构造、编码和速率匹配三个处理过程。首先是构造过程：接收到输入数据(即输入的信息比特，如信息比特为N1个)之后，要根据编码后的目标码长M确定待编码的比特的个数N，待编码的比特包括信息比特(个数为N1)和固定比特(个数为N2)，M＝N1+N2，还要确定信息比特和固定比特的位置，一个比特对应一个极化信道。接着是编码过程：对待编码的比特进行Polar编码，获得Polar编码后的比特。最后是速率匹配过程：由于Polar码编码后的码长为2的正整数次幂，而实际实现当中需要对码长进行灵活配置，因此需要进行速率匹配得到任意码长的编码，具体实现是删掉2的正整数次幂的码长中的部分N-M个比特，得到目标码长。其中N、M、N1、N2均为正整数，本申请提供的编码方法主要涉及图1所示的Polar码的编码过程，最主要涉及构造过程。在现有的构造过程中，现有技术中大多是根据所有极化信道的实际参数以及码率进行信道的可靠度估计从而确定出信息比特的位置，剩下的位置为固定比特的位置，在实际应用当中，信息比特的位置需要用一个序列来指示，可以通过在线计算或者离线存储的方式来统一信息比特的位置，离线存储时需要一个非常大的表来存序列，考虑不同的信道参数，码率和不同的码长，所要存的序列会是上百万个，因此现有的确定信息比特位置的方式对于在线计算与离线存储都有较高的复杂度。针对上述问题，本申请提供一种编码方法，通过Polar码极化信道的极化权重的计算来确定信息比特与固定比特的位置，与信道参数及码率没有关系，可以降低Polar码编码的计算复杂度与存储复杂度。下面结合附图详细说明本申请提供的编码方法和设备。
本申请主要应用于各种无线通信系统，作用于该系统中的数字信号处理单元，提高无线通信的可靠性。
本申请涉及的网元主要是基站和终端，基站实现与终端之间的通信。
图2为本申请编码方法实施例一的编码结构框图，如图2所示，信息比特(个数N1)和Polar码的目标码长M同为输入，接着进行Polar码构造，首先根据Polar码的目标码长M确定出N个待编码比特，固定比特个数为N2，则N＝N1+N2，接着确定出信息比特和固定比特的位置，然后通过编码矩阵GN进行编码，获得Polar编码后的比特。
图3为本申请编码方法实施例一的流程图，如图3所示，本实施例的方法可以包括：
S101、确定N个待编码比特，N个待编码比特中包含信息比特和固定比特。
具体地，由于Polar码编码后的码长为2的正整数次幂，而实际实现当中需要对 码长进行灵活配置，也就是要得到任意码长的Polar码，因此在接收到输入的信息比特后，要根据Polar码的目标码长M确定待编码比特的个数N，N个待编码比特中包含信息比特和固定比特，Polar码的目标码长为Polar码的输出码长。具体有两种情况：一是Polar码的目标码长M等于2的正整数次幂，即就是不需要进行速率匹配，此时确定的待编码比特的个数N等于M。另一种是Polar码的目标码长M不等于2的正整数次幂，即就是需要进行速率匹配，则此时确定的待编码比特的个数
Figure PCTCN2017090359-appb-000050
符号
Figure PCTCN2017090359-appb-000051
表示向下取整。
S102、获取包含N个极化信道的极化权重的第一极化权重向量，极化权重是选择信息比特的依据，N个待编码比特对应N个极化信道。
具体地，一个比特对应一个极化信道，极化信道的极化权重是选择信息比特的依据，极化权重与现有技术中的信道的可靠度不同，对于Polar码的目标码长M是否满足2的正整数次幂极化权重的获取是不同的，下面详细说明在待编码比特的个数N等于Polar码的目标码长M时如何获取第一极化权重向量，具体地，第一极化权重向量中的N个极化信道的极化权重Wi是根据如下公式计算出的：
Figure PCTCN2017090359-appb-000052
其中，
Figure PCTCN2017090359-appb-000053
i为信道索引，Bn-1Bn-2…B0为i的二进制表示，其中Bn-1为最高位，B0为最低位，Bj∈{0,1}，j∈{0,1,···,n-1}，i∈{0,1,···,N-1}，N＝2n，φ与α为根据Polar码的目标码长和码率预设的参数，对于不同码长与码率的Polar码，可对参数φ与α进行调整，得到更好性能的Polar码信息比特指示序列。
可选的，
Figure PCTCN2017090359-appb-000054
中，φ＝0，α＝1/4，计算公式即为：
Figure PCTCN2017090359-appb-000055
通过该公式计算出极化信道的极化权重进而确定出信息比特即就是得到信息比特指示序列，性能较优。以N＝8为例，则n＝log2(8)＝3,对于
Figure PCTCN2017090359-appb-000056
极化权重W3的计算过程如下：
W3＝1*2^(0*(1/4))+1*2^(1*(1/4))+0*2^(2*(1/4))＝2.8192
需要说明的是，本申请中的所有实施例对应的极化权重对应不包含比特逆序操作BN的Polar码编码矩阵FN，若编码矩阵带有比特逆序BN，则需要将计算出来的极化权重进行对应的比特逆序操作。
作为另一种可实施的方式，根据如下公式通过递归计算得到第一极化权重向量W0 N-1：
βi＝(2i-1+φ)α；
Figure PCTCN2017090359-appb-000057
Figure PCTCN2017090359-appb-000058
其中，
Figure PCTCN2017090359-appb-000059
其中，i∈{1,···,N-1}，βi为与信道索引i有关的中间变量，φ与α为根据Polar码的目标码长和码率预设的参数，W0为任意常数。
由上述公式可知，相邻两阶极化码的极化权重的关系可简单描述为WN＝[WN/2,WN/2+βi]，i＝log2(N)。当i＝1时，代入上述递归计算公式，得到递归计算的初始公式为：β1＝(1+φ)α；
W1＝W0+β1；
Figure PCTCN2017090359-appb-000060
例如当W0＝0时，则可得到计算公式
Figure PCTCN2017090359-appb-000061
当W0＝0，φ＝0，α＝1/4，则可得到计算公式
Figure PCTCN2017090359-appb-000062
下面以N＝8为例，递归计算的过程如下：
首先，初始化极化信道的极化权重为W0＝a，a为一常数值，通常可设置为0。然后，根据Polar码的码长N(N＝2n)，取i＝1到n，逐阶增加极化信道的极化权重至目标码长N，计算过程如下所示：
(1)设置初始值，W0＝a。
(2)i＝1，β1＝(1+φ)α，W1＝W0+β1，
Figure PCTCN2017090359-appb-000063
(3)i＝2，β2＝(2+φ)α，[W0,W1,W2,W3]＝[W0,W1,W0+β2,W1+β2]。
(4)i＝3，β3＝(4+φ)α，[W0,W1,W2,W3,W4,W5,W6,W7]＝[W0,W1,W2,W3,W0+β3,W1+β3,W2+β3,W3+β3]。
最终得到：
Figure PCTCN2017090359-appb-000064
S103、根据第一极化权重向量确定信息比特的位置。
具体地，可以是将第一极化权重向量中的极化权重从大到小进行排序，选择前K个极化权重对应的比特作为信息比特，也就是选择出信息比特的位置，其余位置设置为固定比特，得到完整的长度为N的待编码比特。
S104、对N个待编码比特进行Polar编码，获得Polar编码后的比特。
具体地，使用Polar码的编码矩阵FN完成待编码比特的编码过程。
本实施例提供的编码方法，通过接收到输入的信息比特后，根据Polar码的目标码长M确定待编码比特的个数N，然后获取包含N个极化信道的极化权重的第一极化权重向量，接着根据第一极化权重向量确定出信息比特，最后对N个待编码比特进行Polar编码，获得Polar编码后的比特。从而实现了通过Polar码极化信道的极化权重的计算来确定信息比特与固定比特的位置，与信道参数及码率没有关系，可以降低Polar码编码的计算复杂度，而且，对于不同码长和码率的Polar码对应的极化权重有相同的部分，大大降低存储空间，从而还可降低Polar码编码的存储复杂度。
更进一步地，根据图3所示实施例一中的极化权重的计算公式可获知相邻两阶极化码的极化权重之间差一权重增量βi，上述实施例一中S102的一种具体实现方式是通过在线计算获取第一极化权重向量，作为另一种可实施的方式，还可通过离线存储的方式获取，相比较在线计算，在存储空间允许的情况下，离线存储的方式可降低在线计算带来的时延。下面结合附图4详细说明离线存储的方式，需要说明的是，离线存储的方式适用于Polar码的目标码长M满足2的正整数次幂的场景。
图4为本申请编码方法实施例二的流程图，如图4所示，本实施例的方法可以包括：
S201、确定N个待编码比特，N个待编码比特中包含信息比特和固定比特。
S202、从预先存储的第二极化权重向量中获取第一极化权重向量，第一极化权重向量中的元素集合为第二极化权重向量中的元素集合的子集，第二极化权重向量包含Nmax个极化信道的极化权重，Nmax为预设的通信系统支持的最大码长所对应的母码码长，母码码长为2的正整数次幂。
具体来说，可预先根据实际通信场景设定一个通信系统所支持的最大码长所对应 的母码码长Nmax，所述母码码长为2的正整数次幂，预先通过实施例一所示的计算公式计算出第二极化权重向量，并进行离线存储。在使用时，直接从预先存储的第二极化权重向量中获取第一极化权重向量。从实施例一所示的计算公式可以获知，在2的正整数次幂码长时，短码码长下极化权重向量中的元素集合为长码码长权重向量中的元素集合的子集，且索引(序号)相同的极化信道的极化权重值一样。
以N＝4，8，16的极化码为例，图5为本申请实施例二中N＝4，8，16的极化码分别对应的极化权重向量的示意图，如图5所示，N＝8码长时的极化权重向量中的元素集合为N＝16码长时的极化权重向量中的元素集合的子集，N＝4码长的极化权重向量中的元素集合为N＝8码长时的极化权重向量中的元素集合的子集。而且相同位置上极化信道的极化权重相同。因此，预存最长码长Nmax下极化信道的极化权重向量，就可以得到任何码长为N<＝Nmax的极化信道权重向量。
S203、根据第一极化权重向量确定信息比特的位置。
具体地，可以是将第一极化权重向量中的极化权重从大到小进行排序，选择前K个极化权重对应的比特作为信息比特。也就是选择出信息比特的位置，其余位置设置为固定比特，得到完整的长度为N的待编码比特。
S204、对N个待编码比特进行Polar编码，获得Polar编码后的比特。
具体地，使用Polar码的编码矩阵FN完成待编码比特的编码过程。
本实施例提供的编码方法，通过接收到输入的信息比特后，根据Polar码的目标码长M确定待编码比特的个数N，然后从预先存储的第二极化权重向量中获取第一极化权重向量，第二极化权重向量包含通信系统所支持的最大码长所对应的母码码长Nmax个极化信道的极化权重，接着根据第一极化权重向量确定出信息比特，最后对N个待编码比特进行Polar编码，获得Polar编码后的比特。从而实现了通过离线存储的方式获得Polar码极化信道的极化权重来确定信息比特与固定比特的位置，对于不同码长和码率的Polar码，短码码长下极化权重向量中的元素集合为长码码长权重向量中的元素集合的子集，且索引(序号)相同的极化信道的极化权重值一样，因此可降低存储空间，降低Polar码编码的存储复杂度，相比较在线计算，在存储空间允许的情况下，离线存储的方式可降低在线计算带来的时延。
可选的，区别于上述实施例二中S202的一种具体实现方式是通过离线存储的方式获取，作为另一种可实施的方式，还可通过半在线计算半离线存储的方式获取。下面在本申请实施例三中详细说明半在线计算半离线存储的方式，需要说明的是，该方式适用于Polar码的目标码长M满足2的正整数次幂的场景。
S202中从预先存储的第二极化权重向量中获取第一极化权重向量，具体可以是：Polar码的目标码长M＜＝Nmax时，第一极化权重向量中的元素集合为第二极化权重向量中的元素集合的子集；Polar码的目标码长M＞＝Nmax时，信道索引小于或等于Nmax的极化信道的极化权重与第二极化权重向量中的极化权重一一对应，信道索引大于Nmax的极化信道的极化权重等于对应的信道索引小于或等于Nmax的极化信道的极化权重加上权重增量
Figure PCTCN2017090359-appb-000065
其中，φ与α为根据Polar码的目标码长和码率预设的参数。例如，图6为本申请实施例三中N＝4，8，16的极化码分别对应的极化权重向量的示意图，本实施例中Nmax＝8，如图6所示，第二极化权重向量存储的极化权重为W0到W7，其中码长小于Nmax＝8的极化权重从该第二极化权重向量中提取，码长为16的极化权重向量中其索引从8到15的极化权重由索引从到0到7的极化权重增加上权重增量(8+φ)α得到。
可选的，上述实施例中，φ＝0，α＝1/4。
本实施例提供的编码方法，通过接收到输入的信息比特后，根据Polar码的目标 码长M确定待编码比特的个数N，然后从预先存储的第二极化权重向量中获取第一极化权重向量，第二极化权重向量包含通信系统所支持的最大码长Nmax个极化信道的极化权重，接着根据第一极化权重向量确定出信息比特，最后对N个待编码比特进行Polar编码，获得Polar编码后的比特。从而实现了通过半在线计算半离线存储的方式获得Polar码极化信道的极化权重来确定信息比特与固定比特的位置，对于不同码长和码率的Polar码，小于预存的Nmax的Polar码极化权重向量中的元素集合为Nmax权重向量中的元素集合的子集，且索引(序号)相同的极化信道的极化权重值一样，大于预存的Nmax的Polar码极化权重向量中，信道索引小于或等于Nmax的极化信道的极化权重与第二极化权重向量中的极化权重一一对应，信道索引大于Nmax的极化信道的极化权重等于对应的信道索引小于或等于Nmax的极化信道的极化权重加上权重增量
Figure PCTCN2017090359-appb-000066
因此可降低存储空间，降低Polar码编码的存储复杂度，该方式既可降低在线计算带来的时延，还可降低存储复杂度。
图7为本申请编码方法实施例四的流程图，本实施例中详细说明在Polar码的目标码长M不等于2的正整数次幂时，也就是需要进行速率匹配时如何获取第一极化权重向量，如图7所示，本实施例的方法可以包括：
S301、确定N个待编码比特，N个待编码比特中包含信息比特和固定比特。
具体地，由于Polar码编码后的码长为2的正整数次幂，而实际实现当中需要对码长进行灵活配置，也就是要得到任意码长的Polar码，因此在接收到输入的信息比特后，要根据Polar码的目标码长M确定待编码比特的个数N，N个待编码比特中包含信息比特和固定比特。当Polar码的目标码长M不等于2的正整数次幂，即就是需要进行速率匹配，则此时确定的待编码比特的个数
Figure PCTCN2017090359-appb-000067
符号
Figure PCTCN2017090359-appb-000068
表示向下取整。
S302、确定N个待编码比特中要删除的N-M个比特的位置，并根据确定结果计算包含N个待编码比特对应的极化权重的修正系数集合，修正系数用于表征删除的比特对每一极化权重的修正量。
具体地，确定N个待编码比特中要删除的N-M个比特的位置，包括：
(1)确定N个极化信道的信道索引序列
Figure PCTCN2017090359-appb-000069
(2)对信道索引序列中的每一个索引，进行如下操作：
(3)将每一索引对应的二进制数进行比特逆序，再转化为十进制数，得到新的信道索引序列
Figure PCTCN2017090359-appb-000070
需要说明的，该步骤中不限于对每一索引做比特逆序操作，例如还可以是将每一索引对应的二进制数进行交织或扰码等等，或者不对每一索引做处理。
(4)对新的信道索引序列
Figure PCTCN2017090359-appb-000071
中的索引排序；
(5)按照从小到大的顺序选择信道索引序列
Figure PCTCN2017090359-appb-000072
中的N-M个索引为要删除的比特索引。
例如，原始信道索引序列
Figure PCTCN2017090359-appb-000073
对其中的一个索引，其对应的二进制数
Figure PCTCN2017090359-appb-000074
则比特逆序之后，
Figure PCTCN2017090359-appb-000075
对
Figure PCTCN2017090359-appb-000076
中所有元素都进行比特逆序操作后得到
Figure PCTCN2017090359-appb-000077
，将
Figure PCTCN2017090359-appb-000078
中的所有索引重新排序之后，按顺序从小到大取信道索引序列
Figure PCTCN2017090359-appb-000079
中的N-M个索引对应的比特为要删除的比特。
其中，由于引入了比特删除需要对极化权重的系数进行修正，对应的修正系数集合g与蝶形译码树中的每个计算节点一一对应,因此为N×n的向量，根据确定结果计算包含N个比特的修正系数的修正系数集合，具体可以为：
修正系数集合
Figure PCTCN2017090359-appb-000080
修正系数集合g中的每一项g(i,j)按照如下公式计算：
Figure PCTCN2017090359-appb-000081
Figure PCTCN2017090359-appb-000082
其中，i∈{0,1,···,N-1}，j∈{0,1,···,n-1}，N＝2n，pi为信道索引为i的极化信道对应的比特是否要被删除的标识，pi∈{0,1}。
具体地，当j＝n-1时，使用如下公式计算初始的g
Figure PCTCN2017090359-appb-000083
Figure PCTCN2017090359-appb-000084
当j＝[n-2,n-3,,,1,0]时，使用如下公式计算剩余的g系数
Figure PCTCN2017090359-appb-000085
Figure PCTCN2017090359-appb-000086
下面举例说明，以N＝2n为例：
当j＝2时，
g(0,2)＝(P0+P4)/2，g(4,2)＝g(0,2)
g(1,2)＝(P1+P5)/2，g(5,2)＝g(1,2)
g(2,2)＝(P2+P6)/2，g(6,2)＝g(2,2)
g(3,2)＝(P3+P7)/2，g(7,2)＝g(3,2)
当j∈{0,1}时，
g(0,1)＝(g(0,2)+g(2,2))/2，g(2,1)＝g(0,1)
g(1,1)＝(g(1,2)+g(3,2))/2，g(3,1)＝g(1,1)
g(0,0)＝(g(0,1)+g(1,1))/2，g(1,0)＝g(0,0)
剩余的g(i,j)按照相同的规则进行计算。
S303、根据修正系数集合计算N个极化信道的极化权重，得到第一极化权重向量。
具体地，作为一种可实施的方式，根据如下公式计算N个极化信道的极化权重Wi，得到第一极化权重向量：
Figure PCTCN2017090359-appb-000087
其中，
Figure PCTCN2017090359-appb-000088
i为信道索引，Bn-1Bn-2…B0为i的二进制表示，其中Bn-1为最高位，B0为最低位，Bj∈{0,1}，j∈{0,1,···,n-1}，i∈{0,1,···,N-1}，N＝2n，g(i,j)为修正系数集合g中第i行第j列的元素,φ与α为根据Polar码的目标码长和码率预设的参数。
作为另一种可实施的方式，根据如下公式通过递归计算得到第一极化权重向量W0 N-1：
βi＝(2i-1+φ)α；
Figure PCTCN2017090359-appb-000089
Figure PCTCN2017090359-appb-000090
其中，
Figure PCTCN2017090359-appb-000091
其中，i∈{1,···,N-1}，βi为与信道索引i有关的中间变量，φ与α为根据Polar码的目标码长和码率预设的参数，g(i,j)为修正系数集合g中第i行第j列的元素，W0为任意常数。
可选的，上述公式中的φ＝0，α＝1/4。
S304、根据第一极化权重向量确定信息比特的位置。
具体地，可以是将第一极化权重向量中的极化权重从大到小进行排序，选择前K个极化权重对应的比特作为信息比特。也就是选择出信息比特的位置，其余位置设置为固定比特，得到完整的长度为N的待编码比特。
S305、对N个待编码比特进行Polar编码，获得Polar编码后的比特。
具体地，使用Polar码的编码矩阵FN完成待编码比特的编码过程。
本实施例提供的编码方法，通过接收到输入的信息比特后，根据Polar码的目标码长M确定待编码比特的个数N，然后确定N个待编码比特中要删除的N-M个比特的位置，并根据确定结果计算包含N个待编码比特的修正系数的修正系数集合，接着根据修正系数集合计算N个极化信道的极化权重，得到第一极化权重向量，最后根据第一极化权重向量确定出信息比特，对N个待编码比特进行Polar编码，获得Polar编码后的比特。从而实现了对于任意目标码长的Polar码，通过Polar码极化信道的极化权重的计算来确定信息比特与固定比特的位置，与信道参数及码率没有关系，可以降低Polar码编码的计算与实现复杂度。
图8为本申请编码设备实施例一的结构示意图，如图8所示，本实施例的编码设备100可以包括：第一确定模块11、获取模块12、第二确定模块13和编码模块14。其中，第一确定模块11用于确定N个待编码比特，N个待编码比特中包含信息比特和固定比特；获取模块12用于获取包含N个极化信道的极化权重的第一极化权重向量，极化权重是选择信息比特的依据，N个待编码比特对应N个极化信道；第二确定模块13用于根据第一极化权重向量确定信息比特的位置；编码模块14用于对N个待编码比特进行Polar编码，获得Polar编码后的比特。
进一步地，Polar码的目标码长M等于2的正整数次幂，第一确定模块11具体用于：确定N等于M，Polar码的目标码长为Polar码的输出码长。获取模块12具体用于：计算N个极化信道的极化权重，得到第一极化权重向量。
可选的，获取模块12具体用于：根据如下公式计算N个极化信道的极化权重Wi，得到第一极化权重向量：
Figure PCTCN2017090359-appb-000092
其中，
Figure PCTCN2017090359-appb-000093
i为信道索引，Bn-1Bn-2…B0为i的二进制表示，其中Bn-1为最高位，B0为最低位，Bj∈{0,1}，j∈{0,1,···,n-1}，i∈{0,1,···,N-1}，N＝2n，φ与α为根据Polar码的目标码长和码率预设的参数。
可选的，获取模块12具体用于：根据如下公式通过递归计算得到第一极化权重向量W0 N-1：
βi＝(2i-1+φ)α；
Figure PCTCN2017090359-appb-000094
Figure PCTCN2017090359-appb-000095
其中，
Figure PCTCN2017090359-appb-000096
其中，i∈{1,···,N-1}，βi为与信道索引i有关的中间变量，φ与α为根据Polar码的目标码长和码率预设的参数，W0为任意常数。
本实施例的编码设备，可以用于执行图3所示方法实施例的技术方案，其实现原理类似，此处不再赘述。
需要说明说明的，本申请中的编码设备可以是基站或终端。
本实施例提供的编码设备，接收到输入的信息比特后，根据Polar码的目标码长M确定待编码比特的个数N，然后获取包含N个极化信道的极化权重的第一极化权重向量，极化权重是选择信息比特的依据，接着根据第一极化权重向量确定出信息比特，最后对N个待编码比特进行Polar编码，获得Polar编码后的比特。从而实现了通过Polar码极化信道的极化权重的计算来确定信息比特与固定比特的位置，与信道参数及码率没有关系，可以降低Polar码编码的计算复杂度，而且，对于不同码长和码率的Polar码对应的极化权重有相同的部分，大大降低存储空间，从而还可降低Polar码编码的存储复杂度。
可选的，Polar码的目标码长M等于2的正整数次幂，获取模块12具体用于：从预先存储的第二极化权重向量中获取第一极化权重向量，第二极化权重向量包含Nmax个极化信道的极化权重，Nmax为预设的通信系统支持的最大码长所对应的母码码长，母码码长为2的正整数次幂。
本实施方式采用离线存储的方式获取极化权重，相比较在线计算，在存储空间允许的情况下，离线存储的方式可降低在线计算带来的时延。
可选的，Polar码的目标码长M＜＝Nmax时，第一极化权重向量中的元素集合为第二极化权重向量中的元素集合的子集；Polar码的目标码长M＞＝Nmax时，信道索引小于或等于Nmax的极化信道的极化权重与第二极化权重向量中的极化权重一一对应，信道索引大于Nmax的极化信道的极化权重等于对应的信道索引小于或等于Nmax的极化信道的极化权重加上权重增量
Figure PCTCN2017090359-appb-000097
其中，φ与α为根据Polar码的目标码长和码率预设的参数。
本实施方式通过半在线计算半离线存储的方式，既可降低在线计算带来的时延，还可降低存储复杂度。
在上述实施方式中，进一步地，φ＝0，α＝1/4。
进一步地，Polar码的目标码长M不等于2的正整数次幂，第一确定模块11具体用于：确定
Figure PCTCN2017090359-appb-000098
符号
Figure PCTCN2017090359-appb-000099
表示向下取整。
图9为本申请编码设备实施例二的结构示意图，如图9所示，本实施例的编码设备200在图8所示编码设备结构的基础上，进一步地，还可以包括：第三确定模块15和计算模块16，第三确定模块15用于在获取模块12获取包含N个极化信道的极化权重的第一极化权重向量之前，确定N个待编码比特中要删除的N-M个比特的位置。计算模块16用于根据第三确定模块15确定的结果计算包含N个待编码比特对应的极化权重的修正系数集合，修正系数用于表征删除的比特对每一极化权重的修正量；获取模块12具体用于：根据修正系数集合计算N个极化信道的极化权重，得到第一极化权重向量。
进一步地，第三确定模块15具体用于：确定N个极化信道的信道索引序列
Figure PCTCN2017090359-appb-000100
对信道索引序列中的每一个索引，进行如下操作：将每一索引对 应的二进制数进行比特逆序，再转化为十进制数，得到新的信道索引序列
Figure PCTCN2017090359-appb-000101
对新的信道索引序列
Figure PCTCN2017090359-appb-000102
中的索引排序，按照从小到大的顺序选择信道索引序列
Figure PCTCN2017090359-appb-000103
Figure PCTCN2017090359-appb-000104
中的N-M个为要删除的比特索引。
可选的，修正系数集合
Figure PCTCN2017090359-appb-000105
计算模块16具体用于按照如下公式计算修正系数集合g中的每一项
Figure PCTCN2017090359-appb-000106
Figure PCTCN2017090359-appb-000107
Figure PCTCN2017090359-appb-000108
其中，i∈{0,1,···,N-1}，j∈{0,1,···,n-1}，N＝2n，pi为信道索引为i的极化信道对应的比特是否要被删除的标识，pi∈{0,1}。
可选的，获取模块12具体用于：根据如下公式计算N个极化信道的极化权重Wi，得到第一极化权重向量：
Figure PCTCN2017090359-appb-000109
其中，
Figure PCTCN2017090359-appb-000110
i为信道索引，Bn-1Bn-2…B0为i的二进制表示，其中Bn-1为最高位，B0为最低位，Bj∈{0,1}，j∈{0,1,···,n-1}，i∈{0,1,···,N-1}，N＝2n，g(i,j)为修正系数集合g中第i行第j列的元素,φ与α为根据Polar码的目标码长和码率预设的参数。
可选的，获取模块12具体用于：根据如下公式通过递归计算得到第一极化权重向量W0 N-1：
βi＝(2i-1+φ)α；
Figure PCTCN2017090359-appb-000111
Figure PCTCN2017090359-appb-000112
其中，
Figure PCTCN2017090359-appb-000113
其中，i∈{1,···,N-1}，βi为与信道索引i有关的中间变量，φ与α为根据Polar码的目标码长和码率预设的参数，g(i,j)为修正系数集合g中第i行第j列的元素，W0为任意常数。
在上述实施方式中，φ＝0，α＝1/4。
在上述实施方式中，第二确定模块13具体用于：将第一极化权重向量中的极化权重从大到小进行排序，选择前K个极化权重对应的比特作为信息比特。
本实施例的编码设备，可以用于执行图7所示方法实施例的技术方案，其实现原理类似，此处不再赘述。
本实施例提供的编码设备，通过接收到输入的信息比特后，根据Polar码的目标码长M确定待编码比特的个数N，然后确定N个待编码比特中要删除的N-M个比特的位置，并根据确定结果计算包含N个待编码比特的修正系数的修正系数集合，接着根据修正系数集合计算N个极化信道的极化权重，得到第一极化权重向量，最后根据第一极化权重向量确 定出信息比特，对N个待编码比特进行Polar编码，获得Polar编码后的比特。从而实现了对于任意目标码长的Polar码，通过Polar码极化信道的极化权重的计算来确定信息比特与固定比特的位置，与信道参数及码率没有关系，可以降低Polar码编码的计算与实现复杂度。
本领域普通技术人员可以理解：实现上述各方法实施例的全部或部分步骤可以通过程序指令相关的硬件来完成。前述的程序可以存储于一计算机可读取存储介质中。该程序在执行时，执行包括上述各方法实施例的步骤；而前述的存储介质包括：ROM、RAM、磁碟或者光盘等各种可以存储程序代码的介质。
由如上的方法及相应的设备所示，当第一极化权重向量按极化权重从大到小排列的时候，根据按极化信道序号的二进制表示方式对应的公式或多项式计算极化权重的方法，假如一个极化信道的极化权重大于另一个极化信道的极化权重，那么这‘一个极化信道’在第一极化权重向量中的位置必然在‘另一个极化信道’之前。当然，如果第一极化权重向量按极化权重从小到大排列，那么，假如一个极化信道的极化权重大于另一个极化信道的极化权重，那么这‘一个极化信道’在第一极化权重向量中的位置必然在‘另一个极化信道’之后。另外，每一个极化信道在第一极化权重向量中的位置可以看做是极化权重乘于一个因子。
根据以上的包含N个极化信道的极化权重的第一极化权重向量的生成方法以及相应的设备，可以给出以下几个第一极化权重向量的例子，既可以按极化权重从大到小的顺序排列，也可以按极化权重从小到大的顺序排列。不失一般性，这些例子中的序号均从1开始排列，即序号最小值为1。这与序号从0开始排列是等价的，如果序号从0开始排列，那么只需将相应序列中的每个序列号均减1即可。
第一极化权重向量可以按极化权重从大到小排列，这里的排序序号最小值为1，相应地，如果排序序号最小值为0，则所有排序序号均减1即可：
(1)N＝16，第一极化权重向量为：
16,15,14,12,8,13,11,10,7,6,4,9,5,3,2,1；
(2)N＝32，第一极化权重向量为：
32,31,30,28,24,16,29,27,26,23,22,15,20,14,12,25,8,21,19,13,18,11,10,7,6,4,17,9,5,3,2,1；
(3)N＝64，第一极化权重向量为：
64,63,62,60,56,48,61,32,59,58,55,54,47,52,46,31,44,30,57,40,28,53,24,51,45,50,16,43,29,42,39,27,38,26,23,36,22,49,15,20,14,41,12,37,25,8,35,21,34,19,13,18,11,10,7,6,33,4,17,9,5,3,2,1；
(4)N＝128，第一极化权重向量为：
128,127,126,124,120,112,125,96,123,122,119,64,118,111,116,110,95,108,94,121,104,92,63,117,62,88,115,109,60,114,80,107,56,93,106,103,91,48,102,90,61,87,100,32,59,86,113,79,58,84,55,78,105,54,76,47,101,52,89,46,72,99,31,44,85,98,30,57,83,40,77,28,82,53,75,24,51,74,45,71,50,16,43,70,97,29,42,68,39,27,81,38,26,23,36,73,22,49,15,69,20,14,41,67,12,66,37,25,8,35,21,34,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；
(5)N＝256，第一极化权重向量为：
256,255,254,252,248,240,253,224,251,250,247,192,246,239,244,238,128,223,236,222,249,232,220,191,245,190,216,243,237,188,242,127,208,235,184,126,221,234,231,124,219,176,230,218,189,120,215,228,160,187,214,241,112,207,186,212,183,125,206,233,182,96,123,204,175,229,180,122,217,174,119,200,227,64,159,118,172,213,226,111,158,185,116,211,168,110,205,156,210,181,95,108,203,152,179,94,121,202,173,104,199,178,92,63,144,117,171,198,225,62,157,88,170,115,196,167,109,60,155,114,209,166,80,107,154,56,151,164,93,106,201,103,150,177,91,48,143,102,197,148,90,61,142,87,169,100,195,32,59,86,140,113,194,165,79,58,153,84,55,136,163,78,105,54,149,162,76,47,101,52,147,89,46,141,72,99,146,31,44,85,139,98,193,30,57,138,83,40,135,77,28,82,53,134,161,75,24,51,132,74,45,71,50,145,16,43,70,97,29,42,137,68,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；
(6)N＝512，第一极化权重向量为：
512,511,510,508,504,496,509,480,507,506,503,448,502,495,500,494,384,479,492,478,505,488,476,447,501,256,446,472,499,493,444,498,383,464,491,440,382,477,490,487,380,475,432,486,474,255,445,376,471,484,254,416,443,470,497,368,463,252,442,468,439,381,462,489,248,438,352,379,460,431, 485,436,378,473,240,430,375,456,483,253,320,415,374,428,469,482,367,224,414,251,441,372,467,424,366,461,250,412,466,247,437,351,364,459,192,246,408,435,350,377,458,239,429,360,455,244,434,348,238,319,400,373,427,454,481,128,223,318,413,236,344,426,371,452,423,365,222,249,316,411,370,465,232,422,336,363,220,410,191,245,312,407,420,349,362,457,190,359,216,406,243,433,347,237,304,399,358,188,453,242,404,346,127,208,317,398,235,343,425,356,451,184,126,221,288,234,315,342,396,369,450,231,421,335,124,219,314,409,176,340,230,311,392,419,334,361,218,189,120,215,310,405,228,418,332,303,160,357,187,214,241,308,403,345,112,207,302,397,328,186,355,212,402,183,125,206,287,233,300,341,395,354,449,182,96,286,123,204,313,394,175,339,229,296,391,180,333,122,217,284,174,338,119,200,309,390,227,417,331,64,159,118,172,213,280,226,307,388,330,111,301,158,327,185,116,211,306,401,168,110,205,272,299,326,156,353,210,181,95,285,108,203,298,393,324,295,152,179,94,121,202,283,173,337,104,199,294,389,178,92,282,63,144,117,171,198,279,225,292,387,329,62,157,88,170,278,115,196,305,386,167,109,271,60,325,155,114,209,276,166,80,270,107,297,154,323,56,151,164,93,106,201,268,322,103,293,150,177,91,281,48,143,102,197,264,291,148,90,61,142,87,169,277,100,195,290,385,32,59,86,140,113,194,275,165,79,269,58,153,84,274,55,136,163,78,105,267,321,54,149,162,76,266,47,101,263,52,147,89,46,141,72,262,99,289,146,31,44,85,139,98,193,260,30,57,138,83,273,40,135,77,28,82,53,134,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；
(7)N＝1024，第一极化权重向量为：
1024,1023,1022,1020,1016,1008,1021,992,1019,1018,1015,960,1014,1007,1012,1006,896,991,1004,990,1017,1000,988,959,1013,768,958,984,1011,1005,956,1010,895,976,1003,952,894,989,1002,999,512,892,987,944,998,986,767,957,888,983,996,766,928,955,982,1009,880,975,764,954,980,951,893,974,1001,760,950,864,511,891,972,943,997,948,510,890,985,752,942,887,968,995,508,765,832,927,886,940,981,994,879,736,926,763,953,504,884,979,936,878,973,762,924,978,759,949,863,496,876,971,704,758,920,947,862,509,889,970,751,941,872,967,756,946,480,860,507,750,831,912,885,939,966,993,506,640,735,830,925,748,856,938,503,883,964,935,877,734,448,761,828,923,502,882,977,744,934,848,495,875,732,922,703,500,757,824,919,932,861,494,874,969,702,871,728,918,755,945,384,479,859,492,749,816,911,870,700,965,754,916,478,858,505,639,720,829,910,747,855,937,488,868,963,696,476,638,733,800,447,746,827,854,908,501,881,962,743,933,847,256,446,636,731,826,921,472,688,852,499,742,823,904,931,846,493,873,730,444,701,498,632,727,822,917,740,930,383,464,844,491,815,672,869,699,726,440,753,820,915,382,477,857,490,624,719,814,909,840,698,487,867,724,914,695,380,475,637,718,799,432,745,812,853,907,486,866,961,694,474,608,255,798,445,635,716,825,376,906,471,687,851,484,741,808,903,692,845,254,416,634,729,796,443,470,686,850,497,631,712,821,902,739,929,368,463,843,252,442,576,671,468,630,684,725,792,439,738,819,900,381,462,842,489,623,813,670,839,697,248,438,628,723,818,913,352,680,379,460,622,717,784,431,811,838,668,485,865,722,436,693,378,473,607,240,797,430,620,715,810,375,905,456,836,483,807,664,691,606,253,320,415,633,714,795,374,428,469,685,849,482,616,711,806,901,690,367,224,414,604,251,794,441,575,656,372,467,629,683,710,791,424,737,804,899,366,461,841,250,412,574,669,466,600,682,247,790,437,627,708,817,898,351,679,364,459,621,783,192,572,837,667,246,408,626,721,788,435,350,678,377,458,592,239,782,429,619,809,360,666,455,835,244,434,568,663,348,676,605,238,319,400,618,713,780,373,427,454,834,481,615,805,662,689,128,223,318,413,603,236,793,344,426,560,655,371,452,614,709,776,423,803,660,365,222,602,249,316,411,573,654,370,465,599,681,232,789,422,612,707,802,897,336,363,220,410,544,191,571,598,652,245,312,407,625,706,787,420,349,677,362,457,591,781,190,570,359,665,216,406,596,243,786,433,567,648,347,675,590,237,304,399,617,779,358,188,453,833,242,404,566,661,346,674,127,208,317,398,588,235,778,343,425,559,356,451,613,775,184,564,659,126,221,288,601,234,315,342,396,558,653,369,450,584,231,774,421,611,801,658,335,124,219,314,409,543,176,340,556,597,651,230,311,392,610,705,772,419,334,361,218,542,189,569,120,650,215,310,405,595,228,785,418,552,647,332,589,303,160,540,357,187,214,594,241,308,403,565,646,345,673,112,207,302,397,587,777,328,186,355,212,402,536,183,563,644,125,206,287,586,233,300,341,395,557,354,449,583,773,182,562,657,96,286,123,204,313,394,528,175,339,555,582,229,296,391,609,771,180,333,122,217,284,541,174,338,554,119,649,200,309,390,580,227,770,417,551,331,64,159,539,118,172,213,280,593,226,307,388,550,645,330,111,301,158,538,327,185,116,211,306,401,535,168,548,643,110,205,272,585,299,326,156,353,210,534,181,561,642,95,285,108,203,298,393,527,324,581,295,152,532,179,94,121,202,283,526,173,337,553,104,199,294,389,579,769,178,92,282,63,144,524,117,171,198,279,578,225,292,387,549,329,62,157,537,88,170,278,115,196,305,386,520,167,547,109,271,60,325,155,114,209,276,533,166,546,641,80,270,107,297,154,323,56,151,531,164,93,106,201,268,525,322,103,293,150,530,177,91,281,48,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,32,59,86,140,113,194,275,518,165,545,79,269,58,153,84,274,55,136,516,163,78,105,267,321,54,149,529,162,76,266,47,101,26 3,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；
(8)N＝2048，第一极化权重向量为：
2048,2047,2046,2044,2040,2032,2045,2016,2043,2042,2039,1984,2038,2031,2036,2030,1920,2015,2028,2014,2041,2024,2012,1983,2037,1792,1982,2008,2035,2029,1980,2034,1919,2000,2027,1976,1918,2013,2026,2023,1536,1916,2011,1968,2022,2010,1791,1981,1912,2007,2020,1790,1952,1979,2006,2033,1904,1999,1788,1978,2004,1975,1917,1998,2025,1024,1784,1974,1888,1535,1915,1996,1967,2021,1972,1534,1914,2009,1776,1966,1911,1992,2019,1532,1789,1856,1951,1910,1964,2005,2018,1903,1760,1950,1787,1977,1528,1908,2003,1960,1902,1997,1786,1948,1023,2002,1783,1973,1887,1520,1900,1995,1728,1022,1782,1944,1971,1886,1533,1913,1994,1775,1965,1896,1991,1020,1780,1970,1504,1884,1531,1774,1855,1936,1909,1963,1990,2017,1016,1530,1664,1759,1854,1949,1772,1880,1962,1527,1907,1988,1959,1901,1758,1472,1785,1852,1947,1526,1906,1008,2001,1768,1958,1872,1519,1899,1756,1946,1727,1021,1524,1781,1848,1943,1956,1885,1518,1898,1993,1726,992,1895,1752,1019,1942,1779,1969,1408,1503,1883,1516,1773,1840,1935,1894,1724,1989,1018,1778,1940,1502,1015,1882,1529,1663,1744,1853,1934,1771,1879,1961,1512,1892,1987,960,1720,1014,1500,1662,1757,1824,1471,1770,1851,1878,1932,1525,1905,1007,1986,1767,1957,1871,1012,1280,1470,1660,1755,1850,1945,1496,1712,1876,1006,1523,1766,1847,1928,1955,1870,1517,1897,1754,1468,1725,896,991,1522,1656,1751,1846,1004,1941,1764,1954,1407,1488,1868,1515,1839,1696,990,1893,1723,1750,1017,1464,1777,1844,1939,1406,1501,1000,1881,1514,1648,1743,1838,1933,1864,1722,1511,988,1891,1748,959,1938,1719,1013,1404,1499,1661,1742,1823,1456,1769,1836,1877,1931,1510,1890,768,1985,958,1718,984,1498,1632,1011,1279,1822,1469,1659,1740,1849,1400,1930,1495,1711,1875,1005,1508,1765,1832,1927,956,1716,1869,1010,1278,1440,1658,1753,1820,1467,1494,1710,895,1874,976,1521,1655,1736,1845,1003,1926,1763,1953,1392,1487,1867,952,1276,1466,1600,1695,894,989,1492,1654,1708,1749,1816,1002,1463,1762,1843,1924,1405,1486,999,1866,1513,1647,1837,1694,512,1863,1721,892,1272,987,1462,1652,1747,1842,944,1937,1376,1704,998,1403,1484,1646,1741,1808,1455,1835,1862,1692,1509,986,1889,767,1746,957,1460,1717,888,983,1402,1497,1631,996,1264,1821,1454,1644,1739,1834,1399,1929,1480,1860,766,1507,928,1831,1688,955,982,1715,1630,1009,1277,1344,1439,1657,1738,1819,1398,1452,1493,1709,880,1873,975,1506,1640,1735,1830,764,1925,954,1714,1391,980,1248,1438,1628,951,1275,1818,1465,1599,1680,893,1396,974,1491,1653,1707,1734,1815,1001,1448,1761,1828,1923,1390,1485,760,1865,950,1274,1436,1598,1693,864,511,1490,1624,1706,891,1271,1814,972,1461,1651,1732,1841,943,1922,1375,1703,997,1388,1483,1645,1807,948,1216,510,1596,1861,1691,890,1270,985,1432,1650,752,1745,1812,942,1459,1374,1702,887,968,1401,1482,1616,995,1263,1806,1453,1643,1833,1384,1690,1479,508,1859,765,832,1268,927,1458,1592,1687,886,940,981,1372,1700,1629,994,1262,1343,1424,1642,1737,1804,1397,1451,1478,879,1858,736,1505,1639,926,1829,763,1686,953,504,1713,884,1152,979,1247,1342,1437,1627,936,1260,1817,1368,1450,1584,1679,878,1395,973,1476,1638,1733,1800,762,1447,924,1827,1684,1389,978,1246,759,1626,949,1273,1340,1435,1597,1678,863,1394,496,1489,1623,1705,876,1256,1813,971,1446,1636,1731,1826,704,1921,1360,758,1387,920,1244,1434,1568,947,1215,862,509,1595,1622,1676,889,1269,1336,970,1431,1649,751,1730,1811,941,1444,1373,1701,872,967,1386,1481,1615,756,1805,946,1214,480,1594,1383,1689,860,1240,507,1430,1620,750,831,1267,1810,912,1457,1591,1672,885,939,966,1371,1699,1614,993,1261,1328,1423,1641,1803,1382,1212,1477,506,640,1857,735,830,1266,925,1428,1590,748,1685,856,938,503,1370,1698,883,1151,964,1232,1341,1422,1612,935,1259,1802,1367,1449,1583,877,1380,734,1475,1637,448,1799,761,828,1208,923,502,1588,1683,882,1150,977,1245,1312,744,1625,934,1258,1339,1366,1420,1582,1677,848,1393,495,1474,1608,875,1255,1798,732,1445,1635,922,1825,703,1682,1359,500,757,824,1148,919,1243,1338,1433,1567,932,1200,861,1364,494,1580,1621,1675,874,1254,1335,969,1416,1634,1729,1796,702,1443,1358,871,728,1385,918,1242,755,1566,945,1213,384,479,1593,1144,1674,859,1239,1334,492,1429,1619,749,816,1252,1809,911,1442,1576,1671,870,700,965,1356,1613,754,1327,916,1184,478,1564,1381,1211,858,1238,505,639,1618,720,829,1265,1332,910,1427,1589,747,1670,855,937,488,1369,1697,868,1136,963,1231,1326,1421,1611,696,1801,1352,1210,476,638,1379,733,800,1236,447,1426,1560,746,827,1207,854,908,501,1587,1668,881,1149,962,1230,1311,743,1610,933,1257,1324,1365,1419,1581,847,1378,256,1473,1607,446,636,1797,731,826,1206,921,472,1586,688,1681,852,1120,499,1310,742,823,1147,904,1228,1337,1418,1552,931,1199,846,1363,493,1579,1606,873,1253,1320,730,1415,1633,444,1795,701,1204,1357,498,632,727,822,1146,917,1241,1308,740,1565,930,1198,383,1362,464,1578,1143,1673,844,1224,1333,491,1414,1604,815,1251,1794,672,1441,1575,869,699,726,1355,440,753,820,1088,915,1183,382,477,1563,1142,1196,857,1237,1304,490,624,1617,719,814,1250,1331,909,1412,1574,1669,840,698,487,1354,867,1135,724,1325,914,1182,695,1562, 1351,1209,380,475,637,1140,718,799,1235,1330,432,1425,1559,745,812,1192,853,907,486,1572,1667,866,1134,961,1229,1296,1609,694,1323,1350,1180,474,608,1377,255,798,1234,445,635,1558,716,825,1205,376,906,471,1585,687,1666,851,1119,484,1309,741,808,1132,903,1227,1322,1417,1551,692,845,1348,254,1605,416,634,1319,729,796,1176,443,470,1556,686,1203,850,1118,497,631,712,821,1145,902,1226,1307,739,1550,929,1197,368,1361,463,1577,1128,843,1223,1318,252,1413,1603,442,576,1793,671,1202,468,630,684,725,792,1116,439,1306,738,819,1087,900,1168,381,462,1548,1141,1195,842,1222,1303,489,623,1602,813,1249,1316,670,1411,1573,839,697,248,1353,438,628,723,818,1086,913,1181,352,680,1561,1112,1194,379,1302,460,622,1139,717,784,1220,1329,431,1410,1544,811,1191,838,668,485,1571,865,1133,722,1295,436,693,1084,1349,1179,378,473,607,1138,240,797,1233,1300,430,620,1557,715,810,1190,375,905,456,1570,1665,836,1104,483,1294,807,1131,664,1321,1178,691,606,1347,253,320,415,633,1080,714,795,1175,374,428,469,1555,685,1188,849,1117,482,616,711,806,1130,901,1225,1292,1549,690,367,1346,224,1127,414,604,1317,251,794,1174,441,575,1554,656,1201,372,467,629,683,710,791,1115,424,1305,737,804,1072,899,1167,366,461,1547,1126,841,1221,1288,250,1601,412,574,1315,669,1172,466,600,682,247,790,1114,437,627,708,817,1085,898,1166,351,679,1546,1111,1193,364,1301,459,621,1124,783,1219,1314,192,1409,1543,572,837,667,246,408,626,721,788,1056,435,350,678,1083,1110,1164,377,458,592,1137,239,782,1218,1299,429,619,1542,809,1189,360,666,455,1569,835,1103,244,1293,434,568,663,1082,1177,348,676,605,1108,238,319,1298,400,618,1079,713,780,1160,373,427,454,1540,1187,834,1102,481,615,805,1129,662,1291,689,128,1345,223,318,413,603,1078,236,793,1173,344,426,560,1553,655,1186,371,452,614,709,776,1100,423,1290,803,1071,660,365,222,1125,602,1287,249,316,411,573,1076,654,1171,370,465,599,681,232,789,1113,422,612,707,802,1070,897,1165,336,1545,1096,363,1286,220,1123,410,544,1313,191,1170,571,598,652,245,312,407,625,706,787,1055,420,349,677,1068,1109,1163,362,457,591,1122,781,1217,1284,190,1541,570,359,665,216,406,596,243,786,1054,433,567,648,1081,1162,347,675,590,1107,237,304,1297,399,617,1064,779,1159,358,188,453,1539,833,1101,242,404,566,661,1052,346,674,127,1106,208,317,398,588,1077,235,778,1158,343,425,559,1538,1185,356,451,613,775,1099,184,1289,564,659,126,221,288,601,1048,234,315,342,396,558,1075,653,1156,369,450,584,231,774,1098,421,611,801,1069,658,335,1095,124,1285,219,314,409,543,1074,176,1169,340,556,597,651,230,311,392,610,705,772,1040,419,334,1067,1094,361,218,1121,542,1283,189,569,120,650,215,310,405,595,228,785,1053,418,552,647,1066,1161,332,589,1092,303,1282,160,1063,540,357,187,214,594,241,308,403,565,646,1051,345,673,112,1105,207,302,397,587,1062,777,1157,328,186,1537,355,212,402,536,183,1050,563,644,125,206,287,586,1047,233,300,341,395,557,1060,1155,354,449,583,773,1097,182,562,657,96,286,123,1046,204,313,394,528,1073,175,1154,339,555,582,229,296,391,609,771,1039,180,333,1093,122,217,284,541,1044,174,338,554,119,649,200,309,390,580,227,770,1038,417,551,1065,331,1091,64,1281,159,539,118,172,213,280,593,226,307,388,550,645,1036,330,111,1090,301,158,1061,538,327,185,116,211,306,401,535,168,1049,548,643,110,205,272,585,1032,299,326,156,1059,353,210,534,181,561,642,95,285,108,1045,203,298,393,527,1058,1153,324,581,295,152,532,179,94,121,202,283,526,1043,173,337,553,104,199,294,389,579,769,1037,178,92,282,63,1042,144,524,117,171,198,279,578,225,292,387,549,1035,329,1089,62,157,537,88,170,278,115,196,305,386,520,167,1034,547,109,271,1031,60,325,155,114,209,276,533,166,546,641,80,270,107,1030,297,154,1057,323,56,151,531,164,93,106,201,268,525,1028,322,103,293,150,530,177,91,281,48,1041,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,1033,32,59,86,140,113,194,275,518,165,545,79,269,1029,58,153,84,274,55,136,516,163,78,105,267,1027,321,54,149,529,162,76,266,47,1026,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,1025,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；
(9)N＝4096，第一极化权重向量为：
4096,4095,4094,4092,4088,4080,4093,4064,4091,4090,4087,4032,4086,4079,4084,4078,3968,4063,4076,4062,4089,4072,4060,4031,4085,3840,4030,4056,4083,4077,4028,4082,3967,4048,4075,4024,3966,4061,4074,4071,3584,3964,4059,4016,4070,4058,3839,4029,3960,4055,4068,3838,4000,4027,4054,4081,3952,4047,3836,4026,4052,4023,3965,4046,4073,3072,3832,4022,3936,3583,3963,4044,4015,4069,4020,3582,3962,4057,3824,4014,3959,4040,4067,3580,3837,3904,3999,3958,4012,4053,4066,3951,3808,3998,3835,4025,3576,3956,4051,4008,3950,4045,3834,3996,3071,4050,3831,4021,2048,3935,3568,3948,4043,3776,3070,3830,3992,4019,3934,3581,3961,4042,3823,4013,3944,4039,3068,3828,4018,3552,3932,3579,3822,3903,3984,3957,4011,4038,4065,3064,3578,3712,3807,3902,3997,3820,3928,4010,3575,3955,4036,4007,3949,3806,3520,3833,3900,3995,3574,3954,3056,4049,3816,4006,2047,3920,3567,3947,3804,3994,3775,3069,3572,3829,3896,3991,2046,4004,3933,3566,3946,4041,3774,3040,3943,3800,3067,3990,3827,4017,3456,3551,2044,3931,3564,3821,3888,3983,3942,3772,4037,30 66,3826,3988,3550,3063,3930,3577,3711,3792,3901,3982,2040,3819,3927,4009,3560,3940,4035,3008,3768,3062,3548,3710,3805,3872,3519,3818,3899,3926,3980,3573,3953,3055,4034,3815,4005,2032,3919,3060,3328,3518,3708,3803,3898,3993,3544,3760,3924,3054,3571,3814,3895,3976,2045,4003,3918,3565,3945,3802,3516,3773,2944,3039,3570,3704,3799,3894,3052,3989,3812,2016,4002,3455,3536,2043,3916,3563,3887,3744,3038,3941,3771,3798,3065,3512,3825,3892,3987,3454,3549,2042,3048,3929,3562,3696,3791,3886,3981,2039,3912,3770,3559,3036,3939,3796,3007,3986,3767,3061,3452,3547,3709,1984,3790,3871,3504,2038,3817,3884,3925,3979,3558,3938,2816,4033,3006,3766,3032,2031,3546,3680,3059,3327,3870,3517,3707,3788,3897,3448,3978,3543,2036,3759,3923,3053,3556,3813,3880,3975,3004,2030,3764,3917,3058,3326,3488,3706,3801,3868,3515,3542,3758,2943,3922,3024,3569,3703,3784,3893,3051,3974,1920,3811,2015,4001,3440,3535,2028,3915,3000,3324,3514,3648,3743,2942,3037,3540,3702,3756,3797,3864,3050,3511,3810,3891,2014,3972,3453,3534,2041,3047,3914,3561,3695,3885,3742,2024,2560,3911,3769,2940,3320,3035,3510,3700,3795,3890,2992,3985,3424,3752,2012,3046,3451,3532,3694,1983,3789,3856,3503,2037,3883,3910,3740,3557,3034,3937,2815,3794,3005,3508,3765,2936,3031,3450,1792,3545,3679,1982,3044,3312,3869,3502,3692,2008,3787,3882,3447,3977,3528,2035,3908,2814,3555,2976,3879,3736,3003,3030,2029,3763,3678,3057,3325,3392,3487,3705,1980,3786,3867,3446,3500,3541,2034,3757,2928,3921,3023,3554,3688,3783,3878,2812,3973,3002,1919,2000,3762,3439,3028,3296,2027,3486,3676,2999,3323,3866,3513,3647,3728,2941,3444,3022,3539,3701,1976,3755,3782,3863,3049,3496,1918,3809,3876,2013,3971,3438,3533,2026,2808,3913,2998,3322,3484,3646,3741,2912,2023,2559,3538,3672,3754,2939,3319,3862,3020,3509,3699,3780,3889,1536,2991,3970,3423,1916,3751,2011,3045,3436,3531,3693,1968,3855,2996,3264,2022,2558,3644,3909,3739,2938,3318,3033,3480,3698,2800,3793,3860,2990,3507,3422,3750,2935,2010,3016,3449,1791,3530,3664,1981,3043,3311,3854,1912,3501,3691,2007,3881,3432,3738,3527,2020,2556,3907,2813,2880,3316,2975,3506,3640,3735,2934,2988,3029,3420,1790,3748,3677,1952,3042,3310,3391,3472,3690,1979,2006,3785,3852,3445,3499,3526,2033,2927,3906,2784,3553,3687,2974,3877,2811,3734,3001,1904,2552,1999,3761,2932,3200,3027,3295,3390,1788,3485,3675,1978,2984,3308,3865,3416,3498,3632,2004,3727,2926,3443,3021,3524,3686,1975,3781,3848,2810,3495,2972,1917,3875,1998,3732,3437,3026,3294,2025,2807,3674,2997,3321,3388,3483,3645,1024,3726,2911,3442,1784,2544,3537,3671,1974,3753,2924,3304,3861,3019,3494,3684,1888,3779,3874,1535,2752,3969,3408,1915,1996,2806,3435,2968,3292,1967,3482,3616,2995,3263,2910,2021,2557,3643,3670,3724,2937,3317,3384,3018,3479,3697,1972,2799,3778,3859,1534,2989,3492,3421,1914,3749,2920,2009,3015,3434,1776,3529,3663,1966,2804,3853,2994,1911,3262,1992,2528,3642,3431,3737,2908,3288,2019,2555,3478,3668,2798,2879,3315,3858,2960,3505,3639,3720,2933,1532,2987,3014,3419,1789,1856,3747,3662,1951,3041,3309,3376,1910,3471,3689,1964,2005,3851,3430,3260,3525,2018,2554,2688,3905,2783,2878,3314,2973,3476,3638,2796,3733,2904,2986,1903,2551,3418,1760,3746,2931,3199,1950,3012,3280,3389,1787,3470,3660,1977,1528,2983,3307,3850,3415,1908,3497,3631,2003,2925,3428,2782,3523,3685,1960,2496,3847,2809,2876,3256,2971,1902,2550,3636,1997,3731,2930,3198,3025,3293,3360,1786,2792,3673,1948,2982,3306,3387,3414,3468,3630,1023,2002,3725,2896,3441,1783,2543,3522,3656,1973,2923,3303,3846,2780,3493,3683,2970,1887,3873,1520,2751,3730,3407,1900,2548,1995,2805,2872,3196,2967,3291,3386,1728,3481,3615,1022,2980,3248,2909,3412,1782,2542,3628,3669,1944,3723,2922,3302,3383,3017,3464,3682,1971,1886,3777,3844,1533,2750,3491,3406,1913,2919,1994,2776,3433,1775,2966,3290,1965,2803,3614,2993,1896,3261,2432,1991,2527,3641,1020,3192,3722,2907,3287,3382,1780,2540,3477,3667,1970,2797,2864,3300,3857,1504,2959,3490,3624,1884,3719,2918,1531,2748,3013,3404,1774,1855,3661,1936,2802,3375,2964,1909,3232,1963,1990,2526,3612,3429,3259,2906,3286,2017,2553,2687,3666,2768,2877,3313,3380,2958,3475,3637,1016,2795,3718,2903,1530,2985,1664,2536,3417,1759,1854,3745,2916,3184,1949,3011,3279,3374,1772,1880,3469,3659,1962,1527,2744,3849,3400,1907,3258,1988,2524,2686,3427,2781,2848,3284,1959,2495,3474,3608,2794,2875,3255,2902,2956,1901,2549,3635,1758,3716,2929,3197,1472,3010,3278,3359,1785,1852,2791,3658,1947,1526,2981,3305,3372,3413,1906,3467,3629,1008,2001,2895,3426,1768,2304,3521,3655,1958,2494,2684,3845,2779,2874,3254,2969,1872,2520,3634,1519,2736,3729,2900,3168,1899,2547,3358,1756,2790,2871,3195,1946,2952,3276,3385,1727,3466,3600,1021,1524,2979,3247,2894,3411,1781,1848,2541,3627,3654,1943,2921,3301,3368,2778,3463,3681,1956,2492,1885,3843,1518,2749,3252,3405,1898,2546,2680,1993,2775,2870,3194,2965,3289,3356,1726,2788,3613,992,2978,1895,3246,2431,3410,1752,2512,3626,1019,3191,1942,3721,2892,3272,3381,1779,2539,3462,3652,1969,1408,2863,3299,3842,1503,2720,3489,3623,1883,2917,1516,2747,2774,3403,1773,1840,2488,1935,2801,2868,3136,2963,1894,3231,2430,1724,1989,2525,3611,1018,3190,3244,2905,3285,3352,1778,2538,2672,3665,1940,2767,2862,3298,3379,1502,2957,3460,3622,1015,1882,3717,2888,1529,2746,1663,2535,3402,1744,1853,2915,3183,1934,2772,3373,1771,2962,1879,3230,1961,1512,2743,3610,3399,1892,3257,2428,1987,2523,2685,960,3188,2766,2847,3283,3378,1720,2480,3473,3607,1014,2793,2860,3240,2901,1500,2955,1662,2534,3620,1757, 1824,3715,2914,3182,1471,3009,3277,3344,1770,1851,1878,3657,1932,1525,2742,3371,3398,1905,3228,1007,1986,2522,2656,3425,1767,2303,2846,3282,1957,2493,2683,3606,2764,2873,3253,2424,2954,1871,2519,3633,1012,1280,2735,3714,2899,3167,1470,1660,2532,3357,1755,1850,2789,2856,3180,1945,1496,2951,3275,3370,1712,1876,3465,3599,1006,1523,2740,2893,3396,1766,1847,2302,3653,1928,2464,2682,3367,2777,2844,3224,1955,2491,1870,2518,3604,1517,2734,3251,2898,3166,1897,2545,2679,1754,2760,2869,3193,1468,2950,3274,3355,1725,896,2787,3598,991,1522,2977,1656,3245,2416,3409,1751,1846,2511,3625,1004,3176,1941,2891,3271,3366,1764,2300,3461,3651,1954,2490,1407,2624,3841,1488,2719,3250,1868,2516,2678,1515,2732,2773,2840,3164,1839,2487,3354,1696,2786,2867,3135,990,2948,1893,3216,2429,1723,1750,2510,3596,1017,3189,1464,3243,2890,3270,3351,1777,1844,2537,2671,3650,1939,1406,2861,3297,3364,1501,2718,3459,3621,1000,1881,2887,1514,2745,1648,2296,3401,1743,1838,2486,2676,1933,2771,2866,3134,2961,1864,3229,2400,1722,1511,2728,3609,988,3160,1891,3242,2427,3350,1748,2508,2670,959,3187,1938,2765,2832,3268,3377,1719,2479,3458,3592,1013,1404,2859,3239,2886,1499,2716,1661,2533,3619,1742,1823,2913,3181,1456,2770,3343,1769,1836,2484,1877,1931,1510,2741,3132,3397,1890,3227,2426,768,1985,2521,2655,958,3186,2288,2845,3281,3348,1718,2478,2668,3605,984,2763,2858,3238,2423,1498,2953,1632,2504,3618,1011,1279,1822,3713,2884,3152,1469,1659,2531,3342,1740,1849,1400,2855,3179,1930,1495,2712,3369,1711,1875,3226,1005,1508,2739,2654,3395,1765,1832,2301,2368,1927,2463,2681,956,3128,2762,2843,3223,2422,1716,2476,1869,2517,3603,1010,1278,2733,3236,2897,3165,1440,1658,2530,2664,1753,1820,2759,2854,3178,1467,1494,2949,3273,3340,1710,895,1874,3597,976,1521,2738,1655,2415,3394,1736,1845,2272,1003,3175,1926,2462,2652,3365,1763,2299,2842,3222,1953,2489,1392,2623,3602,1487,2704,3249,2420,1867,2515,2677,952,1276,2731,2758,2839,3163,1466,1600,2472,3353,1695,894,2785,2852,3120,989,1492,2947,1654,3215,2414,1708,1749,1816,2509,3595,1002,3174,1463,2889,3269,3336,1762,1843,2298,3649,1924,2460,1405,2622,3363,1486,2717,3220,999,1866,2514,2648,1513,2730,1647,2295,2838,3162,1837,2485,2675,1694,2756,2865,3133,512,2946,1863,3214,2399,1721,892,1272,2727,3594,987,3159,1462,1652,3241,2412,3349,1747,1842,2507,2669,944,3172,1937,1376,2831,3267,3362,1704,2240,3457,3591,998,1403,2620,2885,1484,2715,1646,2294,1741,1808,2456,2674,1455,2769,2836,3104,1835,2483,1862,2398,1692,1509,2726,3131,986,3158,1889,3212,2425,767,1746,2506,2640,957,3185,1460,2287,2830,3266,3347,1717,888,2477,2667,3590,983,1402,2857,3237,2408,1497,2714,1631,2503,3617,996,1264,1821,2883,3151,1454,1644,2292,3341,1739,1834,2482,1399,2616,1929,1480,2711,3130,1860,3225,2396,766,1507,2724,2653,928,3156,1831,2286,2367,3346,1688,2448,2666,955,3127,982,2761,2828,3208,2421,1715,2475,1630,2502,3588,1009,1277,1344,3235,2882,3150,1439,1657,2529,2663,1738,1819,1398,2853,3177,1452,1493,2710,3339,1709,880,1873,975,1506,2737,1640,2176,3393,1735,1830,2271,2366,764,1925,2461,2651,954,3126,2284,2841,3221,2392,1714,2474,1391,2608,3601,980,1248,2703,3234,2419,1438,1628,2500,2662,951,1275,1818,2757,2824,3148,1465,1599,2471,3338,1680,893,1396,2851,3119,974,1491,2708,1653,2413,1707,1734,1815,2270,1001,3173,1448,2650,3335,1761,1828,2297,2364,1923,2459,1390,2621,3124,1485,2702,3219,2418,760,1865,2513,2647,950,1274,2729,2280,2837,3161,1436,1598,2470,2660,1693,864,2755,2850,3118,511,1490,2945,1624,3213,2384,1706,891,1271,1814,3593,972,3144,1461,1651,2411,3334,1732,1841,2268,943,3171,1922,2458,1375,2592,3361,1703,2239,3218,997,1388,2619,2646,1483,2700,1645,2293,2360,1807,2455,2673,948,1216,2754,2835,3103,510,1596,2468,1861,2397,1691,890,1270,2725,3116,985,3157,1432,1650,3211,2410,752,1745,1812,2505,2639,942,3170,1459,1374,2829,3265,3332,1702,887,2238,3589,968,1401,2618,2407,1482,2713,1616,2264,995,1263,1806,2454,2644,1453,1643,2291,2834,3102,1833,2481,1384,2615,1690,1479,2696,3129,508,1859,3210,2395,765,832,1268,2723,2638,927,3155,1458,1592,2285,2352,3345,1687,886,2447,2665,940,3112,981,1372,2827,3207,2406,1700,2236,1629,2501,3587,994,1262,1343,2881,3149,1424,1642,2290,1737,1804,2452,1397,2614,1451,1478,2709,3100,879,1858,2394,736,1505,2722,1639,2175,926,3154,1829,2256,2365,763,1686,2446,2636,953,3125,504,2283,2826,3206,2391,1713,884,2473,1152,2607,3586,979,1247,1342,3233,2404,1437,1627,2499,2661,936,1260,1817,1368,2823,3147,1450,1584,2232,3337,1679,878,1395,2612,973,1476,2707,1638,2174,1733,1800,2269,2336,762,1447,2649,924,3096,1827,2282,2363,2390,1684,2444,1389,2606,3123,978,1246,2701,3204,2417,759,1626,2498,2632,949,1273,1340,2279,2822,3146,1435,1597,2469,2659,1678,863,1394,2849,3117,496,1489,2706,1623,2383,1705,876,1256,1813,971,3143,1446,1636,2172,3333,1731,1826,2267,2362,704,1921,2457,1360,2591,3122,2224,3217,2388,758,1387,2604,2645,920,1244,2699,2278,2359,1434,1568,2440,2658,947,1215,862,2753,2820,3088,509,1595,2467,1622,2382,1676,889,1269,1336,3115,970,3142,1431,1649,2409,751,1730,1811,2266,941,3169,1444,1373,2590,3331,1701,872,2237,967,1386,2617,2168,1481,2698,1615,2263,2358,756,1805,2453,2643,946,1214,2276,2833,3101,480,1594,2466,1383,2600,1689,860,1240,2695,3114,507,1430,1620,3209,2380,750,831,1267,1810,2637,912,3140,1457,1591,2351,3330,1672,885,2208,939,3111,966,1371,2588,2405,1699,2235,1614,2262,993,1261,1328,2642,1423,1641,2289,2356,1803,2451,1382,2613,1212,1477,2694,3099,5 06,640,1857,2393,735,830,1266,2721,2160,925,3153,1428,1590,2255,2350,748,1685,856,2445,2635,938,3110,503,1370,2825,3205,2376,1698,883,2234,1151,3585,964,1232,1341,2403,1422,1612,2260,935,1259,1802,2450,1367,2584,1449,1583,2231,3098,877,1380,2611,734,1475,2692,1637,2173,448,1799,2254,2335,761,828,1208,2634,923,3095,502,1588,2281,2348,2389,1683,882,2443,1150,2605,3108,977,1245,1312,3203,2402,744,1625,2497,2631,934,1258,1339,1366,2821,3145,1420,1582,2230,1677,848,1393,2610,495,1474,2705,1608,2144,875,1255,1798,2334,732,1445,1635,2171,922,3094,1825,2252,2361,703,1682,2442,1359,2576,3121,500,2223,3202,2387,757,824,1148,2603,2630,919,1243,1338,2277,2344,1433,1567,2439,2657,932,1200,861,1364,2819,3087,494,1580,2228,1621,2381,1675,874,1254,1335,969,3141,1416,1634,2170,1729,1796,2265,2332,702,1443,1358,2589,3092,871,2222,2386,728,1385,2602,2167,918,1242,2697,2248,2357,755,1566,2438,2628,945,1213,384,2275,2818,3086,479,1593,2465,1144,2599,1674,859,1239,1334,3113,492,1429,1619,2379,749,816,1252,1809,911,3139,1442,1576,2112,3329,1671,870,2207,700,965,1356,2587,2166,2220,1613,2261,2328,754,1327,2641,916,1184,2274,2355,478,1564,2436,1381,2598,1211,858,1238,2693,3084,505,639,1618,2378,720,829,1265,1332,2159,910,3138,1427,1589,2349,747,1670,855,2206,937,3109,488,1369,2586,2375,1697,868,2233,1136,963,1231,1326,2164,1421,1611,2259,2354,696,1801,2449,1352,2583,1210,2216,3097,476,638,1379,2596,733,800,1236,2691,2158,447,1426,1560,2253,2320,746,827,1207,854,2633,908,3080,501,1587,2347,2374,1668,881,2204,1149,3107,962,1230,1311,2401,743,1610,2258,933,1257,1324,1365,2582,1419,1581,2229,847,1378,2609,256,1473,2690,1607,2143,446,636,1797,2333,731,826,1206,2156,921,3093,472,1586,2251,2346,688,1681,852,2441,1120,2575,3106,499,1310,3201,2372,742,823,1147,2629,904,1228,1337,2343,1418,1552,2200,931,1199,846,1363,2580,493,1579,2227,1606,2142,873,1253,1320,730,1415,1633,2169,444,1795,2250,2331,701,1204,1357,2574,3091,498,632,2221,2385,727,822,1146,2601,2152,917,1241,1308,2247,2342,740,1565,2437,2627,930,1198,383,1362,2817,3085,464,1578,2226,1143,1673,844,1224,1333,491,1414,1604,2140,815,1251,1794,2330,672,1441,1575,2111,3090,869,2192,699,726,1355,2572,2165,440,2219,2246,2327,753,820,1088,2626,915,1183,382,2273,2340,477,1563,2435,1142,2597,1196,857,1237,1304,3083,490,624,1617,2377,719,814,1250,1331,909,3137,1412,1574,2110,1669,840,2205,698,487,1354,2585,2136,867,2218,1135,2326,724,1325,2163,914,1182,2244,2353,695,1562,2434,1351,2568,1209,380,2215,3082,475,637,1140,2595,718,799,1235,1330,2157,432,1425,1559,2319,745,812,1192,853,907,3079,486,1572,2108,2373,1667,866,2203,1134,961,1229,1296,2162,1609,2257,2324,694,1323,1350,2581,1180,2214,474,608,1377,2594,255,798,1234,2689,2128,445,635,1558,2318,716,825,1205,376,2155,906,3078,471,1585,2345,687,1666,851,2202,1119,3105,484,1309,2371,741,808,1132,903,1227,1322,2104,1417,1551,2199,692,845,1348,2579,254,2212,1605,2141,416,634,1319,729,796,1176,2154,443,470,1556,2249,2316,686,1203,850,1118,2573,3076,497,631,2370,712,821,1145,2151,902,1226,1307,2341,739,1550,2198,929,1197,368,1361,2578,463,1577,2225,1128,843,1223,1318,252,1413,1603,2139,442,576,1793,2329,671,1202,2096,3089,468,630,2191,684,725,792,1116,2571,2150,439,1306,2245,2312,738,819,1087,2625,900,1168,381,2339,462,1548,2196,1141,1195,842,1222,1303,489,623,1602,2138,813,1249,1316,670,1411,1573,2109,839,2190,697,248,1353,2570,2135,438,628,2217,2325,723,818,1086,2148,913,1181,352,2243,2338,680,1561,2433,1112,2567,1194,379,1302,3081,460,622,1139,717,784,1220,1329,431,1410,1544,2080,811,1191,838,668,485,1571,2107,2134,865,2188,1133,722,1295,2161,436,2242,2323,693,1084,1349,2566,1179,378,2213,473,607,1138,2593,240,797,1233,1300,2127,430,620,1557,2317,715,810,1190,375,905,3077,456,1570,2106,1665,836,2201,1104,483,1294,2132,807,1131,2322,664,1321,2103,1178,2184,691,606,1347,2564,253,320,2211,2126,415,633,1080,714,795,1175,374,2153,428,469,1555,2315,685,1188,849,1117,3075,482,616,2369,711,806,1130,901,1225,1292,2102,1549,2197,690,367,1346,2577,224,2210,1127,414,604,1317,251,794,1174,2124,441,575,1554,2314,656,1201,372,2095,3074,467,629,683,710,791,1115,2149,424,1305,2311,737,804,1072,899,1167,366,2100,461,1547,2195,1126,841,1221,1288,250,1601,2137,412,574,1315,669,1172,2094,466,600,2189,682,247,790,1114,2569,2120,437,627,2310,708,817,1085,2147,898,1166,351,2337,679,1546,2194,1111,1193,364,1301,459,621,1124,783,1219,1314,192,1409,1543,2079,572,837,667,246,2092,2133,408,626,2187,721,788,1056,2146,435,350,2241,2308,678,1083,1110,2565,1164,377,458,592,1137,239,782,1218,1299,429,619,1542,2078,809,1189,360,666,455,1569,2105,835,2186,1103,244,1293,2131,434,568,2321,663,1082,2088,1177,348,2183,676,605,1108,2563,238,319,1298,2125,400,618,1079,713,780,1160,373,427,454,1540,2076,1187,834,1102,481,615,2130,805,1129,662,1291,2101,2182,689,128,1345,2562,223,318,2209,413,603,1078,236,793,1173,344,2123,426,560,1553,2313,655,1186,371,3073,452,614,709,776,1100,423,1290,2072,803,1071,660,365,2099,222,2180,1125,602,1287,249,316,2122,411,573,1076,654,1171,370,2093,465,599,681,232,789,1113,2119,422,612,2309,707,802,1070,897,1165,336,2098,1545,2193,1096,363,1286,220,1123,410,544,1313,191,1170,2064,571,598,652,245,312,2091,2118,407,625,706,787,1055,2145,420,349,2307,677,1068,1109,1163,362,457,591,1122,781,1217,1284,190,1541,2077,570,359,665,216,2090,406,596,2185,243,786,1054,2116,433,567,2306,648,1081,2087,1162,347,675,590,1107,237,304,1297,399,617,1 064,779,1159,358,188,453,1539,2075,833,1101,242,2129,404,566,661,1052,2086,346,2181,674,127,1106,2561,208,317,398,588,1077,235,778,1158,343,425,559,1538,2074,1185,356,451,613,775,1099,184,1289,2071,564,659,126,2084,221,288,2179,601,1048,234,315,342,2121,396,558,1075,653,1156,369,450,584,231,774,1098,421,611,2070,801,1069,658,335,2097,2178,1095,124,1285,219,314,409,543,1074,176,1169,340,2063,556,597,651,230,311,2117,392,610,705,772,1040,419,334,2068,1067,1094,361,218,1121,542,1283,189,2062,569,120,650,215,310,2089,405,595,228,785,1053,2115,418,552,2305,647,1066,1161,332,589,1092,303,1282,160,1063,540,357,187,214,2060,594,241,308,2114,403,565,646,1051,2085,345,673,112,1105,207,302,397,587,1062,777,1157,328,186,1537,2073,355,212,402,536,183,1050,2056,563,644,125,2083,206,287,586,1047,233,300,341,395,557,1060,1155,354,449,583,773,1097,182,2069,562,657,96,2082,286,2177,123,1046,204,313,394,528,1073,175,1154,339,555,582,229,296,391,609,771,1039,180,333,2067,1093,122,217,284,541,1044,174,338,2061,554,119,649,200,309,390,580,227,770,1038,417,551,2066,1065,331,1091,64,1281,159,539,118,172,213,280,2059,593,226,307,2113,388,550,645,1036,330,111,1090,301,158,1061,538,327,185,2058,116,211,306,401,535,168,1049,2055,548,643,110,205,272,585,1032,299,326,156,1059,353,210,534,181,2054,561,642,95,2081,285,108,1045,203,298,393,527,1058,1153,324,581,295,152,532,179,94,2052,121,202,283,526,1043,173,337,553,104,199,294,389,579,769,1037,178,2065,92,282,63,1042,144,524,117,171,198,279,578,225,292,387,549,1035,329,1089,62,157,537,88,170,278,2057,115,196,305,386,520,167,1034,547,109,271,1031,60,325,155,114,209,276,533,166,2053,546,641,80,270,107,1030,297,154,1057,323,56,151,531,164,93,2051,106,201,268,525,1028,322,103,293,150,530,177,2050,91,281,48,1041,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,1033,32,59,86,140,113,194,275,518,165,545,79,269,1029,58,153,84,274,55,136,516,163,78,105,267,1027,321,54,149,529,162,2049,76,266,47,1026,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,1025,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1。
第一极化权重向量还可以按极化权重从小到大排列，这里的排序序号最小值为1，类似地，如果排序序号最小值为0，则所有排序序号均减1即可：
(1)N＝16，第一极化权重向量为：
1,2,3,5,9,4,6,7,10,11,13,8,12,14,15,16；
(2)N＝32，第一极化权重向量为：
1,2,3,5,9,17,4,6,7,10,11,18,13,19,21,8,25,12,14,20,15,22,23,26,27,29,16,24,28,30,31,32；
(3)N＝64，第一极化权重向量为：
1,2,3,5,9,17,4,33,6,7,10,11,18,13,19,34,21,35,8,25,37,12,41,14,20,15,49,22,36,23,26,38,27,39,42,29,43,16,50,45,51,24,53,28,40,57,30,44,31,46,52,47,54,55,58,59,32,61,48,56,60,62,63,64；
(4)N＝128，第一极化权重向量为：
1,2,3,5,9,17,4,33,6,7,10,65,11,18,13,19,34,21,35,8,25,37,66,12,67,41,14,20,69,15,49,22,73,36,23,26,38,81,27,39,68,42,29,97,70,43,16,50,71,45,74,51,24,75,53,82,28,77,40,83,57,30,98,85,44,31,99,72,46,89,52,101,47,76,54,105,78,55,84,58,79,113,86,59,32,100,87,61,90,102,48,91,103,106,93,56,107,80,114,60,109,115,88,62,117,63,92,104,121,94,108,95,110,116,111,118,64,119,122,123,96,125,112,120,124,126,127,128；
(5)N＝256，第一极化权重向量为：
1,2,3,5,9,17,4,33,6,7,10,65,11,18,13,19,129,34,21,35,8,25,37,66,12,67,41,14,20,69,15,130,49,22,73,131,36,23,26,133,38,81,27,39,68,137,42,29,97,70,43,16,145,50,71,45,74,132,51,24,75,161,134,53,82,28,77,135,40,83,138,57,30,193,98,139,85,44,31,146,99,72,141,46,89,147,52,101,47,76,162,149,54,105,78,163,136,55,84,153,58,79,165,194,113,140,86,59,32,195,100,169,87,142,61,90,148,197,102,143,48,91,177,150,103,201,106,93,164,151,56,154,107,80,166,209,114,155,60,109,167,196,115,170,88,157,62,225,198,171,117,144,63,92,178,199,104,173,202,121,94,179,152,203,108,95,181,210,156,205,110,168,211,116,185,158,111,226,213,172,118,159,64,227,200,119,174,217,122,180,229,175,204,123,96,182,233,206,125,183,212,186,207,112,241,214,187,160,228,215,120,189,218,230,176,219,124,231,234,221,126,184,235,208,127,242,188,237,243,216,190,245,191,220,232,249,222,236,223,128,238,244,239,246,192,247,250,251,224,253,240,248,252,254,255,256；
(6)N＝512，第一极化权重向量为：
1,2,3,5,9,17,4,33,6,7,10,65,11,18,13,19,129,34,21,35,8,25,37,66,12,257,67,41,14,20,69,15,130,49,22,73,131,36,23,26,133,38,81,27,39,258,68,137,42,29,259,97,70,43,16,145,50,261,71,45,74,132,51,24,265,75,161,134,53,82,28,77,135,40,273,83,138,57,30,260,193,98,139,85,44,31,146,289,99,262,72,141,46,89,147,52,263,101,47,266,76,162,149,54,321,267,105,78,163,136,55,274,84,153,58,269,79,165,2 75,194,113,140,86,59,32,385,290,195,100,277,169,87,142,61,90,148,291,264,197,102,143,48,281,91,177,150,293,103,322,268,201,106,93,164,151,56,323,154,297,107,270,80,166,276,209,114,155,325,60,271,109,167,386,305,196,115,278,170,88,157,62,329,387,292,225,279,198,171,117,144,63,282,92,178,389,294,199,104,337,173,283,202,121,94,179,152,295,324,393,298,203,108,285,95,181,210,353,156,326,299,272,205,110,168,401,306,211,116,185,327,158,301,111,330,388,307,226,280,213,172,118,159,64,331,417,227,390,309,200,119,338,174,284,217,122,333,180,391,296,229,339,175,394,313,204,123,286,96,182,449,354,395,341,300,233,287,206,125,183,402,212,355,186,328,397,302,207,112,345,403,308,241,214,187,357,160,303,332,418,228,405,310,215,120,189,218,361,334,419,392,311,230,340,176,409,314,219,124,335,421,231,450,369,396,342,315,234,288,221,126,184,451,356,425,343,235,398,317,208,127,346,404,242,453,188,358,399,304,237,347,433,243,406,216,359,190,457,362,349,420,407,312,245,191,410,220,363,336,422,232,465,370,411,316,249,222,365,423,452,371,426,344,236,413,318,223,128,481,454,427,373,400,319,238,348,434,244,455,360,429,239,458,377,350,435,408,246,192,459,364,351,437,247,466,412,250,461,366,424,467,372,441,251,414,224,367,482,469,428,374,415,320,253,483,456,375,430,240,473,378,436,485,431,460,379,352,438,248,489,462,381,439,468,442,252,463,368,497,470,443,416,254,484,471,376,445,255,474,486,432,475,380,487,490,477,382,440,491,464,383,498,444,493,499,472,446,256,501,447,476,488,505,478,492,479,384,494,500,495,502,448,503,506,507,480,509,496,504,508,510,511,512；
(7)N＝1024，第一极化权重向量为：
1,2,3,5,9,17,4,33,6,7,10,65,11,18,13,19,129,34,21,35,8,25,37,66,12,257,67,41,14,20,69,15,130,49,22,73,131,36,23,26,513,133,38,81,27,39,258,68,137,42,29,259,97,70,43,16,145,50,261,71,45,74,132,51,24,265,75,161,514,134,53,82,28,77,515,135,40,273,83,138,57,30,517,260,193,98,139,85,44,31,146,289,99,262,72,521,141,46,89,147,52,263,101,47,266,76,162,529,149,54,321,267,105,78,163,516,136,55,274,84,153,58,269,79,545,165,518,275,194,113,140,86,59,32,519,385,290,195,100,277,169,87,522,142,61,90,148,291,577,264,197,102,523,143,48,281,91,177,530,150,293,103,322,525,268,201,106,93,164,531,151,56,323,154,297,107,270,80,641,546,166,533,276,209,114,155,325,60,271,109,547,167,520,386,305,196,115,278,170,88,537,157,62,329,549,387,292,225,578,279,198,171,117,524,144,63,282,92,178,769,579,389,294,199,104,553,337,173,526,283,202,121,94,179,532,152,295,581,324,527,393,298,203,108,285,95,642,561,181,534,210,353,156,326,299,585,272,205,110,643,548,168,535,401,306,211,116,185,327,538,158,301,111,330,645,550,388,307,226,593,280,213,172,118,539,159,64,331,551,417,770,227,580,390,309,200,649,119,554,338,174,541,284,217,122,333,180,771,609,391,296,229,582,555,339,175,528,394,313,204,123,286,96,657,562,182,773,583,449,354,557,395,341,300,233,586,287,206,125,644,563,183,536,402,212,355,186,328,777,587,397,302,207,112,673,345,646,565,403,308,241,594,214,187,357,540,160,303,589,332,647,552,418,785,228,595,405,310,215,650,120,569,189,542,218,361,334,419,772,705,610,392,311,230,651,597,556,340,176,543,409,314,219,124,335,658,801,611,421,774,231,584,450,369,653,558,396,342,315,234,601,288,221,126,659,564,184,775,613,451,356,559,425,343,778,235,588,398,317,208,127,674,346,661,566,404,242,833,453,188,358,779,617,399,304,237,590,675,347,648,567,433,786,243,596,406,216,665,359,570,190,781,591,457,362,677,349,420,787,706,625,407,312,245,652,598,571,191,544,410,220,363,336,897,802,707,612,422,789,232,681,599,465,370,654,573,411,316,249,602,222,365,660,803,423,776,709,614,452,371,655,560,426,344,793,236,603,413,318,223,128,689,662,805,615,481,834,454,427,373,780,713,618,400,319,238,605,676,348,663,568,434,244,835,455,666,360,809,619,429,782,239,592,458,377,678,350,435,788,721,626,408,246,667,837,572,192,783,621,459,364,679,351,898,817,708,627,437,790,247,682,600,466,669,574,412,250,841,461,366,899,804,737,424,791,710,683,629,467,372,656,575,441,794,251,604,414,224,367,690,901,806,711,616,482,849,685,469,428,374,795,714,633,415,320,253,606,691,664,807,483,836,456,905,375,810,715,620,430,797,240,607,473,378,693,436,722,865,485,668,838,811,431,784,717,622,460,379,680,352,913,818,723,628,438,248,697,839,670,813,623,489,842,462,381,900,819,738,439,792,725,684,630,468,671,576,442,252,843,463,368,929,739,902,821,712,631,497,850,686,470,443,796,729,634,416,254,845,692,903,808,741,484,851,687,471,906,376,825,716,635,445,798,255,608,474,694,961,866,486,907,853,812,745,432,799,718,637,475,380,695,914,724,867,487,698,840,909,814,719,624,490,857,477,382,915,820,753,440,726,699,869,672,815,491,844,464,383,930,740,917,822,727,632,498,701,444,730,873,493,846,931,904,823,742,499,852,688,472,921,826,731,636,446,256,847,933,743,962,881,501,908,854,827,746,447,800,733,638,476,696,963,868,488,937,855,747,910,829,720,639,505,858,478,916,754,965,700,870,911,816,749,492,859,479,384,945,755,918,728,871,702,969,874,494,861,932,919,824,757,500,703,922,732,875,495,848,934,744,977,882,502,923,828,761,448,734,877,935,964,883,503,938,856,748,925,830,735,640,506,993,966,939,885,912,831,750,507,860,480,946,756,967,872,941,751,970,889,509,862,947,920,758,704,971,876,496,863,949,759,978,924,762,973,878,936,979,884,504,953,763,926,736,879,994,981,940,886,927,832,765,508,995,968,887,942,752,985,890,510,948,997,943,972,891,511,864,950,760,1001,974,893,951,980,954,764,975,880,1009,982,955,928,766,996,983,88 8,957,767,986,998,944,987,892,512,999,1002,989,894,952,1003,976,895,1010,956,1005,1011,984,958,768,1013,959,988,1000,1017,990,1004,991,896,1006,1012,1007,1014,960,1015,1018,1019,992,1021,1008,1016,1020,1022,1023,1024；
(8)N＝2048，第一极化权重向量为：
1,2,3,5,9,17,4,33,6,7,10,65,11,18,13,19,129,34,21,35,8,25,37,66,12,257,67,41,14,20,69,15,130,49,22,73,131,36,23,26,513,133,38,81,27,39,258,68,137,42,29,259,97,70,43,16,145,50,261,71,45,74,132,51,24,1025,265,75,161,514,134,53,82,28,77,515,135,40,273,83,138,57,30,517,260,193,98,139,85,44,31,146,289,99,262,72,521,141,46,89,147,52,263,101,1026,47,266,76,162,529,149,54,321,1027,267,105,78,163,516,136,55,274,84,153,58,1029,269,79,545,165,518,275,194,113,140,86,59,32,1033,519,385,290,195,100,277,169,87,522,142,61,90,148,291,577,264,197,102,523,143,1041,48,281,91,177,530,150,293,103,322,1028,525,268,201,106,93,164,531,151,56,323,1057,154,297,1030,107,270,80,641,546,166,533,276,209,114,155,325,60,1031,271,109,547,1034,167,520,386,305,196,115,278,170,88,537,157,62,1089,329,1035,549,387,292,225,578,279,198,171,117,524,144,1042,63,282,92,178,1037,769,579,389,294,199,104,553,337,173,1043,526,283,202,121,94,179,532,152,295,581,324,1153,1058,527,393,298,203,1045,108,285,95,642,561,181,534,210,353,1059,156,326,299,1032,585,272,205,110,643,548,1049,168,535,401,306,211,116,185,327,538,1061,158,301,1090,111,330,1036,645,550,388,307,226,593,280,213,172,118,539,159,1281,64,1091,331,1065,551,417,1038,770,227,580,390,309,200,649,119,554,338,174,1044,541,284,217,122,1093,333,180,1039,771,609,391,296,229,582,555,339,1154,175,1073,528,394,313,204,1046,123,286,96,657,562,182,1097,773,583,449,354,1155,1060,557,395,341,300,233,1047,586,287,206,125,644,563,1050,183,536,402,212,355,1537,186,328,1157,777,1062,587,397,302,207,1105,112,673,345,1051,646,565,403,308,241,594,214,187,357,540,1063,160,1282,303,1092,589,332,1161,1066,647,552,418,1053,785,228,595,405,310,215,650,120,569,189,1283,542,1121,218,361,1094,1067,334,419,1040,772,705,610,392,311,230,651,597,556,340,1169,176,1074,543,409,314,219,1285,124,1095,335,658,1069,801,611,421,1098,774,231,584,450,369,1156,653,1075,558,396,342,315,234,1048,601,288,221,126,659,564,1289,184,1099,775,613,451,356,1185,1538,559,425,343,1158,778,235,1077,588,398,317,208,1106,127,674,346,1052,661,566,404,242,1101,833,1539,453,188,358,1159,779,1064,617,399,1297,304,237,1107,590,675,347,1162,1081,648,567,433,1054,786,243,596,406,216,665,359,570,1541,190,1284,1217,781,1122,591,457,362,1163,1109,1068,677,349,420,1055,787,706,625,407,312,245,652,598,571,1170,191,1313,544,410,1123,220,1286,363,1096,1545,336,1165,897,1070,802,707,612,422,1113,789,232,681,599,465,370,1171,654,1076,573,411,316,249,1287,602,1125,222,365,660,1071,803,1290,423,1100,776,709,614,452,371,1186,655,1553,560,426,344,1173,793,236,1078,603,413,318,223,1345,128,689,1291,662,1129,805,615,481,1102,834,1187,1540,454,427,373,1160,780,713,1079,618,400,1298,319,238,1108,605,676,348,1177,1082,663,568,434,1293,244,1103,835,1569,455,666,360,1189,809,1542,619,429,1299,1218,782,239,1137,592,458,377,1164,1110,1083,678,350,435,1056,788,721,626,408,246,667,837,572,1543,1409,192,1314,1219,783,1124,621,459,1301,364,1193,1111,1546,679,351,1166,898,1085,817,708,627,437,1114,790,247,682,600,466,1172,669,1315,574,412,1601,250,1288,1221,841,1126,1547,461,366,1167,899,1072,804,737,1305,424,1115,791,710,683,629,467,372,1201,656,1554,575,441,1174,794,251,1317,604,414,1127,224,1346,367,690,1549,1292,1225,901,1130,806,711,616,482,1117,849,1188,685,1555,469,428,374,1175,795,714,1080,633,415,320,253,1347,606,691,1178,1321,664,1131,807,1294,483,1104,836,1665,1570,456,905,375,1190,810,715,1557,620,430,1300,1233,797,240,1138,607,473,378,1179,1349,1084,693,436,1295,722,1133,865,1571,485,668,838,1191,811,1544,1410,431,1329,1220,784,717,1139,622,460,1302,379,1194,1112,1561,680,352,1181,913,1086,818,723,628,438,1353,248,697,839,1573,1411,670,1316,1249,813,1602,623,489,1303,1222,842,1195,1141,1548,462,381,1168,900,1087,819,738,1306,439,1116,792,725,684,630,468,1202,671,1793,576,442,1603,1413,252,1318,1223,843,1128,1577,463,1361,368,1197,929,1550,739,1307,1226,902,1145,821,712,631,497,1118,850,1203,686,1556,470,443,1176,796,729,1319,634,416,1605,254,1348,845,692,1551,1417,1322,1227,903,1132,808,741,1309,484,1119,851,1666,687,1585,471,906,376,1205,825,716,1558,635,445,1234,798,255,1377,608,474,1180,1350,1323,694,1609,1296,1229,961,1134,866,1667,1572,486,907,853,1192,812,745,1559,1425,432,1330,1235,799,718,1140,637,475,380,1209,1351,1562,695,1182,914,1325,724,1135,867,1354,487,698,840,1669,1574,1412,909,1331,1250,814,719,1617,624,490,1304,1237,857,1196,1142,1563,477,382,1183,915,1088,820,753,440,1355,726,699,869,1575,1441,672,1794,1251,815,1604,1414,491,1333,1224,844,1673,1143,1578,464,1362,383,1198,930,1565,740,1308,1241,917,1146,822,727,632,498,1357,1204,701,1795,444,1633,1415,730,1320,1253,873,1606,1579,493,1363,846,1199,931,1552,1418,1337,1228,904,1147,823,742,1310,499,1120,852,1681,688,1586,472,921,1206,826,731,1797,636,446,1607,1473,256,1378,847,1581,1419,1365,1324,1257,933,1610,743,1311,1230,962,1149,881,1668,1587,501,908,854,1207,827,746,1560,1426,447,1236,800,733,1379,638,476,1210,1352,1801,696,1611,1421,1326,1231,963,1136,868,1697,1369,488,937,855,1670,747,1589,1427,910,1332,1265,829,720,1618,639,505,1238,858,1211,1381,1564,478,1184,916, 1327,754,1613,1356,965,700,870,1671,1576,1442,911,1809,1252,816,749,1619,1429,492,1334,1239,859,1674,1144,1593,479,384,1213,945,1566,755,1242,918,1385,728,871,1358,1443,702,1796,1729,1634,1416,969,1335,1254,874,1675,1621,1580,494,1364,861,1200,932,1567,1433,1338,1243,919,1148,824,757,500,1359,1682,703,1825,922,1635,1445,732,1798,1255,875,1608,1474,495,1393,848,1677,1582,1420,1366,1339,1258,934,1625,744,1312,1245,977,1150,882,1683,1588,502,923,1208,828,761,1799,448,1637,1475,734,1380,877,1583,1449,1367,1802,1259,935,1612,1422,1341,1232,964,1151,883,1698,1370,503,938,856,1685,748,1590,1428,925,1266,830,735,1857,640,506,1477,1212,1382,1803,1641,1423,1328,1261,993,1614,1699,1371,966,939,885,1672,1591,1457,912,1810,1267,831,750,1620,1430,507,1240,860,1689,1383,1594,480,1214,946,1805,756,1615,1481,1386,967,872,1701,1373,1444,941,1811,1730,751,1649,1431,970,1336,1269,889,1676,1622,1595,509,862,1215,947,1568,1434,1244,920,1387,758,1360,1921,704,1826,1731,1636,1446,971,1813,1256,876,1705,1623,1489,496,1394,863,1678,1597,1435,1340,1273,949,1626,759,1246,978,1389,1684,1827,924,1447,762,1800,1733,1638,1476,973,1395,878,1679,1584,1450,1368,1817,1260,936,1627,1437,1342,1247,979,1152,884,1713,504,953,1686,763,1829,926,1639,1505,736,1858,879,1478,1451,1397,1804,1737,1642,1424,1343,1262,994,1629,1700,1372,981,940,886,1687,1592,1458,927,1268,832,765,1859,508,1479,1690,1384,1833,1643,1453,1806,1263,995,1616,1482,1401,968,887,1702,1374,1459,942,1812,1745,752,1650,1432,985,1270,890,1691,1861,1596,510,1216,948,1807,1645,1483,1388,997,1703,1375,1922,943,1841,1732,1651,1461,972,1814,1271,891,1706,1624,1490,511,864,1693,1598,1436,1274,950,1865,760,1485,1390,1923,1828,1761,1448,1001,1815,1734,1707,1653,1491,974,1396,893,1680,1599,1465,1818,1275,951,1628,1438,1248,980,1391,1714,954,1925,764,1830,1735,1640,1506,975,1873,880,1709,1493,1452,1398,1819,1738,1657,1439,1344,1277,1009,1630,1715,982,955,1688,1831,928,1507,766,1860,1480,1929,1399,1834,1739,1644,1454,1821,1264,996,1631,1497,1402,983,888,1717,1460,957,1746,767,1889,986,1509,1692,1862,1835,1455,1808,1741,1646,1484,1403,998,1704,1376,1937,944,1842,1747,1652,1462,987,1272,892,1721,1863,512,1694,1837,1647,1513,1866,999,1486,1405,1924,1843,1762,1463,1002,1816,1749,1708,1654,1492,989,894,1695,1600,1466,1276,952,1867,1487,1392,1953,1763,1926,1003,1845,1736,1655,1521,976,1874,895,1710,1494,1467,1820,1753,1658,1440,1278,1010,1869,1716,956,1927,1832,1765,1508,1005,1875,1711,1495,1930,1400,1849,1740,1659,1469,1822,1279,1011,1632,1498,984,1718,958,1985,768,1890,1510,1931,1877,1836,1769,1456,1823,1742,1661,1499,1404,1013,1719,1938,959,1748,1891,988,1511,1722,1864,1933,1838,1743,1648,1514,1881,1000,1501,1406,1939,1844,1777,1464,1017,1750,1723,1893,990,1696,1839,1515,1868,1488,1407,1954,1764,1941,1004,1846,1751,1656,1522,991,896,1725,1468,1754,1897,1517,1870,1955,1928,1847,1766,1523,1006,1876,1712,1496,1945,1850,1755,1660,1470,1280,1012,1871,1957,1767,1986,1007,1905,1525,1932,1878,1851,1770,1471,1824,1757,1662,1500,1014,1720,960,1987,1892,1512,1961,1879,1771,1934,1853,1744,1663,1529,1882,1015,1502,1940,1778,1018,1989,1724,1894,1935,1840,1773,1516,1883,1503,1408,1969,1779,1942,1019,1752,1895,992,1726,1993,1898,1518,1885,1956,1943,1848,1781,1524,1021,1727,1946,1756,1899,1519,1872,1958,1768,2001,1008,1906,1526,1947,1852,1785,1472,1758,1901,1959,1988,1907,1527,1962,1880,1772,1949,1854,1759,1664,1530,1016,2017,1990,1963,1909,1936,1855,1774,1531,1884,1504,1970,1780,1020,1991,1896,1965,1775,1994,1913,1533,1886,1971,1944,1782,1022,1728,1995,1900,1520,1887,1973,1783,2002,1023,1948,1786,1997,1902,1960,2003,1908,1528,1977,1787,1950,1760,1903,2018,2005,1964,1910,1951,1856,1789,1532,2019,1992,1911,1966,1776,2009,1914,1534,1972,2021,1967,1996,1915,1535,1888,1974,1784,1024,2025,1998,1917,1975,2004,1978,1788,1999,1904,2033,2006,1979,1952,1790,2020,2007,1912,1981,1791,2010,2022,1968,2011,1916,1536,2023,2026,2013,1918,1976,2027,2000,1919,2034,1980,2029,2035,2008,1982,1792,2037,1983,2012,2024,2041,2014,2028,2015,1920,2030,2036,2031,2038,1984,2039,2042,2043,2016,2045,2032,2040,2044,2046,2047,2048；
(9)N＝4096，第一极化权重向量为：
1,2,3,5,9,17,4,33,6,7,10,65,11,18,13,19,129,34,21,35,8,25,37,66,12,257,67,41,14,20,69,15,130,49,22,73,131,36,23,26,513,133,38,81,27,39,258,68,137,42,29,259,97,70,43,16,145,50,261,71,45,74,132,51,24,1025,265,75,161,514,134,53,82,28,77,515,135,40,273,83,138,57,30,517,260,193,98,139,85,44,31,146,289,99,262,72,521,141,46,89,147,52,263,101,1026,47,266,76,2049,162,529,149,54,321,1027,267,105,78,163,516,136,55,274,84,153,58,1029,269,79,545,165,518,275,194,113,140,86,59,32,1033,519,385,290,195,100,277,169,87,522,142,61,90,148,291,577,264,197,102,523,143,1041,48,281,91,2050,177,530,150,293,103,322,1028,525,268,201,106,2051,93,164,531,151,56,323,1057,154,297,1030,107,270,80,641,546,2053,166,533,276,209,114,155,325,60,1031,271,109,547,1034,167,520,386,305,196,115,2057,278,170,88,537,157,62,1089,329,1035,549,387,292,225,578,279,198,171,117,524,144,1042,63,282,92,2065,178,1037,769,579,389,294,199,104,553,337,173,1043,526,283,202,121,2052,94,179,532,152,295,581,324,1153,1058,527,393,298,203,1045,108,285,2081,95,642,561,2054,181,534,210,353,1059,156,326,299,1032,585,272,205,110,643,548,2055,1049,168,535,401,306,211,116,2058,185,327,538, 1061,158,301,1090,111,330,1036,645,550,388,2113,307,226,593,2059,280,213,172,118,539,159,1281,64,1091,331,1065,2066,551,417,1038,770,227,580,390,309,200,649,119,554,2061,338,174,1044,541,284,217,122,1093,2067,333,180,1039,771,609,391,296,229,582,555,339,1154,175,1073,528,394,313,204,1046,123,2177,286,2082,96,657,562,2069,182,1097,773,583,449,354,1155,1060,557,395,341,300,233,1047,586,287,206,2083,125,644,563,2056,1050,183,536,402,212,355,2073,1537,186,328,1157,777,1062,587,397,302,207,1105,112,673,345,2085,1051,646,565,403,2114,308,241,594,2060,214,187,357,540,1063,160,1282,303,1092,589,332,1161,1066,647,2305,552,418,2115,1053,785,228,595,405,2089,310,215,650,120,569,2062,189,1283,542,1121,218,361,1094,1067,2068,334,419,1040,772,705,610,392,2117,311,230,651,597,556,2063,340,1169,176,1074,543,409,314,219,1285,124,1095,2178,2097,335,658,1069,801,2070,611,421,1098,774,231,584,450,369,1156,653,1075,558,396,2121,342,315,234,1048,601,2179,288,221,2084,126,659,564,2071,1289,184,1099,775,613,451,356,1185,2074,1538,559,425,343,1158,778,235,1077,588,398,317,208,2561,1106,127,674,2181,346,2086,1052,661,566,404,2129,242,1101,833,2075,1539,453,188,358,1159,779,1064,617,399,1297,304,237,1107,590,675,347,1162,2087,1081,648,2306,567,433,2116,1054,786,243,2185,596,406,2090,216,665,359,570,2077,1541,190,1284,1217,781,1122,591,457,362,1163,1109,1068,677,2307,349,420,2145,1055,787,706,625,407,2118,2091,312,245,652,598,571,2064,1170,191,1313,544,410,1123,220,1286,363,1096,2193,1545,2098,336,1165,897,1070,802,707,2309,612,422,2119,1113,789,232,681,599,465,2093,370,1171,654,1076,573,411,2122,316,249,1287,602,1125,2180,222,2099,365,660,1071,803,2072,1290,423,1100,776,709,614,452,3073,371,1186,655,2313,1553,560,426,2123,344,1173,793,236,1078,603,413,2209,318,223,2562,1345,128,689,2182,2101,1291,662,1129,805,2130,615,481,1102,834,1187,2076,1540,454,427,373,1160,780,713,1079,618,400,2125,1298,319,238,2563,1108,605,676,2183,348,1177,2088,1082,663,2321,568,434,2131,1293,244,1103,2186,835,2105,1569,455,666,360,1189,809,2078,1542,619,429,1299,1218,782,239,1137,592,458,377,1164,2565,1110,1083,678,2308,2241,350,435,2146,1056,788,721,2187,626,408,2133,2092,246,667,837,572,2079,1543,1409,192,1314,1219,783,1124,621,459,1301,364,1193,1111,2194,1546,679,2337,351,1166,898,2147,1085,817,708,2310,627,437,2120,2569,1114,790,247,682,2189,600,466,2094,1172,669,1315,574,412,2137,1601,250,1288,1221,841,1126,2195,1547,461,2100,366,1167,899,1072,804,737,2311,1305,424,2149,1115,791,710,683,629,467,3074,2095,372,1201,656,2314,1554,575,441,2124,1174,794,251,1317,604,414,1127,2210,224,2577,1346,367,690,2197,1549,2102,1292,1225,901,1130,806,711,2369,616,482,3075,1117,849,1188,685,2315,1555,469,428,2153,374,1175,795,714,1080,633,415,2126,2211,320,253,2564,1347,606,691,2184,1178,2103,1321,664,2322,1131,807,2132,1294,483,1104,2201,836,1665,2106,1570,456,3077,905,375,1190,810,715,2317,1557,620,430,2127,1300,1233,797,240,2593,1138,607,473,2213,378,1179,2566,1349,1084,693,2323,2242,436,2161,1295,722,1133,2188,865,2134,2107,1571,485,668,838,1191,811,2080,1544,1410,431,1329,1220,784,717,1139,622,460,3081,1302,379,1194,2567,1112,2433,1561,680,2338,2243,352,1181,913,2148,1086,818,723,2325,2217,628,438,2135,2570,1353,248,697,2190,839,2109,1573,1411,670,1316,1249,813,2138,1602,623,489,1303,1222,842,1195,1141,2196,1548,462,2339,381,1168,900,2625,1087,819,738,2312,2245,1306,439,2150,2571,1116,792,725,684,2191,630,468,3089,2096,1202,671,2329,1793,576,442,2139,1603,1413,252,1318,1223,843,1128,2225,1577,463,2578,1361,368,1197,929,2198,1550,739,2341,1307,1226,902,2151,1145,821,712,2370,631,497,3076,2573,1118,850,1203,686,2316,2249,1556,470,443,2154,1176,796,729,1319,634,416,2141,1605,2212,254,2579,1348,845,692,2199,1551,1417,2104,1322,1227,903,1132,808,741,2371,1309,484,3105,1119,2202,851,1666,687,2345,1585,471,3078,906,2155,376,1205,825,716,2318,1558,635,445,2128,2689,1234,798,255,2594,1377,608,474,2214,1180,2581,1350,1323,694,2324,2257,1609,2162,1296,1229,961,1134,2203,866,1667,2373,2108,1572,486,3079,907,853,1192,812,745,2319,1559,1425,432,2157,1330,1235,799,718,2595,1140,637,475,3082,2215,380,1209,2568,1351,2434,1562,695,2353,2244,1182,914,2163,1325,724,2326,1135,2218,867,2136,2585,1354,487,698,2205,840,1669,2110,1574,1412,3137,909,1331,1250,814,719,2377,1617,624,490,3083,1304,1237,857,1196,2597,1142,2435,1563,477,2340,2273,382,1183,915,2626,1088,820,753,2327,2246,2219,440,2165,2572,1355,726,699,2192,869,3090,2111,1575,1441,672,2330,1794,1251,815,2140,1604,1414,491,1333,1224,844,1673,1143,2226,1578,464,3085,2817,1362,383,1198,930,2627,2437,1565,740,2342,2247,1308,1241,917,2152,2601,1146,822,727,2385,2221,632,498,3091,2574,1357,1204,701,2331,2250,1795,444,2169,1633,1415,730,1320,1253,873,2142,1606,2227,1579,493,2580,1363,846,1199,931,2200,1552,1418,2343,1337,1228,904,2629,1147,823,742,2372,3201,1310,499,3106,2575,1120,2441,852,1681,688,2346,2251,1586,472,3093,921,2156,1206,826,731,2333,1797,636,446,2143,1607,2690,1473,256,2609,1378,847,2229,1581,1419,2582,1365,1324,1257,933,2258,1610,743,2401,1311,1230,962,3107,1149,2204,881,1668,2374,2347,1587,501,3080,908,2633,854,1207,827,746,2320,2253,1560,1426,447,2158,2691,1236,800,733,2596,1379,638,476,3097,2216,1210,2583,1352,2449,1801,696,2354,2259,1611,1421,2164,1326,1231,963,1136,2233,868,1697,2375,2586,1369,488,3109,937,2206,855,1670,747,2349,1589,1427,3138,910,2159,1332,1265,829,720,2378,1618,639,505,3084,2693,1238,8 58,1211,2598,1381,2436,1564,478,2355,2274,1184,916,2641,1327,754,2328,2261,1613,2220,2166,2587,1356,965,700,2207,870,1671,3329,2112,1576,1442,3139,911,1809,1252,816,749,2379,1619,1429,492,3113,1334,1239,859,1674,2599,1144,2465,1593,479,3086,2818,2275,384,1213,945,2628,2438,1566,755,2357,2248,2697,1242,918,2167,2602,1385,728,2386,2222,871,3092,2589,1358,1443,702,2332,2265,1796,1729,2170,1634,1416,3141,969,1335,1254,874,1675,2381,1621,2228,1580,494,3087,2819,1364,861,1200,932,2657,2439,1567,1433,2344,2277,1338,1243,919,2630,2603,1148,824,757,2387,3202,2223,500,3121,2576,1359,2442,1682,703,2361,2252,1825,3094,922,2171,1635,1445,732,2334,1798,1255,875,2144,1608,2705,1474,495,2610,1393,848,1677,2230,1582,1420,3145,2821,1366,1339,1258,934,2631,2497,1625,744,2402,3203,1312,1245,977,3108,2605,1150,2443,882,1683,2389,2348,2281,1588,502,3095,923,2634,1208,828,761,2335,2254,1799,448,2173,1637,2692,1475,734,2611,1380,877,3098,2231,1583,1449,2584,1367,2450,1802,1259,935,2260,1612,1422,2403,1341,1232,964,3585,1151,2234,883,1698,2376,3205,2825,1370,503,3110,938,2635,2445,856,1685,748,2350,2255,1590,1428,3153,925,2160,2721,1266,830,735,2393,1857,640,506,3099,2694,1477,1212,2613,1382,2451,1803,2356,2289,1641,1423,2642,1328,1261,993,2262,1614,2235,1699,2405,2588,1371,966,3111,939,2208,885,1672,3330,2351,1591,1457,3140,912,2637,1810,1267,831,750,2380,3209,1620,1430,507,3114,2695,1240,860,1689,2600,1383,2466,1594,480,3101,2833,2276,1214,946,2643,2453,1805,756,2358,2263,1615,2698,1481,2168,2617,1386,967,2237,872,1701,3331,2590,1373,1444,3169,941,2266,1811,1730,751,2409,1649,1431,3142,970,3115,1336,1269,889,1676,2382,1622,2467,1595,509,3088,2820,2753,862,1215,947,2658,2440,1568,1434,2359,2278,2699,1244,920,2645,2604,1387,758,2388,3217,2224,3122,2591,1360,2457,1921,704,2362,2267,1826,1731,3333,2172,1636,1446,3143,971,1813,1256,876,1705,2383,1623,2706,1489,496,3117,2849,1394,863,1678,2659,2469,1597,1435,3146,2822,2279,1340,1273,949,2632,2498,1626,759,2417,3204,2701,1246,978,3123,2606,1389,2444,1684,2390,2363,2282,1827,3096,924,2649,1447,762,2336,2269,1800,1733,2174,1638,2707,1476,973,2612,1395,878,1679,3337,2232,1584,1450,3147,2823,1368,1817,1260,936,2661,2499,1627,1437,2404,3233,1342,1247,979,3586,2607,1152,2473,884,1713,2391,3206,2826,2283,504,3125,953,2636,2446,1686,763,2365,2256,1829,3154,926,2175,1639,2722,1505,736,2394,1858,879,3100,2709,1478,1451,2614,1397,2452,1804,1737,2290,1642,1424,3149,2881,1343,1262,994,3587,2501,1629,2236,1700,2406,3207,2827,1372,981,3112,940,2665,2447,886,1687,3345,2352,2285,1592,1458,3155,927,2638,2723,1268,832,765,2395,3210,1859,508,3129,2696,1479,1690,2615,1384,2481,1833,3102,2834,2291,1643,1453,2644,2454,1806,1263,995,2264,1616,2713,1482,2407,2618,1401,968,3589,2238,887,1702,3332,3265,2829,1374,1459,3170,942,2639,2505,1812,1745,752,2410,3211,1650,1432,3157,985,3116,2725,1270,890,1691,2397,1861,2468,1596,510,3103,2835,2754,1216,948,2673,2455,1807,2360,2293,1645,2700,1483,2646,2619,1388,997,3218,2239,1703,3361,2592,1375,2458,1922,3171,943,2268,1841,1732,3334,2411,1651,1461,3144,972,3593,1814,1271,891,1706,2384,3213,1624,2945,1490,511,3118,2850,2755,864,1693,2660,2470,1598,1436,3161,2837,2280,2729,1274,950,2647,2513,1865,760,2418,3219,2702,1485,3124,2621,1390,2459,1923,2364,2297,1828,1761,3335,2650,1448,3173,1001,2270,1815,1734,1707,2413,1653,2708,1491,974,3119,2851,1396,893,1680,3338,2471,1599,1465,3148,2824,2757,1818,1275,951,2662,2500,1628,1438,2419,3234,2703,1248,980,3601,2608,1391,2474,1714,2392,3221,2841,2284,3126,954,2651,2461,1925,764,2366,2271,1830,1735,3393,2176,1640,2737,1506,975,1873,880,1709,3339,2710,1493,1452,3177,2853,1398,1819,1738,2663,2529,1657,1439,3150,2882,3235,1344,1277,1009,3588,2502,1630,2475,1715,2421,3208,2828,2761,982,3127,955,2666,2448,1688,3346,2367,2286,1831,3156,928,2653,2724,1507,766,2396,3225,1860,3130,2711,1480,1929,2616,1399,2482,1834,1739,3341,2292,1644,1454,3151,2883,1821,1264,996,3617,2503,1631,2714,1497,2408,3237,2857,1402,983,3590,2667,2477,888,1717,3347,3266,2830,2287,1460,3185,957,2640,2506,1746,767,2425,3212,1889,3158,986,3131,2726,1509,1692,2398,1862,2483,1835,3104,2836,2769,1455,2674,2456,1808,1741,2294,1646,2715,1484,2885,2620,1403,998,3591,3457,2240,1704,3362,3267,2831,1376,1937,3172,944,2669,2507,1842,1747,3349,2412,3241,1652,1462,3159,987,3594,2727,1272,892,1721,2399,3214,1863,2946,512,3133,2865,2756,1694,2675,2485,1837,3162,2838,2295,1647,2730,1513,2648,2514,1866,999,3220,2717,1486,3363,2622,1405,2460,1924,3649,2298,1843,1762,3336,3269,2889,1463,3174,1002,3595,2509,1816,1749,1708,2414,3215,1654,2947,1492,989,3120,2852,2785,894,1695,3353,2472,1600,1466,3163,2839,2758,2731,1276,952,2677,2515,1867,2420,3249,2704,1487,3602,2623,1392,2489,1953,3222,2842,2299,1763,3365,2652,2462,1926,3175,1003,2272,1845,1736,3394,2415,1655,2738,1521,976,3597,1874,895,1710,3340,3273,2949,1494,1467,3178,2854,2759,1820,1753,2664,2530,1658,1440,3165,2897,3236,2733,1278,1010,3603,2517,1869,2476,1716,2422,3223,2843,2762,3128,956,2681,2463,1927,2368,2301,1832,1765,3395,2654,2739,1508,1005,3226,1875,1711,3369,2712,1495,1930,3179,2855,1400,1849,1740,3342,2531,1659,1469,3152,2884,3713,1822,1279,1011,3618,2504,1632,2953,1498,2423,3238,2858,2763,984,3605,2668,2478,1718,3348,3281,2845,2288,3186,958,2655,2521,1985,768,2426,3227,1890,3397,3132,2741,1510,1931,1877,2484,1836,1769,3343,2770,1456,3181,2913,1823,1742,3619,2533 ,1661,2716,1499,2886,3239,2859,1404,1013,3592,3458,2479,1719,3377,3268,2832,2765,1938,3187,959,2670,2508,1748,3350,2427,3242,1891,3160,988,3609,2728,1511,1722,2400,3229,1864,2961,3134,2866,2771,1933,2676,2486,1838,1743,3401,2296,1648,2745,1514,2887,1881,1000,3621,3459,2718,1501,3364,3297,2861,1406,1939,3650,2671,2537,1844,1777,3351,3270,2890,3243,1464,3189,1017,3596,2510,1750,1723,2429,3216,1893,2948,990,3135,2867,2786,1696,3354,2487,1839,3164,2840,2773,2732,1515,2678,2516,1868,3250,2719,1488,3841,2624,1407,2490,1954,3651,3461,2300,1764,3366,3271,2891,1941,3176,1004,3625,2511,1846,1751,3409,2416,3245,1656,2977,1522,991,3598,2787,896,1725,3355,3274,2950,1468,3193,2869,2760,1754,2679,2545,1897,3166,2898,3251,2734,1517,3604,2518,1870,2491,1955,3224,2844,2777,3367,2682,2464,1928,3653,2302,1847,1766,3396,2893,2740,1523,1006,3599,3465,1876,1712,3370,3275,2951,1496,1945,3180,2856,2789,1850,1755,3357,2532,1660,1470,3167,2899,3714,2735,1280,1012,3633,2519,1871,2954,2424,3253,2873,2764,3606,2683,2493,1957,3282,2846,2303,1767,3425,2656,2522,1986,1007,3228,1905,3398,3371,2742,1525,1932,3657,1878,1851,1770,3344,3277,3009,1471,3182,2914,3715,1824,1757,3620,2534,1662,2955,1500,2901,3240,2860,2793,1014,3607,3473,2480,1720,3378,3283,2847,2766,3188,960,2685,2523,1987,2428,3257,1892,3399,3610,2743,1512,1961,3230,1879,2962,1771,3373,2772,1934,3183,2915,1853,1744,3402,2535,1663,2746,1529,2888,3717,1882,1015,3622,3460,2957,1502,3379,3298,2862,2767,1940,3665,2672,2538,1778,3352,3285,2905,3244,3190,1018,3611,2525,1989,1724,2430,3231,1894,2963,3136,2868,2801,1935,2488,1840,1773,3403,2774,2747,1516,2917,1883,3623,3489,2720,1503,3842,3299,2863,1408,1969,3652,3462,2539,1779,3381,3272,2892,3721,1942,3191,1019,3626,2512,1752,3410,2431,3246,1895,2978,992,3613,2788,1726,3356,3289,2965,3194,2870,2775,1993,2680,2546,1898,3405,3252,2749,1518,3843,1885,2492,1956,3681,3463,2778,3368,3301,2921,1943,3654,3627,2541,1848,1781,3411,2894,3247,2979,1524,1021,3600,3466,1727,3385,3276,2952,1946,3195,2871,2790,1756,3358,2547,1899,3168,2900,3729,2736,1519,3634,2520,1872,2969,3254,2874,2779,3845,2684,2494,1958,3655,3521,2304,1768,3426,2895,2001,1008,3629,3467,1906,3413,3372,3305,2981,1526,1947,3658,2791,1852,1785,3359,3278,3010,1472,3197,2929,3716,1758,3635,2549,1901,2956,2902,3255,2875,2794,3608,3474,2495,1959,3284,2848,2781,3427,2686,2524,1988,3258,1907,3400,3849,2744,1527,1962,3659,3469,1880,1772,3374,3279,3011,1949,3184,2916,3745,1854,1759,3417,2536,1664,2985,1530,2903,3718,2795,1016,3637,3475,2958,3380,3313,2877,2768,3666,2687,2553,2017,3286,2906,3259,3429,3612,2526,1990,1963,3232,1909,2964,3375,2802,1936,3661,1855,1774,3404,3013,2748,1531,2918,3719,1884,3624,3490,2959,1504,3857,3300,2864,2797,1970,3667,3477,2540,1780,3382,3287,2907,3722,3192,1020,3641,2527,1991,2432,3261,1896,2993,3614,2803,1965,3290,2966,1775,3433,2776,1994,2919,1913,3406,3491,2750,1533,3844,3777,1886,1971,3682,3464,3017,3383,3302,2922,3723,1944,3669,3628,2542,1782,3412,2909,3248,2980,1022,3615,3481,1728,3386,3291,2967,3196,2872,2805,1995,2548,1900,3407,3730,2751,1520,3873,1887,2970,3683,3493,2780,3846,3303,2923,1973,3656,3522,2543,1783,3441,2896,3725,2002,1023,3630,3468,3414,3387,3306,2982,1948,3673,2792,1786,3360,3293,3025,3198,2930,3731,1997,3636,2550,1902,2971,3256,2876,2809,3847,2496,1960,3685,3523,2782,3428,2925,2003,3631,3497,1908,3415,3850,3307,2983,1528,1977,3660,3470,1787,3389,3280,3012,1950,3199,2931,3746,1760,3418,2551,1903,2986,2904,3733,2796,3638,3476,2973,3314,2878,2783,3905,2688,2554,2018,3525,3260,3430,3851,2005,1964,3689,3471,1910,3376,3309,3041,1951,3662,3747,1856,1789,3419,3014,2987,1532,2933,3720,3639,3505,2960,3858,3315,2879,2798,3668,3478,2555,2019,3288,2908,3737,3431,3642,2528,1992,3262,1911,2994,3853,2804,1966,3663,3529,1776,3434,3015,2009,2920,3749,1914,3421,3492,2989,1534,3859,3778,2799,1972,3697,3479,3018,3384,3317,2937,3724,3670,3643,2557,2021,2910,3263,2995,3616,3482,1967,3292,2968,3435,2806,1996,1915,3408,3969,2752,1535,3874,3779,1888,3684,3494,3019,3861,3304,2924,3753,1974,3671,3537,2544,1784,3442,2911,3726,1024,3645,3483,3388,3321,2997,3674,2807,2025,3294,3026,3437,3732,1998,3875,1917,2972,3495,2810,3848,3781,1975,3686,3524,3021,3443,2926,3727,2004,3632,3498,3416,3865,3308,2984,1978,3675,3485,1788,3390,3295,3027,3200,2932,3761,1999,2552,1904,3001,3734,2811,3877,2974,3687,3553,2784,3906,2927,2033,3526,3499,3445,3852,3785,2006,1979,3690,3472,3391,3310,3042,1952,3677,3748,1790,3420,3029,2988,2934,3735,3640,3506,2975,3316,2880,2813,3907,2556,2020,3527,3738,3432,3881,2007,3691,3501,1912,3854,3311,3043,1981,3664,3530,1791,3449,3016,2010,2935,3750,3422,3507,2990,3860,3793,2800,3698,3480,3033,3318,2938,3739,3909,3644,2558,2022,3264,2996,3855,1968,3693,3531,3436,3045,2011,3751,1916,3423,3970,2991,1536,3889,3780,3699,3509,3020,3862,3319,2939,3754,3672,3538,2559,2023,2912,3741,3646,3484,3322,2998,3913,2808,2026,3533,3438,3971,2013,3876,3809,1918,3496,3049,3863,3782,3755,1976,3701,3539,3022,3444,2941,3728,3647,3513,3866,3323,2999,3676,3486,2027,3296,3028,3439,3762,2000,1919,3002,3973,2812,3878,3783,3688,3554,3023,3921,2928,3757,2034,3541,3500,3446,3867,3786,1980,3705,3487,3392,3325,3057,3678,3763,2029,3030,3003,3736,3879,2976,3555,2814,3908,2035,3528,3977,3447,3882,3787,2008,3692,3502,3869,3312,3044,1982,3679,3545,1792,3450,3031,2936,3765,3508,3005,3794,2815,3937,3034,3557,3740,3910,3883,20 37,3503,3856,3789,1983,3694,3532,3451,3046,2012,3752,3424,3985,2992,3890,3795,3700,3510,3035,3320,2940,3769,3911,2560,2024,3742,3885,3695,3561,3914,3047,2041,3534,3453,3972,2014,3891,3810,3511,3050,3864,3797,3756,3702,3540,3037,2942,3743,3648,3514,3324,3000,3915,2028,3535,3440,4001,2015,3811,1920,3974,3051,3893,3784,3703,3569,3024,3922,2943,3758,3542,3515,3868,3801,3706,3488,3326,3058,3917,3764,2030,3004,3975,3880,3813,3556,3053,3923,3759,2036,3543,3978,3448,3897,3788,3707,3517,3870,3327,3059,3680,3546,2031,3032,3766,3006,4033,2816,3938,3558,3979,3925,3884,3817,2038,3504,3871,3790,1984,3709,3547,3452,3061,3767,3986,3007,3796,3939,3036,3559,3770,3912,2039,3981,3886,3791,3696,3562,3929,3048,2042,3549,3454,3987,3892,3825,3512,3065,3798,3771,3941,3038,3744,3887,3563,3916,2043,3536,3455,4002,2016,3812,3989,3052,3894,3799,3704,3570,3039,2944,3773,3516,3802,3945,3565,3918,4003,2045,3976,3895,3814,3571,3054,3924,3760,3544,3993,3898,3803,3708,3518,3328,3060,3919,2032,4005,3815,4034,3055,3953,3573,3980,3926,3899,3818,3519,3872,3805,3710,3548,3062,3768,3008,4035,3940,3560,4009,3927,3819,2040,3982,3901,3792,3711,3577,3930,3063,3550,3988,3826,3066,4037,3772,3942,3983,3888,3821,3564,3931,2044,3551,3456,4017,3827,3990,3067,3800,3943,3040,3774,4041,3946,3566,3933,4004,2046,3991,3896,3829,3572,3069,3775,3994,3804,3947,3567,3920,2047,4006,3816,4049,3056,3954,3574,3995,3900,3833,3520,3806,3949,4007,4036,3955,3575,4010,3928,3820,3997,3902,3807,3712,3578,3064,4065,4038,4011,3957,3984,3903,3822,3579,3932,3552,4018,3828,3068,4039,3944,4013,3823,4042,3961,3581,3934,4019,3992,3830,3070,3776,4043,3948,3568,3935,2048,4021,3831,4050,3071,3996,3834,4045,3950,4008,4051,3956,3576,4025,3835,3998,3808,3951,4066,4053,4012,3958,3999,3904,3837,3580,4067,4040,3959,4014,3824,4057,3962,3582,4020,4069,4015,4044,3963,3583,3936,4022,3832,3072,4073,4046,3965,4023,4052,4026,3836,4047,3952,4081,4054,4027,4000,3838,4068,4055,3960,4029,3839,4058,4070,4016,4059,3964,3584,4071,4074,4061,3966,4024,4075,4048,3967,4082,4028,4077,4083,4056,4030,3840,4085,4031,4060,4072,4089,4062,4076,4063,3968,4078,4084,4079,4086,4032,4087,4090,4091,4064,4093,4080,4088,4092,4094,4095,4096。
不难看出，按极化权重从小到大排序对应的第一极化权重向量与按极化权重从大到小排序对应的第一极化权重向量互为逆序，即前者可以按逆序依次读取后者得到，或者反之。
无论第一极化权重向量是按极化权重从大到小排列还是从小到大排列，对于任一N或Nmax，均可预存。
图10示例性示出了本申请提供的一种通信装置的结构示意图。该通信装置可以是基站或终端。基于相同构思，本申请提供一种通信装置，用于执行上述方法流程，如图10所示，该装置1000包括处理器1001、存储器1002和通信接口1003。其中，处理器1001、存储器1002和通信接口1003相互耦合。
存储器1002可以包括易失性存储器(volatile memory)，例如RAM；存储器也可以包括非易失性存储器(non-volatile memory)，例如快闪存储器(flash memory)，HDD或SSD；存储器1002还可以包括上述种类的存储器的组合。
通信接口1003可以为有线通信接入口，无线通信接口或其组合，其中，有线通信接口例如可以为以太网接口。以太网接口可以是光接口，电接口或其组合。无线通信接口可以为WLAN接口。
处理器1001可以是CPU，NP或者CPU和NP的组合。
处理器1001还可以进一步包括硬件芯片。上述硬件芯片可以是ASIC，PLD或其组合。上述PLD可以是CPLD，FPGA，GAL或其任意组合。在有些实施例中，存储器1002还可以与处理器1001合并，例如用电路实现。
可选地，存储器1002还可以用于存储执行各项操作的指令，处理器1001调用该存储器1002中存储的指令，可以执行上述实施例中的一个或多个步骤，或其中可选的实施方式，使得通信装置1000实现上述方法，例如计算或存储至少一个N对应的按极化权重大小顺序依次排列的第一极化权重向量，其中每个极化信道的极化权重可以由包括但不限于上述各实施例揭示的方法计算得到。
在上述实施例中，可以全部或部分地通过软件、硬件、固件或者其任意组合来实现。当使用软件实现时，可以全部或部分地以计算机程序产品的形式实现。计算机程序产品包 括一个或多个计算机指令。在计算机上加载和执行计算机程序指令时，全部或部分地产生按照本发明实施例的流程或功能。计算机可以是通用计算机、专用计算机、计算机网络、或者其他可编程装置。计算机指令可以存储在计算机可读存储介质中，或者从一个计算机可读存储介质向另一个计算机可读存储介质传输，例如，计算机指令可以从一个网站站点、计算机、服务器或数据中心通过有线(例如同轴电缆、光纤、数字用户线(DSL))或无线(例如红外、无线、微波等)方式向另一个网站站点、计算机、服务器或数据中心进行传输。计算机可读存储介质可以是计算机能够存取的任何可用介质或者是包含一个或多个可用介质集成的服务器、数据中心等数据存储设备。可用介质可以是磁性介质，(例如，软盘、硬盘、磁带)、光介质(例如，DVD)、或者半导体介质(例如固态硬盘Solid State Disk(SSD))等。
本领域内的技术人员应明白，本发明的实施例可提供为方法、或计算机程序产品。因此，本发明可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且，本发明可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。
本发明是参照根据本发明实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器，使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。
这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中，使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品，该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。
这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上，使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理，从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。
尽管已描述了本发明的优选实施例，但本领域内的技术人员一旦得知了基本创造性概念，则可对这些实施例作出另外的变更和修改。所以，所附权利要求意欲解释为包括优选实施例以及落入本发明范围的所有变更和修改。
显然，本领域的技术人员可以对本发明进行各种改动和变型而不脱离本发明的精神和范围。这样，倘若本发明的这些修改和变型属于本发明权利要求及其等同技术的范围之内，则本发明也意图包含这些改动和变型在内。

Claims (55)

  1. 一种编码方法，其特征在于，包括：
    确定N个待编码比特，所述N个待编码比特中包含信息比特和固定比特，N为正整数；
    获取包含N个极化信道的极化权重的第一极化权重向量，所述极化权重是选择信息比特的依据，所述N个待编码比特对应所述N个极化信道；
    根据所述第一极化权重向量确定所述信息比特的位置；
    对所述N个待编码比特进行Polar编码，获得Polar编码后的比特。
  2. 根据权利要求1所述的方法，其特征在于，Polar码的目标码长M等于2的正整数次幂，M为正整数，所述确定N个待编码比特，包括：
    N等于M，所述Polar码的目标码长为Polar码的输出码长；
    所述获取包含N个极化信道的极化权重的第一极化权重向量，包括：
    计算所述N个极化信道的极化权重，得到所述第一极化权重向量。
  3. 根据权利要求2所述的方法，其特征在于，所述计算所述N个极化信道的极化权重，得到所述第一极化权重向量，包括：
    根据如下公式计算所述N个极化信道的极化权重Wi，得到所述第一极化权重向量：
    Figure PCTCN2017090359-appb-100001
    其中，
    Figure PCTCN2017090359-appb-100002
    i为信道索引，Bn-1Bn-2…B0为i的二进制表示，其中Bn-1为最高位，B0为最低位，Bj∈{0,1}，j∈{0,1,···,n-1}，i∈{0,1,···,N-1}，N＝2n，φ与α为根据Polar码的目标码长和码率预设的参数，n为正整数。
  4. 根据权利要求2所述的方法，其特征在于，所述计算所述N个极化信道的极化权重，得到所述第一极化权重向量，包括：
    根据如下公式通过递归计算得到所述第一极化权重向量W0 N-1：
    βi＝(2i-1+φ)α；
    Figure PCTCN2017090359-appb-100003
    Figure PCTCN2017090359-appb-100004
    其中，
    Figure PCTCN2017090359-appb-100005
    其中，i∈{1,···,N-1}，βi为与信道索引i有关的中间变量，φ与α为根据Polar码的目标码长和码率预设的参数，W0为任意常数。
  5. 根据权利要求1所述的方法，其特征在于，Polar码的目标码长M等于2的正整数次幂，所述获取包含N个极化信道的极化权重的第一极化权重向量，包括：
    从预先存储的第二极化权重向量中获取所述第一极化权重向量，所述第二极化权重向量包含Nmax个极化信道的极化权重，Nmax为预设的通信系统支持的最大码长所对应的母码码长，所述母码码长为2的正整数次幂。
  6. 根据权利要求5所述的方法，其特征在于，
    Polar码的目标码长M＜＝Nmax时，所述第一极化权重向量中的元素集合为所述第二极化权重向量中的元素集合的子集；
    Polar码的目标码长M＞＝Nmax时，信道索引小于或等于Nmax的极化信道的极化权重与所述第二极化权重向量中的极化权重一一对应，信道索引大于Nmax的极化信道的极化权重等于对应的所述信道索引小于或等于Nmax的极化信道的极化权重加上权 重增量
    Figure PCTCN2017090359-appb-100006
    其中，φ与α为根据Polar码的目标码长和码率预设的参数。
  7. 根据权利要求1所述的方法，其特征在于，Polar码的目标码长M不等于2的正整数次幂，所述确定N个待编码比特，包括：
    Figure PCTCN2017090359-appb-100007
    符号
    Figure PCTCN2017090359-appb-100008
    表示向下取整。
  8. 根据权利要求7所述的方法，其特征在于，所述获取包含N个极化信道的极化权重的第一极化权重向量之前，还包括：
    确定所述N个待编码比特中要删除的N-M个比特的位置，并根据确定结果计算包含N个待编码比特对应的极化权重的修正系数集合，所述修正系数用于表征删除的比特对每一极化权重的修正量；
    所述获取包含N个极化信道的极化权重的第一极化权重向量，包括：
    根据所述修正系数集合计算所述N个极化信道的极化权重，得到所述第一极化权重向量。
  9. 根据权利要求8所述的方法，其特征在于，所述确定所述N个比特中要删除的N-M个比特的位置，包括：
    确定所述N个极化信道的信道索引序列
    Figure PCTCN2017090359-appb-100009
    对所述信道索引序列中的每一个索引，进行如下操作：
    将每一索引对应的二进制数进行比特逆序，再转化为十进制数，得到新的信道索引序列
    Figure PCTCN2017090359-appb-100010
    对新的信道索引序列
    Figure PCTCN2017090359-appb-100011
    中的索引排序；
    按照从小到大的顺序选择所述信道索引序列
    Figure PCTCN2017090359-appb-100012
    中的N-M个索引为要删除的比特索引。
  10. 根据权利要求9所述的方法，其特征在于，所述根据确定结果计算包含N个比特的修正系数的修正系数集合，包括：
    所述修正系数集合
    Figure PCTCN2017090359-appb-100013
    所述修正系数集合g中的每一项g(i,j)按照如下公式计算：
    Figure PCTCN2017090359-appb-100014
    Figure PCTCN2017090359-appb-100015
    其中，i∈{0,1,···,N-1}，j∈{0,1,···,n-1}，N＝2n，pi为信道索引为i的极化信道对应的比特是否要被删除的标识，pi∈{0,1}。
  11. 根据权利要求7～10任一项所述的方法，其特征在于，所述根据所述修正系数集合计算所述N个极化信道的极化权重，得到所述第一极化权重向量，包括：
    根据如下公式计算所述N个极化信道的极化权重Wi，得到所述第一极化权重向量：
    Figure PCTCN2017090359-appb-100016
    其中，
    Figure PCTCN2017090359-appb-100017
    i为信道索引，Bn-1Bn-2…B0为i的二进制表示，其中Bn-1为最高位，B0为最低位，Bj∈{0,1}，j∈{0,1,···,n-1}，i∈{0,1,···,N-1}，N＝2n，g(i,j)为修正系数集合g中第i行第j列的元素,φ与α为根据Polar码的目标码长和码率预设的参数。
  12. 根据权利要求7～10任一项所述的方法，其特征在于，所述根据所述修正系数集合计算所述N个极化信道的极化权重，得到所述第一极化权重向量，包括：
    根据如下公式通过递归计算得到所述第一极化权重向量W0 N-1：
    βi＝(2i-1+φ)α；
    Figure PCTCN2017090359-appb-100018
    其中，
    Figure PCTCN2017090359-appb-100020
    其中，i∈{1,···,N-1}，βi为与信道索引i有关的中间变量，φ与α为根据Polar码的目标码长和码率预设的参数，g(i,j)为修正系数集合g中第i行第j列的元素，W0为任意常数。
  13. 根据权利要求3或4或6或11或12所述的方法，其特征在于，φ＝0，α＝1/4。
  14. 根据权利要求1所述的方法，其特征在于，所述根据所述第一极化权重向量确定所述信息比特的位置，包括：
    将所述第一极化权重向量中的极化权重从大到小进行排序，选择前K个极化权重对应的比特作为所述信息比特。
  15. 根据权利要求1-14中任一权利要求所述的方法，其特征在于，当所述第一极化权重向量中的极化信道按极化权重从大到小排序且所述极化信道的序号最小值为1时：
    若N＝16，所述第一极化权重向量为下列极化权重向量：
    16,15,14,12,8,13,11,10,7,6,4,9,5,3,2,1；或
    若N＝32，所述第一极化权重向量为下列极化权重向量：
    32,31,30,28,24,16,29,27,26,23,22,15,20,14,12,25,8,21,19,13,18,11,10,7,6,4,17,9,5,3,2,1；或
    若N＝64，所述第一极化权重向量为下列极化权重向量：
    64,63,62,60,56,48,61,32,59,58,55,54,47,52,46,31,44,30,57,40,28,53,24,51,45,50,16,43,29,42,39,27,38,26,23,36,22,49,15,20,14,41,12,37,25,8,35,21,34,19,13,18,11,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝128，所述第一极化权重向量为下列极化权重向量：
    128,127,126,124,120,112,125,96,123,122,119,64,118,111,116,110,95,108,94,121,104,92,63,117,62,88,115,109,60,114,80,107,56,93,106,103,91,48,102,90,61,87,100,32,59,86,113,79,58,84,55,78,105,54,76,47,101,52,89,46,72,99,31,44,85,98,30,57,83,40,77,28,82,53,75,24,51,74,45,71,50,16,43,70,97,29,42,68,39,27,81,38,26,23,36,73,22,49,15,69,20,14,41,67,12,66,37,25,8,35,21,34,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝256，所述第一极化权重向量为下列极化权重向量：
    256,255,254,252,248,240,253,224,251,250,247,192,246,239,244,238,128,223,236,222,249,232,220,191,245,190,216,243,237,188,242,127,208,235,184,126,221,234,231,124,219,176,230,218,189,120,215,228,160,187,214,241,112,207,186,212,183,125,206,233,182,96,123,204,175,229,180,122,217,174,119,200,227,64,159,118,172,213,226,111,158,185,116,211,168,110,205,156,210,181,95,108,203,152,179,94,121,202,173,104,199,178,92,63,144,117,171,198,225,62,157,88,170,115,196,167,109,60,155,114,209,166,80,107,154,56,151,164,93,106,201,103,150,177,91,48,143,102,197,148,90,61,142,87,169,100,195,32,59,86,140,113,194,165,79,58,153,84,55,136,163,78,105,54,149,162,76,47,101,52,147,89,46,141,72,99,146,31,44,85,139,98,193,30,57,138,83,40,135,77,28,82,53,134,161,75,24,51,132,74,45,71,50,145,16,43,70,97,29,42,137,68,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,12,66,37, 25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝512，所述第一极化权重向量为下列极化权重向量：
    512,511,510,508,504,496,509,480,507,506,503,448,502,495,500,494,384,479,492,478,505,488,476,447,501,256,446,472,499,493,444,498,383,464,491,440,382,477,490,487,380,475,432,486,474,255,445,376,471,484,254,416,443,470,497,368,463,252,442,468,439,381,462,489,248,438,352,379,460,431,485,436,378,473,240,430,375,456,483,253,320,415,374,428,469,482,367,224,414,251,441,372,467,424,366,461,250,412,466,247,437,351,364,459,192,246,408,435,350,377,458,239,429,360,455,244,434,348,238,319,400,373,427,454,481,128,223,318,413,236,344,426,371,452,423,365,222,249,316,411,370,465,232,422,336,363,220,410,191,245,312,407,420,349,362,457,190,359,216,406,243,433,347,237,304,399,358,188,453,242,404,346,127,208,317,398,235,343,425,356,451,184,126,221,288,234,315,342,396,369,450,231,421,335,124,219,314,409,176,340,230,311,392,419,334,361,218,189,120,215,310,405,228,418,332,303,160,357,187,214,241,308,403,345,112,207,302,397,328,186,355,212,402,183,125,206,287,233,300,341,395,354,449,182,96,286,123,204,313,394,175,339,229,296,391,180,333,122,217,284,174,338,119,200,309,390,227,417,331,64,159,118,172,213,280,226,307,388,330,111,301,158,327,185,116,211,306,401,168,110,205,272,299,326,156,353,210,181,95,285,108,203,298,393,324,295,152,179,94,121,202,283,173,337,104,199,294,389,178,92,282,63,144,117,171,198,279,225,292,387,329,62,157,88,170,278,115,196,305,386,167,109,271,60,325,155,114,209,276,166,80,270,107,297,154,323,56,151,164,93,106,201,268,322,103,293,150,177,91,281,48,143,102,197,264,291,148,90,61,142,87,169,277,100,195,290,385,32,59,86,140,113,194,275,165,79,269,58,153,84,274,55,136,163,78,105,267,321,54,149,162,76,266,47,101,263,52,147,89,46,141,72,262,99,289,146,31,44,85,139,98,193,260,30,57,138,83,273,40,135,77,28,82,53,134,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝1024，所述第一极化权重向量为下列极化权重向量：
    1024,1023,1022,1020,1016,1008,1021,992,1019,1018,1015,960,1014,1007,1012,1006,896,991,1004,990,1017,1000,988,959,1013,768,958,984,1011,1005,956,1010,895,976,1003,952,894,989,1002,999,512,892,987,944,998,986,767,957,888,983,996,766,928,955,982,1009,880,975,764,954,980,951,893,974,1001,760,950,864,511,891,972,943,997,948,510,890,985,752,942,887,968,995,508,765,832,927,886,940,981,994,879,736,926,763,953,504,884,979,936,878,973,762,924,978,759,949,863,496,876,971,704,758,920,947,862,509,889,970,751,941,872,967,756,946,480,860,507,750,831,912,885,939,966,993,506,640,735,830,925,748,856,938,503,883,964,935,877,734,448,761,828,923,502,882,977,744,934,848,495,875,732,922,703,500,757,824,919,932,861,494,874,969,702,871,728,918,755,945,384,479,859,492,749,816,911,870,700,965,754,916,478,858,505,639,720,829,910,747,855,937,488,868,963,696,476,638,733,800,447,746,827,854,908,501,881,962,743,933,847,256,446,636,731,826,921,472,688,852,499,742,823,904,931,846,493,873,730,444,701,498,632,727,822,917,740,930,383,464,844,491,815,672,869,699,726,440,753,820,915,382,477,857,490,624,719,814,909,840,698,487,867,724,914,695,380,475,637,718,799,432,745,812,853,907,486,866,961,694,474,608,255,798,445,635,716,825,376,906,471,687,851,484,741,808,903,692,845,254,416,634,729,796,443,470,686,850,497,631,712,821,902,739,929,368,463,843,252,442,576,671,468,630,684,725,792,439,738,819,900,381,462,842,489,623,813,670,839,697,248,438,628,723,818,913,352,680,379,460,622,717,784,431,811,838,668,485,865,722,436,693,378,473,607,240,797,430,620,715,810,375,905,456,836,483,807,664,691,606,253,320,415,633,714,795,374,428,469,685,849,482,616,711,806,901,690,367,224,414,604,251,794,441,575,656,372,467,629,683,710,791,424,737,804,899,366,461,841,250,412,574,669,466,600,682,247,790,437,627,708,817,898,351,679,364,459,621,783,192,572,837,667,246,408,626,721,788,435,350,678,377,458,592,239,782,429,619,809,360,666,455,835,244,434,568,663,348,676,605,238,319,400,618,713,780,373,427,454,834,481,615,805,662,689,128,223,318,413,603,236,793,344,426,560,655,371,452,614,709,776,423,803,660,365,222,602,249,316,411,573,654,370,465,599,681,232,789,422,612,707,802,897,336,363,220,410,544,191,571,598,652,245,312,407,625,706,787,420,349,677,362,457,591,781,190,570,359,665,216,406,596,243,786,433,567,648,347,675,590,237,304,399,617,779,358,188,453,833,242,404,566,661,346,674,127,208,317,398,588,235,778,343,425,559,356,451,613,775,184,564,659,126,221,288,601,234,315,342,396,558,653,369,450,584,231,774,421,611,801,658,335,124,219,314,409,543,176,340,556,597,651,230,311,392,610,705,772,419,334,361,218,542,189,569,120,650,215,310,405,595,228,785,418,552,647,332,589,303,160,540,357,187,214,594,241,308,403,565,646,345,673,112,207,302,397,587,777,328,186,355,212,402,536,183,563,644,125,206,287,586,233,300,341,395,557,354,449,583,773,182,562,657,96,286,123,204,313,394,528,175,339,555,582,229,296,391,609,771,180,333,122,217,284,541,174,338,554,119,649,200,309,390,580,227,770,417,551,331,64,159,539,118,172,213,280,593,226,307,388,550,645,330,111,301,158,538,327,185,116,211,306,401,535,168,548,643,110,205,272,585,299,326,156,353,2 10,534,181,561,642,95,285,108,203,298,393,527,324,581,295,152,532,179,94,121,202,283,526,173,337,553,104,199,294,389,579,769,178,92,282,63,144,524,117,171,198,279,578,225,292,387,549,329,62,157,537,88,170,278,115,196,305,386,520,167,547,109,271,60,325,155,114,209,276,533,166,546,641,80,270,107,297,154,323,56,151,531,164,93,106,201,268,525,322,103,293,150,530,177,91,281,48,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,32,59,86,140,113,194,275,518,165,545,79,269,58,153,84,274,55,136,516,163,78,105,267,321,54,149,529,162,76,266,47,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝2048，所述第一极化权重向量为下列极化权重向量：
    2048,2047,2046,2044,2040,2032,2045,2016,2043,2042,2039,1984,2038,2031,2036,2030,1920,2015,2028,2014,2041,2024,2012,1983,2037,1792,1982,2008,2035,2029,1980,2034,1919,2000,2027,1976,1918,2013,2026,2023,1536,1916,2011,1968,2022,2010,1791,1981,1912,2007,2020,1790,1952,1979,2006,2033,1904,1999,1788,1978,2004,1975,1917,1998,2025,1024,1784,1974,1888,1535,1915,1996,1967,2021,1972,1534,1914,2009,1776,1966,1911,1992,2019,1532,1789,1856,1951,1910,1964,2005,2018,1903,1760,1950,1787,1977,1528,1908,2003,1960,1902,1997,1786,1948,1023,2002,1783,1973,1887,1520,1900,1995,1728,1022,1782,1944,1971,1886,1533,1913,1994,1775,1965,1896,1991,1020,1780,1970,1504,1884,1531,1774,1855,1936,1909,1963,1990,2017,1016,1530,1664,1759,1854,1949,1772,1880,1962,1527,1907,1988,1959,1901,1758,1472,1785,1852,1947,1526,1906,1008,2001,1768,1958,1872,1519,1899,1756,1946,1727,1021,1524,1781,1848,1943,1956,1885,1518,1898,1993,1726,992,1895,1752,1019,1942,1779,1969,1408,1503,1883,1516,1773,1840,1935,1894,1724,1989,1018,1778,1940,1502,1015,1882,1529,1663,1744,1853,1934,1771,1879,1961,1512,1892,1987,960,1720,1014,1500,1662,1757,1824,1471,1770,1851,1878,1932,1525,1905,1007,1986,1767,1957,1871,1012,1280,1470,1660,1755,1850,1945,1496,1712,1876,1006,1523,1766,1847,1928,1955,1870,1517,1897,1754,1468,1725,896,991,1522,1656,1751,1846,1004,1941,1764,1954,1407,1488,1868,1515,1839,1696,990,1893,1723,1750,1017,1464,1777,1844,1939,1406,1501,1000,1881,1514,1648,1743,1838,1933,1864,1722,1511,988,1891,1748,959,1938,1719,1013,1404,1499,1661,1742,1823,1456,1769,1836,1877,1931,1510,1890,768,1985,958,1718,984,1498,1632,1011,1279,1822,1469,1659,1740,1849,1400,1930,1495,1711,1875,1005,1508,1765,1832,1927,956,1716,1869,1010,1278,1440,1658,1753,1820,1467,1494,1710,895,1874,976,1521,1655,1736,1845,1003,1926,1763,1953,1392,1487,1867,952,1276,1466,1600,1695,894,989,1492,1654,1708,1749,1816,1002,1463,1762,1843,1924,1405,1486,999,1866,1513,1647,1837,1694,512,1863,1721,892,1272,987,1462,1652,1747,1842,944,1937,1376,1704,998,1403,1484,1646,1741,1808,1455,1835,1862,1692,1509,986,1889,767,1746,957,1460,1717,888,983,1402,1497,1631,996,1264,1821,1454,1644,1739,1834,1399,1929,1480,1860,766,1507,928,1831,1688,955,982,1715,1630,1009,1277,1344,1439,1657,1738,1819,1398,1452,1493,1709,880,1873,975,1506,1640,1735,1830,764,1925,954,1714,1391,980,1248,1438,1628,951,1275,1818,1465,1599,1680,893,1396,974,1491,1653,1707,1734,1815,1001,1448,1761,1828,1923,1390,1485,760,1865,950,1274,1436,1598,1693,864,511,1490,1624,1706,891,1271,1814,972,1461,1651,1732,1841,943,1922,1375,1703,997,1388,1483,1645,1807,948,1216,510,1596,1861,1691,890,1270,985,1432,1650,752,1745,1812,942,1459,1374,1702,887,968,1401,1482,1616,995,1263,1806,1453,1643,1833,1384,1690,1479,508,1859,765,832,1268,927,1458,1592,1687,886,940,981,1372,1700,1629,994,1262,1343,1424,1642,1737,1804,1397,1451,1478,879,1858,736,1505,1639,926,1829,763,1686,953,504,1713,884,1152,979,1247,1342,1437,1627,936,1260,1817,1368,1450,1584,1679,878,1395,973,1476,1638,1733,1800,762,1447,924,1827,1684,1389,978,1246,759,1626,949,1273,1340,1435,1597,1678,863,1394,496,1489,1623,1705,876,1256,1813,971,1446,1636,1731,1826,704,1921,1360,758,1387,920,1244,1434,1568,947,1215,862,509,1595,1622,1676,889,1269,1336,970,1431,1649,751,1730,1811,941,1444,1373,1701,872,967,1386,1481,1615,756,1805,946,1214,480,1594,1383,1689,860,1240,507,1430,1620,750,831,1267,1810,912,1457,1591,1672,885,939,966,1371,1699,1614,993,1261,1328,1423,1641,1803,1382,1212,1477,506,640,1857,735,830,1266,925,1428,1590,748,1685,856,938,503,1370,1698,883,1151,964,1232,1341,1422,1612,935,1259,1802,1367,1449,1583,877,1380,734,1475,1637,448,1799,761,828,1208,923,502,1588,1683,882,1150,977,1245,1312,744,1625,934,1258,1339,1366,1420,1582,1677,848,1393,495,1474,1608,875,1255,1798,732,1445,1635,922,1825,703,1682,1359,500,757,824,1148,919,1243,1338,1433,1567,932,1200,861,1364,494,1580,1621,1675,874,1254,1335,969,1416,1634,1729,1796,702,1443,1358,871,728,1385,918,1242,755,1566,945,1213,384,479,1593,1144,1674,859,1239,1334,492,1429,1619,749,816,1252,1809,911,1442,1576,1671,870,700,965,1356,1613,754,1327,916,1184,478,1564,1381,1211,858,1238,505,639,1618,720,829,1265,1332,910,1427,1589,747,1670,855,937,488,1369,1697,868,1136,963,1231,1326,1421,1611,696,1801,1352,1210,476,638,1379,733,800,1236,447,1426,1560,746,827,1207,854,908,501,1587,1668,881,1149,962,1230,1311,743,1610, 933,1257,1324,1365,1419,1581,847,1378,256,1473,1607,446,636,1797,731,826,1206,921,472,1586,688,1681,852,1120,499,1310,742,823,1147,904,1228,1337,1418,1552,931,1199,846,1363,493,1579,1606,873,1253,1320,730,1415,1633,444,1795,701,1204,1357,498,632,727,822,1146,917,1241,1308,740,1565,930,1198,383,1362,464,1578,1143,1673,844,1224,1333,491,1414,1604,815,1251,1794,672,1441,1575,869,699,726,1355,440,753,820,1088,915,1183,382,477,1563,1142,1196,857,1237,1304,490,624,1617,719,814,1250,1331,909,1412,1574,1669,840,698,487,1354,867,1135,724,1325,914,1182,695,1562,1351,1209,380,475,637,1140,718,799,1235,1330,432,1425,1559,745,812,1192,853,907,486,1572,1667,866,1134,961,1229,1296,1609,694,1323,1350,1180,474,608,1377,255,798,1234,445,635,1558,716,825,1205,376,906,471,1585,687,1666,851,1119,484,1309,741,808,1132,903,1227,1322,1417,1551,692,845,1348,254,1605,416,634,1319,729,796,1176,443,470,1556,686,1203,850,1118,497,631,712,821,1145,902,1226,1307,739,1550,929,1197,368,1361,463,1577,1128,843,1223,1318,252,1413,1603,442,576,1793,671,1202,468,630,684,725,792,1116,439,1306,738,819,1087,900,1168,381,462,1548,1141,1195,842,1222,1303,489,623,1602,813,1249,1316,670,1411,1573,839,697,248,1353,438,628,723,818,1086,913,1181,352,680,1561,1112,1194,379,1302,460,622,1139,717,784,1220,1329,431,1410,1544,811,1191,838,668,485,1571,865,1133,722,1295,436,693,1084,1349,1179,378,473,607,1138,240,797,1233,1300,430,620,1557,715,810,1190,375,905,456,1570,1665,836,1104,483,1294,807,1131,664,1321,1178,691,606,1347,253,320,415,633,1080,714,795,1175,374,428,469,1555,685,1188,849,1117,482,616,711,806,1130,901,1225,1292,1549,690,367,1346,224,1127,414,604,1317,251,794,1174,441,575,1554,656,1201,372,467,629,683,710,791,1115,424,1305,737,804,1072,899,1167,366,461,1547,1126,841,1221,1288,250,1601,412,574,1315,669,1172,466,600,682,247,790,1114,437,627,708,817,1085,898,1166,351,679,1546,1111,1193,364,1301,459,621,1124,783,1219,1314,192,1409,1543,572,837,667,246,408,626,721,788,1056,435,350,678,1083,1110,1164,377,458,592,1137,239,782,1218,1299,429,619,1542,809,1189,360,666,455,1569,835,1103,244,1293,434,568,663,1082,1177,348,676,605,1108,238,319,1298,400,618,1079,713,780,1160,373,427,454,1540,1187,834,1102,481,615,805,1129,662,1291,689,128,1345,223,318,413,603,1078,236,793,1173,344,426,560,1553,655,1186,371,452,614,709,776,1100,423,1290,803,1071,660,365,222,1125,602,1287,249,316,411,573,1076,654,1171,370,465,599,681,232,789,1113,422,612,707,802,1070,897,1165,336,1545,1096,363,1286,220,1123,410,544,1313,191,1170,571,598,652,245,312,407,625,706,787,1055,420,349,677,1068,1109,1163,362,457,591,1122,781,1217,1284,190,1541,570,359,665,216,406,596,243,786,1054,433,567,648,1081,1162,347,675,590,1107,237,304,1297,399,617,1064,779,1159,358,188,453,1539,833,1101,242,404,566,661,1052,346,674,127,1106,208,317,398,588,1077,235,778,1158,343,425,559,1538,1185,356,451,613,775,1099,184,1289,564,659,126,221,288,601,1048,234,315,342,396,558,1075,653,1156,369,450,584,231,774,1098,421,611,801,1069,658,335,1095,124,1285,219,314,409,543,1074,176,1169,340,556,597,651,230,311,392,610,705,772,1040,419,334,1067,1094,361,218,1121,542,1283,189,569,120,650,215,310,405,595,228,785,1053,418,552,647,1066,1161,332,589,1092,303,1282,160,1063,540,357,187,214,594,241,308,403,565,646,1051,345,673,112,1105,207,302,397,587,1062,777,1157,328,186,1537,355,212,402,536,183,1050,563,644,125,206,287,586,1047,233,300,341,395,557,1060,1155,354,449,583,773,1097,182,562,657,96,286,123,1046,204,313,394,528,1073,175,1154,339,555,582,229,296,391,609,771,1039,180,333,1093,122,217,284,541,1044,174,338,554,119,649,200,309,390,580,227,770,1038,417,551,1065,331,1091,64,1281,159,539,118,172,213,280,593,226,307,388,550,645,1036,330,111,1090,301,158,1061,538,327,185,116,211,306,401,535,168,1049,548,643,110,205,272,585,1032,299,326,156,1059,353,210,534,181,561,642,95,285,108,1045,203,298,393,527,1058,1153,324,581,295,152,532,179,94,121,202,283,526,1043,173,337,553,104,199,294,389,579,769,1037,178,92,282,63,1042,144,524,117,171,198,279,578,225,292,387,549,1035,329,1089,62,157,537,88,170,278,115,196,305,386,520,167,1034,547,109,271,1031,60,325,155,114,209,276,533,166,546,641,80,270,107,1030,297,154,1057,323,56,151,531,164,93,106,201,268,525,1028,322,103,293,150,530,177,91,281,48,1041,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,1033,32,59,86,140,113,194,275,518,165,545,79,269,1029,58,153,84,274,55,136,516,163,78,105,267,1027,321,54,149,529,162,76,266,47,1026,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,1025,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝4096，所述第一极化权重向量为下列极化权重向量：
    4096,4095,4094,4092,4088,4080,4093,4064,4091,4090,4087,4032,4086,4079,4084,4078,3968,4063,4076,4062,4089,4072,4060,4031,4085,3840,4030,4056,4083,4077,4028,4082,3967,4048,4075,4024,3966,4061,4074,4071,3584,3964,4059,4016,4070,4058,3839,4029,3960,4055,4068,3838,4000,4027,4054,4081,3952,4047,3836,4026,4052,4023,3965,4046,4073,3072,3832,4022,3936,3583,3963,4044,4015,4069,4020,3582,3962,4057,3824,4014,3959,4040,4067,3580,3837,3904,3999,3958,4012,4053,4066, 3951,3808,3998,3835,4025,3576,3956,4051,4008,3950,4045,3834,3996,3071,4050,3831,4021,2048,3935,3568,3948,4043,3776,3070,3830,3992,4019,3934,3581,3961,4042,3823,4013,3944,4039,3068,3828,4018,3552,3932,3579,3822,3903,3984,3957,4011,4038,4065,3064,3578,3712,3807,3902,3997,3820,3928,4010,3575,3955,4036,4007,3949,3806,3520,3833,3900,3995,3574,3954,3056,4049,3816,4006,2047,3920,3567,3947,3804,3994,3775,3069,3572,3829,3896,3991,2046,4004,3933,3566,3946,4041,3774,3040,3943,3800,3067,3990,3827,4017,3456,3551,2044,3931,3564,3821,3888,3983,3942,3772,4037,3066,3826,3988,3550,3063,3930,3577,3711,3792,3901,3982,2040,3819,3927,4009,3560,3940,4035,3008,3768,3062,3548,3710,3805,3872,3519,3818,3899,3926,3980,3573,3953,3055,4034,3815,4005,2032,3919,3060,3328,3518,3708,3803,3898,3993,3544,3760,3924,3054,3571,3814,3895,3976,2045,4003,3918,3565,3945,3802,3516,3773,2944,3039,3570,3704,3799,3894,3052,3989,3812,2016,4002,3455,3536,2043,3916,3563,3887,3744,3038,3941,3771,3798,3065,3512,3825,3892,3987,3454,3549,2042,3048,3929,3562,3696,3791,3886,3981,2039,3912,3770,3559,3036,3939,3796,3007,3986,3767,3061,3452,3547,3709,1984,3790,3871,3504,2038,3817,3884,3925,3979,3558,3938,2816,4033,3006,3766,3032,2031,3546,3680,3059,3327,3870,3517,3707,3788,3897,3448,3978,3543,2036,3759,3923,3053,3556,3813,3880,3975,3004,2030,3764,3917,3058,3326,3488,3706,3801,3868,3515,3542,3758,2943,3922,3024,3569,3703,3784,3893,3051,3974,1920,3811,2015,4001,3440,3535,2028,3915,3000,3324,3514,3648,3743,2942,3037,3540,3702,3756,3797,3864,3050,3511,3810,3891,2014,3972,3453,3534,2041,3047,3914,3561,3695,3885,3742,2024,2560,3911,3769,2940,3320,3035,3510,3700,3795,3890,2992,3985,3424,3752,2012,3046,3451,3532,3694,1983,3789,3856,3503,2037,3883,3910,3740,3557,3034,3937,2815,3794,3005,3508,3765,2936,3031,3450,1792,3545,3679,1982,3044,3312,3869,3502,3692,2008,3787,3882,3447,3977,3528,2035,3908,2814,3555,2976,3879,3736,3003,3030,2029,3763,3678,3057,3325,3392,3487,3705,1980,3786,3867,3446,3500,3541,2034,3757,2928,3921,3023,3554,3688,3783,3878,2812,3973,3002,1919,2000,3762,3439,3028,3296,2027,3486,3676,2999,3323,3866,3513,3647,3728,2941,3444,3022,3539,3701,1976,3755,3782,3863,3049,3496,1918,3809,3876,2013,3971,3438,3533,2026,2808,3913,2998,3322,3484,3646,3741,2912,2023,2559,3538,3672,3754,2939,3319,3862,3020,3509,3699,3780,3889,1536,2991,3970,3423,1916,3751,2011,3045,3436,3531,3693,1968,3855,2996,3264,2022,2558,3644,3909,3739,2938,3318,3033,3480,3698,2800,3793,3860,2990,3507,3422,3750,2935,2010,3016,3449,1791,3530,3664,1981,3043,3311,3854,1912,3501,3691,2007,3881,3432,3738,3527,2020,2556,3907,2813,2880,3316,2975,3506,3640,3735,2934,2988,3029,3420,1790,3748,3677,1952,3042,3310,3391,3472,3690,1979,2006,3785,3852,3445,3499,3526,2033,2927,3906,2784,3553,3687,2974,3877,2811,3734,3001,1904,2552,1999,3761,2932,3200,3027,3295,3390,1788,3485,3675,1978,2984,3308,3865,3416,3498,3632,2004,3727,2926,3443,3021,3524,3686,1975,3781,3848,2810,3495,2972,1917,3875,1998,3732,3437,3026,3294,2025,2807,3674,2997,3321,3388,3483,3645,1024,3726,2911,3442,1784,2544,3537,3671,1974,3753,2924,3304,3861,3019,3494,3684,1888,3779,3874,1535,2752,3969,3408,1915,1996,2806,3435,2968,3292,1967,3482,3616,2995,3263,2910,2021,2557,3643,3670,3724,2937,3317,3384,3018,3479,3697,1972,2799,3778,3859,1534,2989,3492,3421,1914,3749,2920,2009,3015,3434,1776,3529,3663,1966,2804,3853,2994,1911,3262,1992,2528,3642,3431,3737,2908,3288,2019,2555,3478,3668,2798,2879,3315,3858,2960,3505,3639,3720,2933,1532,2987,3014,3419,1789,1856,3747,3662,1951,3041,3309,3376,1910,3471,3689,1964,2005,3851,3430,3260,3525,2018,2554,2688,3905,2783,2878,3314,2973,3476,3638,2796,3733,2904,2986,1903,2551,3418,1760,3746,2931,3199,1950,3012,3280,3389,1787,3470,3660,1977,1528,2983,3307,3850,3415,1908,3497,3631,2003,2925,3428,2782,3523,3685,1960,2496,3847,2809,2876,3256,2971,1902,2550,3636,1997,3731,2930,3198,3025,3293,3360,1786,2792,3673,1948,2982,3306,3387,3414,3468,3630,1023,2002,3725,2896,3441,1783,2543,3522,3656,1973,2923,3303,3846,2780,3493,3683,2970,1887,3873,1520,2751,3730,3407,1900,2548,1995,2805,2872,3196,2967,3291,3386,1728,3481,3615,1022,2980,3248,2909,3412,1782,2542,3628,3669,1944,3723,2922,3302,3383,3017,3464,3682,1971,1886,3777,3844,1533,2750,3491,3406,1913,2919,1994,2776,3433,1775,2966,3290,1965,2803,3614,2993,1896,3261,2432,1991,2527,3641,1020,3192,3722,2907,3287,3382,1780,2540,3477,3667,1970,2797,2864,3300,3857,1504,2959,3490,3624,1884,3719,2918,1531,2748,3013,3404,1774,1855,3661,1936,2802,3375,2964,1909,3232,1963,1990,2526,3612,3429,3259,2906,3286,2017,2553,2687,3666,2768,2877,3313,3380,2958,3475,3637,1016,2795,3718,2903,1530,2985,1664,2536,3417,1759,1854,3745,2916,3184,1949,3011,3279,3374,1772,1880,3469,3659,1962,1527,2744,3849,3400,1907,3258,1988,2524,2686,3427,2781,2848,3284,1959,2495,3474,3608,2794,2875,3255,2902,2956,1901,2549,3635,1758,3716,2929,3197,1472,3010,3278,3359,1785,1852,2791,3658,1947,1526,2981,3305,3372,3413,1906,3467,3629,1008,2001,2895,3426,1768,2304,3521,3655,1958,2494,2684,3845,2779,2874,3254,2969,1872,2520,3634,1519,2736,3729,2900,3168,1899,2547,3358,1756,2790,2871,3195,1946,2952,3276,3385,1727,3466,3600,1021,1524,2979,3247,2894,3411,1781,1848,2541,3627,3654,1943,2921,3301,3368,2778,3463,3681,1956,2492,1885,3843,1518,2749,3252,3405,1898,2546,2680,1993,2775,2870,3194,2965,3289,3356,1726,2788,3613,992,2978,1895,3246,2431,3410,1752,2512,3626,1019,31 91,1942,3721,2892,3272,3381,1779,2539,3462,3652,1969,1408,2863,3299,3842,1503,2720,3489,3623,1883,2917,1516,2747,2774,3403,1773,1840,2488,1935,2801,2868,3136,2963,1894,3231,2430,1724,1989,2525,3611,1018,3190,3244,2905,3285,3352,1778,2538,2672,3665,1940,2767,2862,3298,3379,1502,2957,3460,3622,1015,1882,3717,2888,1529,2746,1663,2535,3402,1744,1853,2915,3183,1934,2772,3373,1771,2962,1879,3230,1961,1512,2743,3610,3399,1892,3257,2428,1987,2523,2685,960,3188,2766,2847,3283,3378,1720,2480,3473,3607,1014,2793,2860,3240,2901,1500,2955,1662,2534,3620,1757,1824,3715,2914,3182,1471,3009,3277,3344,1770,1851,1878,3657,1932,1525,2742,3371,3398,1905,3228,1007,1986,2522,2656,3425,1767,2303,2846,3282,1957,2493,2683,3606,2764,2873,3253,2424,2954,1871,2519,3633,1012,1280,2735,3714,2899,3167,1470,1660,2532,3357,1755,1850,2789,2856,3180,1945,1496,2951,3275,3370,1712,1876,3465,3599,1006,1523,2740,2893,3396,1766,1847,2302,3653,1928,2464,2682,3367,2777,2844,3224,1955,2491,1870,2518,3604,1517,2734,3251,2898,3166,1897,2545,2679,1754,2760,2869,3193,1468,2950,3274,3355,1725,896,2787,3598,991,1522,2977,1656,3245,2416,3409,1751,1846,2511,3625,1004,3176,1941,2891,3271,3366,1764,2300,3461,3651,1954,2490,1407,2624,3841,1488,2719,3250,1868,2516,2678,1515,2732,2773,2840,3164,1839,2487,3354,1696,2786,2867,3135,990,2948,1893,3216,2429,1723,1750,2510,3596,1017,3189,1464,3243,2890,3270,3351,1777,1844,2537,2671,3650,1939,1406,2861,3297,3364,1501,2718,3459,3621,1000,1881,2887,1514,2745,1648,2296,3401,1743,1838,2486,2676,1933,2771,2866,3134,2961,1864,3229,2400,1722,1511,2728,3609,988,3160,1891,3242,2427,3350,1748,2508,2670,959,3187,1938,2765,2832,3268,3377,1719,2479,3458,3592,1013,1404,2859,3239,2886,1499,2716,1661,2533,3619,1742,1823,2913,3181,1456,2770,3343,1769,1836,2484,1877,1931,1510,2741,3132,3397,1890,3227,2426,768,1985,2521,2655,958,3186,2288,2845,3281,3348,1718,2478,2668,3605,984,2763,2858,3238,2423,1498,2953,1632,2504,3618,1011,1279,1822,3713,2884,3152,1469,1659,2531,3342,1740,1849,1400,2855,3179,1930,1495,2712,3369,1711,1875,3226,1005,1508,2739,2654,3395,1765,1832,2301,2368,1927,2463,2681,956,3128,2762,2843,3223,2422,1716,2476,1869,2517,3603,1010,1278,2733,3236,2897,3165,1440,1658,2530,2664,1753,1820,2759,2854,3178,1467,1494,2949,3273,3340,1710,895,1874,3597,976,1521,2738,1655,2415,3394,1736,1845,2272,1003,3175,1926,2462,2652,3365,1763,2299,2842,3222,1953,2489,1392,2623,3602,1487,2704,3249,2420,1867,2515,2677,952,1276,2731,2758,2839,3163,1466,1600,2472,3353,1695,894,2785,2852,3120,989,1492,2947,1654,3215,2414,1708,1749,1816,2509,3595,1002,3174,1463,2889,3269,3336,1762,1843,2298,3649,1924,2460,1405,2622,3363,1486,2717,3220,999,1866,2514,2648,1513,2730,1647,2295,2838,3162,1837,2485,2675,1694,2756,2865,3133,512,2946,1863,3214,2399,1721,892,1272,2727,3594,987,3159,1462,1652,3241,2412,3349,1747,1842,2507,2669,944,3172,1937,1376,2831,3267,3362,1704,2240,3457,3591,998,1403,2620,2885,1484,2715,1646,2294,1741,1808,2456,2674,1455,2769,2836,3104,1835,2483,1862,2398,1692,1509,2726,3131,986,3158,1889,3212,2425,767,1746,2506,2640,957,3185,1460,2287,2830,3266,3347,1717,888,2477,2667,3590,983,1402,2857,3237,2408,1497,2714,1631,2503,3617,996,1264,1821,2883,3151,1454,1644,2292,3341,1739,1834,2482,1399,2616,1929,1480,2711,3130,1860,3225,2396,766,1507,2724,2653,928,3156,1831,2286,2367,3346,1688,2448,2666,955,3127,982,2761,2828,3208,2421,1715,2475,1630,2502,3588,1009,1277,1344,3235,2882,3150,1439,1657,2529,2663,1738,1819,1398,2853,3177,1452,1493,2710,3339,1709,880,1873,975,1506,2737,1640,2176,3393,1735,1830,2271,2366,764,1925,2461,2651,954,3126,2284,2841,3221,2392,1714,2474,1391,2608,3601,980,1248,2703,3234,2419,1438,1628,2500,2662,951,1275,1818,2757,2824,3148,1465,1599,2471,3338,1680,893,1396,2851,3119,974,1491,2708,1653,2413,1707,1734,1815,2270,1001,3173,1448,2650,3335,1761,1828,2297,2364,1923,2459,1390,2621,3124,1485,2702,3219,2418,760,1865,2513,2647,950,1274,2729,2280,2837,3161,1436,1598,2470,2660,1693,864,2755,2850,3118,511,1490,2945,1624,3213,2384,1706,891,1271,1814,3593,972,3144,1461,1651,2411,3334,1732,1841,2268,943,3171,1922,2458,1375,2592,3361,1703,2239,3218,997,1388,2619,2646,1483,2700,1645,2293,2360,1807,2455,2673,948,1216,2754,2835,3103,510,1596,2468,1861,2397,1691,890,1270,2725,3116,985,3157,1432,1650,3211,2410,752,1745,1812,2505,2639,942,3170,1459,1374,2829,3265,3332,1702,887,2238,3589,968,1401,2618,2407,1482,2713,1616,2264,995,1263,1806,2454,2644,1453,1643,2291,2834,3102,1833,2481,1384,2615,1690,1479,2696,3129,508,1859,3210,2395,765,832,1268,2723,2638,927,3155,1458,1592,2285,2352,3345,1687,886,2447,2665,940,3112,981,1372,2827,3207,2406,1700,2236,1629,2501,3587,994,1262,1343,2881,3149,1424,1642,2290,1737,1804,2452,1397,2614,1451,1478,2709,3100,879,1858,2394,736,1505,2722,1639,2175,926,3154,1829,2256,2365,763,1686,2446,2636,953,3125,504,2283,2826,3206,2391,1713,884,2473,1152,2607,3586,979,1247,1342,3233,2404,1437,1627,2499,2661,936,1260,1817,1368,2823,3147,1450,1584,2232,3337,1679,878,1395,2612,973,1476,2707,1638,2174,1733,1800,2269,2336,762,1447,2649,924,3096,1827,2282,2363,2390,1684,2444,1389,2606,3123,978,1246,2701,3204,2417,759,1626,2498,2632,949,1273,1340,2279,2822,3146,1435,1597,2469,2659,1678,863,1394,2849,3117,496,1489,2706,1623,2383,1705,876,1256,1813,971,3143,1446,1636,2172,3333,1731,1826,2267,2362,704,1921,2457,1360,2591,3122,2224,3217,2388,758,1387,2604,2645,920,12 44,2699,2278,2359,1434,1568,2440,2658,947,1215,862,2753,2820,3088,509,1595,2467,1622,2382,1676,889,1269,1336,3115,970,3142,1431,1649,2409,751,1730,1811,2266,941,3169,1444,1373,2590,3331,1701,872,2237,967,1386,2617,2168,1481,2698,1615,2263,2358,756,1805,2453,2643,946,1214,2276,2833,3101,480,1594,2466,1383,2600,1689,860,1240,2695,3114,507,1430,1620,3209,2380,750,831,1267,1810,2637,912,3140,1457,1591,2351,3330,1672,885,2208,939,3111,966,1371,2588,2405,1699,2235,1614,2262,993,1261,1328,2642,1423,1641,2289,2356,1803,2451,1382,2613,1212,1477,2694,3099,506,640,1857,2393,735,830,1266,2721,2160,925,3153,1428,1590,2255,2350,748,1685,856,2445,2635,938,3110,503,1370,2825,3205,2376,1698,883,2234,1151,3585,964,1232,1341,2403,1422,1612,2260,935,1259,1802,2450,1367,2584,1449,1583,2231,3098,877,1380,2611,734,1475,2692,1637,2173,448,1799,2254,2335,761,828,1208,2634,923,3095,502,1588,2281,2348,2389,1683,882,2443,1150,2605,3108,977,1245,1312,3203,2402,744,1625,2497,2631,934,1258,1339,1366,2821,3145,1420,1582,2230,1677,848,1393,2610,495,1474,2705,1608,2144,875,1255,1798,2334,732,1445,1635,2171,922,3094,1825,2252,2361,703,1682,2442,1359,2576,3121,500,2223,3202,2387,757,824,1148,2603,2630,919,1243,1338,2277,2344,1433,1567,2439,2657,932,1200,861,1364,2819,3087,494,1580,2228,1621,2381,1675,874,1254,1335,969,3141,1416,1634,2170,1729,1796,2265,2332,702,1443,1358,2589,3092,871,2222,2386,728,1385,2602,2167,918,1242,2697,2248,2357,755,1566,2438,2628,945,1213,384,2275,2818,3086,479,1593,2465,1144,2599,1674,859,1239,1334,3113,492,1429,1619,2379,749,816,1252,1809,911,3139,1442,1576,2112,3329,1671,870,2207,700,965,1356,2587,2166,2220,1613,2261,2328,754,1327,2641,916,1184,2274,2355,478,1564,2436,1381,2598,1211,858,1238,2693,3084,505,639,1618,2378,720,829,1265,1332,2159,910,3138,1427,1589,2349,747,1670,855,2206,937,3109,488,1369,2586,2375,1697,868,2233,1136,963,1231,1326,2164,1421,1611,2259,2354,696,1801,2449,1352,2583,1210,2216,3097,476,638,1379,2596,733,800,1236,2691,2158,447,1426,1560,2253,2320,746,827,1207,854,2633,908,3080,501,1587,2347,2374,1668,881,2204,1149,3107,962,1230,1311,2401,743,1610,2258,933,1257,1324,1365,2582,1419,1581,2229,847,1378,2609,256,1473,2690,1607,2143,446,636,1797,2333,731,826,1206,2156,921,3093,472,1586,2251,2346,688,1681,852,2441,1120,2575,3106,499,1310,3201,2372,742,823,1147,2629,904,1228,1337,2343,1418,1552,2200,931,1199,846,1363,2580,493,1579,2227,1606,2142,873,1253,1320,730,1415,1633,2169,444,1795,2250,2331,701,1204,1357,2574,3091,498,632,2221,2385,727,822,1146,2601,2152,917,1241,1308,2247,2342,740,1565,2437,2627,930,1198,383,1362,2817,3085,464,1578,2226,1143,1673,844,1224,1333,491,1414,1604,2140,815,1251,1794,2330,672,1441,1575,2111,3090,869,2192,699,726,1355,2572,2165,440,2219,2246,2327,753,820,1088,2626,915,1183,382,2273,2340,477,1563,2435,1142,2597,1196,857,1237,1304,3083,490,624,1617,2377,719,814,1250,1331,909,3137,1412,1574,2110,1669,840,2205,698,487,1354,2585,2136,867,2218,1135,2326,724,1325,2163,914,1182,2244,2353,695,1562,2434,1351,2568,1209,380,2215,3082,475,637,1140,2595,718,799,1235,1330,2157,432,1425,1559,2319,745,812,1192,853,907,3079,486,1572,2108,2373,1667,866,2203,1134,961,1229,1296,2162,1609,2257,2324,694,1323,1350,2581,1180,2214,474,608,1377,2594,255,798,1234,2689,2128,445,635,1558,2318,716,825,1205,376,2155,906,3078,471,1585,2345,687,1666,851,2202,1119,3105,484,1309,2371,741,808,1132,903,1227,1322,2104,1417,1551,2199,692,845,1348,2579,254,2212,1605,2141,416,634,1319,729,796,1176,2154,443,470,1556,2249,2316,686,1203,850,1118,2573,3076,497,631,2370,712,821,1145,2151,902,1226,1307,2341,739,1550,2198,929,1197,368,1361,2578,463,1577,2225,1128,843,1223,1318,252,1413,1603,2139,442,576,1793,2329,671,1202,2096,3089,468,630,2191,684,725,792,1116,2571,2150,439,1306,2245,2312,738,819,1087,2625,900,1168,381,2339,462,1548,2196,1141,1195,842,1222,1303,489,623,1602,2138,813,1249,1316,670,1411,1573,2109,839,2190,697,248,1353,2570,2135,438,628,2217,2325,723,818,1086,2148,913,1181,352,2243,2338,680,1561,2433,1112,2567,1194,379,1302,3081,460,622,1139,717,784,1220,1329,431,1410,1544,2080,811,1191,838,668,485,1571,2107,2134,865,2188,1133,722,1295,2161,436,2242,2323,693,1084,1349,2566,1179,378,2213,473,607,1138,2593,240,797,1233,1300,2127,430,620,1557,2317,715,810,1190,375,905,3077,456,1570,2106,1665,836,2201,1104,483,1294,2132,807,1131,2322,664,1321,2103,1178,2184,691,606,1347,2564,253,320,2211,2126,415,633,1080,714,795,1175,374,2153,428,469,1555,2315,685,1188,849,1117,3075,482,616,2369,711,806,1130,901,1225,1292,2102,1549,2197,690,367,1346,2577,224,2210,1127,414,604,1317,251,794,1174,2124,441,575,1554,2314,656,1201,372,2095,3074,467,629,683,710,791,1115,2149,424,1305,2311,737,804,1072,899,1167,366,2100,461,1547,2195,1126,841,1221,1288,250,1601,2137,412,574,1315,669,1172,2094,466,600,2189,682,247,790,1114,2569,2120,437,627,2310,708,817,1085,2147,898,1166,351,2337,679,1546,2194,1111,1193,364,1301,459,621,1124,783,1219,1314,192,1409,1543,2079,572,837,667,246,2092,2133,408,626,2187,721,788,1056,2146,435,350,2241,2308,678,1083,1110,2565,1164,377,458,592,1137,239,782,1218,1299,429,619,1542,2078,809,1189,360,666,455,1569,2105,835,2186,1103,244,1293,2131,434,568,2321,663,1082,2088,1177,348,2183,676,605,1108,2563,238,319,1298,2125,400,618,1079,713,780,1160,373,427,454,1540,2076,1187,834,1102,481,615,2130,805,1129,662,1291,2101,2182,689,128,1345,2562,223,318,2209,413,603,1078,236,793,1173,3 44,2123,426,560,1553,2313,655,1186,371,3073,452,614,709,776,1100,423,1290,2072,803,1071,660,365,2099,222,2180,1125,602,1287,249,316,2122,411,573,1076,654,1171,370,2093,465,599,681,232,789,1113,2119,422,612,2309,707,802,1070,897,1165,336,2098,1545,2193,1096,363,1286,220,1123,410,544,1313,191,1170,2064,571,598,652,245,312,2091,2118,407,625,706,787,1055,2145,420,349,2307,677,1068,1109,1163,362,457,591,1122,781,1217,1284,190,1541,2077,570,359,665,216,2090,406,596,2185,243,786,1054,2116,433,567,2306,648,1081,2087,1162,347,675,590,1107,237,304,1297,399,617,1064,779,1159,358,188,453,1539,2075,833,1101,242,2129,404,566,661,1052,2086,346,2181,674,127,1106,2561,208,317,398,588,1077,235,778,1158,343,425,559,1538,2074,1185,356,451,613,775,1099,184,1289,2071,564,659,126,2084,221,288,2179,601,1048,234,315,342,2121,396,558,1075,653,1156,369,450,584,231,774,1098,421,611,2070,801,1069,658,335,2097,2178,1095,124,1285,219,314,409,543,1074,176,1169,340,2063,556,597,651,230,311,2117,392,610,705,772,1040,419,334,2068,1067,1094,361,218,1121,542,1283,189,2062,569,120,650,215,310,2089,405,595,228,785,1053,2115,418,552,2305,647,1066,1161,332,589,1092,303,1282,160,1063,540,357,187,214,2060,594,241,308,2114,403,565,646,1051,2085,345,673,112,1105,207,302,397,587,1062,777,1157,328,186,1537,2073,355,212,402,536,183,1050,2056,563,644,125,2083,206,287,586,1047,233,300,341,395,557,1060,1155,354,449,583,773,1097,182,2069,562,657,96,2082,286,2177,123,1046,204,313,394,528,1073,175,1154,339,555,582,229,296,391,609,771,1039,180,333,2067,1093,122,217,284,541,1044,174,338,2061,554,119,649,200,309,390,580,227,770,1038,417,551,2066,1065,331,1091,64,1281,159,539,118,172,213,280,2059,593,226,307,2113,388,550,645,1036,330,111,1090,301,158,1061,538,327,185,2058,116,211,306,401,535,168,1049,2055,548,643,110,205,272,585,1032,299,326,156,1059,353,210,534,181,2054,561,642,95,2081,285,108,1045,203,298,393,527,1058,1153,324,581,295,152,532,179,94,2052,121,202,283,526,1043,173,337,553,104,199,294,389,579,769,1037,178,2065,92,282,63,1042,144,524,117,171,198,279,578,225,292,387,549,1035,329,1089,62,157,537,88,170,278,2057,115,196,305,386,520,167,1034,547,109,271,1031,60,325,155,114,209,276,533,166,2053,546,641,80,270,107,1030,297,154,1057,323,56,151,531,164,93,2051,106,201,268,525,1028,322,103,293,150,530,177,2050,91,281,48,1041,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,1033,32,59,86,140,113,194,275,518,165,545,79,269,1029,58,153,84,274,55,136,516,163,78,105,267,1027,321,54,149,529,162,2049,76,266,47,1026,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,1025,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1。
  16. 如权利要求15所述的方法，当所述第一极化权重向量的最小序号为0时，所述第一极化权重向量中的每个序号依次减1。
  17. 如权利要求1-16中任一权利要求所述的方法，第一极化信道的极化权重大于第二极化信道时，在所述第一极化权重向量中，第一极化信道在第二极化信道之前。
  18. 如权利要求15所述的方法，所述极化信道按极化权重从大到小排序时，所述第一极化权重向量为所述极化权重向量按逆序依次读取形成的向量。
  19. 一种编码设备，其特征在于，包括：
    第一确定模块，用于确定N个待编码比特，所述N个待编码比特中包含信息比特和固定比特，N为正整数；
    获取模块，用于获取包含N个极化信道的极化权重的第一极化权重向量，所述极化权重是选择信息比特的依据，所述N个待编码比特对应所述N个极化信道；
    第二确定模块，用于根据所述第一极化权重向量确定所述信息比特的位置；
    编码模块，用于对所述N个待编码比特进行Polar编码，获得Polar编码后的比特。
  20. 根据权利要求19所述的编码设备，其特征在于，Polar码的目标码长M等于2的正整数次幂，N为正整数，所述第一确定模块具体用于：
    确定N等于M，所述Polar码的目标码长为Polar码的输出码长；
    所述获取模块具体用于：
    计算所述N个极化信道的极化权重，得到所述第一极化权重向量。
  21. 根据权利要求20所述的编码设备，其特征在于，所述获取模块具体用于：
    根据如下公式计算所述N个极化信道的极化权重Wi，得到所述第一极化权重向量：
    Figure PCTCN2017090359-appb-100021
    其中，
    Figure PCTCN2017090359-appb-100022
    i为信道索引，Bn-1Bn-2…B0为i的二进制表示，其中Bn-1为最高位，B0为最低位，Bj∈{0,1}，j∈{0,1,···,n-1}，i∈{0,1,···,N-1}，N＝2n，φ与α为根据Polar码的目标码长和码率预设的参数，n为正整数。
  22. 根据权利要求20所述的编码设备，其特征在于，所述获取模块具体用于：
    根据如下公式通过递归计算得到所述第一极化权重向量W0 N-1：
    βi＝(2i-1+φ)α；
    Figure PCTCN2017090359-appb-100023
    Figure PCTCN2017090359-appb-100024
    其中，
    Figure PCTCN2017090359-appb-100025
    其中，i∈{1,···,N-1}，βi为与信道索引i有关的中间变量，φ与α为根据Polar码的目标码长和码率预设的参数，W0为任意常数。
  23. 根据权利要求19所述的编码设备，其特征在于，Polar码的目标码长M等于2的正整数次幂，所述获取模块具体用于：
    从预先存储的第二极化权重向量中获取所述第一极化权重向量，所述第二极化权重向量包含Nmax个极化信道的极化权重，Nmax为预设的通信系统支持的最大码长所对应的母码码长，母码码长为2的正整数次幂。
  24. 根据权利要求23所述的编码设备，其特征在于，
    Polar码的目标码长M＜＝Nmax时，所述第一极化权重向量中的元素集合为所述第二极化权重向量中的元素集合的子集；
    Polar码的目标码长M＞＝Nmax时，信道索引小于或等于Nmax的极化信道的极化权重与所述第二极化权重向量中的极化权重一一对应，信道索引大于Nmax的极化信道的极化权重等于对应的所述信道索引小于或等于Nmax的极化信道的极化权重加上权重增量
    Figure PCTCN2017090359-appb-100026
    其中，φ与α为根据Polar码的目标码长和码率预设的参数。
  25. 根据权利要求19所述的编码设备，其特征在于，Polar码的目标码长M不等于2的正整数次幂，所述第一确定模块具体用于：
    确定
    Figure PCTCN2017090359-appb-100027
    符号
    Figure PCTCN2017090359-appb-100028
    表示向下取整。
  26. 根据权利要求25所述的编码设备，其特征在于，还包括：
    第三确定模块，用于在所述获取模块获取包含N个极化信道的极化权重的第一极化权重向量之前，确定所述N个待编码比特中要删除的N-M个比特的位置；
    计算模块，用于根据所述第三确定模块确定的结果计算包含N个待编码比特对应的极化权重的修正系数集合，所述修正系数用于表征删除的比特对每一极化权重的修正量；
    所述获取模块具体用于：
    根据所述修正系数集合计算所述N个极化信道的极化权重，得到所述第一极化权重向量。
  27. 根据权利要求26所述的编码设备，其特征在于，所述第三确定模块具体用于：
    确定所述N个极化信道的信道索引序列
    Figure PCTCN2017090359-appb-100029
    对所述信道索引序列中的每一个索引，进行如下操作：
    将每一索引对应的二进制数进行比特逆序，再转化为十进制数，得到新的信道索引序列
    Figure PCTCN2017090359-appb-100030
    对新的信道索引序列
    Figure PCTCN2017090359-appb-100031
    中的索引排序；
    按照从小到大的顺序选择所述信道索引序列
    Figure PCTCN2017090359-appb-100032
    中的N-M个为要删除的比特索引。
  28. 根据权利要求27所述的编码设备，其特征在于，
    所述修正系数集合
    Figure PCTCN2017090359-appb-100033
    所述计算模块具体用于按照如下公式计算所述修正系数集合g中的每一项g(i,j)：
    Figure PCTCN2017090359-appb-100034
    Figure PCTCN2017090359-appb-100035
    其中，i∈{0,1,···,N-1}，j∈{0,1,···,n-1}，N＝2n，pi为信道索引为i的极化信道对应的比特是否要被删除的标识，pi∈{0,1}。
  29. 根据权利要求25～28任一项所述的编码设备，其特征在于，所述获取模块具体用于：
    根据如下公式计算所述N个极化信道的极化权重Wi，得到所述第一极化权重向量：
    Figure PCTCN2017090359-appb-100036
    其中，
    Figure PCTCN2017090359-appb-100037
    i为信道索引，Bn-1Bn-2…B0为i的二进制表示，其中Bn-1为最高位，B0为最低位，Bj∈{0,1}，j∈{0,1,···,n-1}，i∈{0,1,···,N-1}，N＝2n，g(i,j)为修正系数集合g中第i行第j列的元素,φ与α为根据Polar码的目标码长和码率预设的参数。
  30. 根据权利要求25～28任一项所述的编码设备，其特征在于，所述获取模块具体用于：
    根据如下公式通过递归计算得到所述第一极化权重向量W0 N-1：
    βi＝(2i-1+φ)α；
    Figure PCTCN2017090359-appb-100038
    Figure PCTCN2017090359-appb-100039
    其中，
    Figure PCTCN2017090359-appb-100040
    其中，i∈{1,···,N-1}，βi为与信道索引i有关的中间变量，φ与α为根据Polar码的目标码长和码率预设的参数，g(i,j)为修正系数集合g中第i行第j列的元素，W0为任意常数。
  31. 根据权利要求21或22或24或29或30所述的编码设备，其特征在于，φ＝0，α＝1/4。
  32. 根据权利要求19所述的编码设备，其特征在于，所述第二确定模块具体用于：
    将所述第一极化权重向量中的极化权重从大到小进行排序，选择前K个极化权重对应的比特作为所述信息比特。
  33. 根据权利要求19-32中任一权利要求所述的设备，其特征在于，当所述第一极化权重向量中的极化信道按极化权重从大到小排序且所述极化信道的序号最小值为1时：
    若N＝16，所述第一极化权重向量为下列极化权重向量：
    16,15,14,12,8,13,11,10,7,6,4,9,5,3,2,1；或
    若N＝32，所述第一极化权重向量为下列极化权重向量：
    32,31,30,28,24,16,29,27,26,23,22,15,20,14,12,25,8,21,19,13,18,11,10,7,6,4,17,9,5,3,2,1；或
    若N＝64，所述第一极化权重向量为下列极化权重向量：
    64,63,62,60,56,48,61,32,59,58,55,54,47,52,46,31,44,30,57,40,28,53,24,51,45,50,16,43,29,42,39,27,38,26,23,36,22,49,15,20,14,41,12,37,25,8,35,21,34,19,13,18,11,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝128，所述第一极化权重向量为下列极化权重向量：
    128,127,126,124,120,112,125,96,123,122,119,64,118,111,116,110,95,108,94,121,104,92,63,117,62,88,115,109,60,114,80,107,56,93,106,103,91,48,102,90,61,87,100,32,59,86,113,79,58,84,55,78,105,54,76,47,101,52,89,46,72,99,31,44,85,98,30,57,83,40,77,28,82,53,75,24,51,74,45,71,50,16,43,70,97,29,42,68,39,27,81,38,26,23,36,73,22,49,15,69,20,14,41,67,12,66,37,25,8,35,21,34,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝256，所述第一极化权重向量为下列极化权重向量：
    256,255,254,252,248,240,253,224,251,250,247,192,246,239,244,238,128,223,236,222,249,232,220,191,245,190,216,243,237,188,242,127,208,235,184,126,221,234,231,124,219,176,230,218,189,120,215,228,160,187,214,241,112,207,186,212,183,125,206,233,182,96,123,204,175,229,180,122,217,174,119,200,227,64,159,118,172,213,226,111,158,185,116,211,168,110,205,156,210,181,95,108,203,152,179,94,121,202,173,104,199,178,92,63,144,117,171,198,225,62,157,88,170,115,196,167,109,60,155,114,209,166,80,107,154,56,151,164,93,106,201,103,150,177,91,48,143,102,197,148,90,61,142,87,169,100,195,32,59,86,140,113,194,165,79,58,153,84,55,136,163,78,105,54,149,162,76,47,101,52,147,89,46,141,72,99,146,31,44,85,139,98,193,30,57,138,83,40,135,77,28,82,53,134,161,75,24,51,132,74,45,71,50,145,16,43,70,97,29,42,137,68,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝512，所述第一极化权重向量为下列极化权重向量：
    512,511,510,508,504,496,509,480,507,506,503,448,502,495,500,494,384,479,492,478,505,488,476,447,501,256,446,472,499,493,444,498,383,464,491,440,382,477,490,487,380,475,432,486,474,255,445,376,471,484,254,416,443,470,497,368,463,252,442,468,439,381,462,489,248,438,352,379,460,431,485,436,378,473,240,430,375,456,483,253,320,415,374,428,469,482,367,224,414,251,441,372,467,424,366,461,250,412,466,247,437,351,364,459,192,246,408,435,350,377,458,239,429,360,455,244,434,348,238,319,400,373,427,454,481,128,223,318,413,236,344,426,371,452,423,365,222,249,316,411,370,465,232,422,336,363,220,410,191,245,312,407,420,349,362,457,190,359,216,406,243,433,347,237,304,399,358,188,453,242,404,346,127,208,317,398,235,343,425,356,451,184,126,221,288,234,315,342,396,369,450,231,421,335,124,219,314,409,176,340,230,311,392,419,334,361,218,189,120,215,310,405,228,418,332,303,160,357,187,214,241,308,403,345,112,207,302,397,328,186,355,212,402,183,125,206,287,233,300,341,395,354,449,182,96,286,123,204,313,394,175,339,229,296,391,180,333,122,217,284,174,338,119,200,309,390,227,417,331,64,159,118,172,213,280,226,307,388,330,111,301,158,327,185,116,211,306,401,168,110,205,272,299,326,156,353,210,181,95,285,108,203,298,393,324,295,152,179,94,121,202,283,173,337,104,199,294,389,178,92,282,63,144,117,171,198,279,225,292,387,329,62,157,88,170,278,115,196,305,386,167,109,271,60,325,155,114,209,276,166,80,270,107,297,154,323,56,151,164,93,106,201,268,322,103,293,150,177,91,281,48,143,102,197,264,291,148,90,61,142,87,169,277,100,195,290,385,32,59,86,140,113,194,275,165,79,269,58,153,84,274,55,136,163,78,105,267,321,54,149,162,76,266,47,101,263,52,147,89,46,141,72,262,99,289,146,31,44,85,139,98,193,260,30,57,138,83,273,40,135,77,28,82,53,134,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝1024，所述第一极化权重向量为下列极化权重向量：
    1024,1023,1022,1020,1016,1008,1021,992,1019,1018,1015,960,1014,1007,1012,1006,896,991,10 04,990,1017,1000,988,959,1013,768,958,984,1011,1005,956,1010,895,976,1003,952,894,989,1002,999,512,892,987,944,998,986,767,957,888,983,996,766,928,955,982,1009,880,975,764,954,980,951,893,974,1001,760,950,864,511,891,972,943,997,948,510,890,985,752,942,887,968,995,508,765,832,927,886,940,981,994,879,736,926,763,953,504,884,979,936,878,973,762,924,978,759,949,863,496,876,971,704,758,920,947,862,509,889,970,751,941,872,967,756,946,480,860,507,750,831,912,885,939,966,993,506,640,735,830,925,748,856,938,503,883,964,935,877,734,448,761,828,923,502,882,977,744,934,848,495,875,732,922,703,500,757,824,919,932,861,494,874,969,702,871,728,918,755,945,384,479,859,492,749,816,911,870,700,965,754,916,478,858,505,639,720,829,910,747,855,937,488,868,963,696,476,638,733,800,447,746,827,854,908,501,881,962,743,933,847,256,446,636,731,826,921,472,688,852,499,742,823,904,931,846,493,873,730,444,701,498,632,727,822,917,740,930,383,464,844,491,815,672,869,699,726,440,753,820,915,382,477,857,490,624,719,814,909,840,698,487,867,724,914,695,380,475,637,718,799,432,745,812,853,907,486,866,961,694,474,608,255,798,445,635,716,825,376,906,471,687,851,484,741,808,903,692,845,254,416,634,729,796,443,470,686,850,497,631,712,821,902,739,929,368,463,843,252,442,576,671,468,630,684,725,792,439,738,819,900,381,462,842,489,623,813,670,839,697,248,438,628,723,818,913,352,680,379,460,622,717,784,431,811,838,668,485,865,722,436,693,378,473,607,240,797,430,620,715,810,375,905,456,836,483,807,664,691,606,253,320,415,633,714,795,374,428,469,685,849,482,616,711,806,901,690,367,224,414,604,251,794,441,575,656,372,467,629,683,710,791,424,737,804,899,366,461,841,250,412,574,669,466,600,682,247,790,437,627,708,817,898,351,679,364,459,621,783,192,572,837,667,246,408,626,721,788,435,350,678,377,458,592,239,782,429,619,809,360,666,455,835,244,434,568,663,348,676,605,238,319,400,618,713,780,373,427,454,834,481,615,805,662,689,128,223,318,413,603,236,793,344,426,560,655,371,452,614,709,776,423,803,660,365,222,602,249,316,411,573,654,370,465,599,681,232,789,422,612,707,802,897,336,363,220,410,544,191,571,598,652,245,312,407,625,706,787,420,349,677,362,457,591,781,190,570,359,665,216,406,596,243,786,433,567,648,347,675,590,237,304,399,617,779,358,188,453,833,242,404,566,661,346,674,127,208,317,398,588,235,778,343,425,559,356,451,613,775,184,564,659,126,221,288,601,234,315,342,396,558,653,369,450,584,231,774,421,611,801,658,335,124,219,314,409,543,176,340,556,597,651,230,311,392,610,705,772,419,334,361,218,542,189,569,120,650,215,310,405,595,228,785,418,552,647,332,589,303,160,540,357,187,214,594,241,308,403,565,646,345,673,112,207,302,397,587,777,328,186,355,212,402,536,183,563,644,125,206,287,586,233,300,341,395,557,354,449,583,773,182,562,657,96,286,123,204,313,394,528,175,339,555,582,229,296,391,609,771,180,333,122,217,284,541,174,338,554,119,649,200,309,390,580,227,770,417,551,331,64,159,539,118,172,213,280,593,226,307,388,550,645,330,111,301,158,538,327,185,116,211,306,401,535,168,548,643,110,205,272,585,299,326,156,353,210,534,181,561,642,95,285,108,203,298,393,527,324,581,295,152,532,179,94,121,202,283,526,173,337,553,104,199,294,389,579,769,178,92,282,63,144,524,117,171,198,279,578,225,292,387,549,329,62,157,537,88,170,278,115,196,305,386,520,167,547,109,271,60,325,155,114,209,276,533,166,546,641,80,270,107,297,154,323,56,151,531,164,93,106,201,268,525,322,103,293,150,530,177,91,281,48,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,32,59,86,140,113,194,275,518,165,545,79,269,58,153,84,274,55,136,516,163,78,105,267,321,54,149,529,162,76,266,47,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝2048，所述第一极化权重向量为下列极化权重向量：
    2048,2047,2046,2044,2040,2032,2045,2016,2043,2042,2039,1984,2038,2031,2036,2030,1920,2015,2028,2014,2041,2024,2012,1983,2037,1792,1982,2008,2035,2029,1980,2034,1919,2000,2027,1976,1918,2013,2026,2023,1536,1916,2011,1968,2022,2010,1791,1981,1912,2007,2020,1790,1952,1979,2006,2033,1904,1999,1788,1978,2004,1975,1917,1998,2025,1024,1784,1974,1888,1535,1915,1996,1967,2021,1972,1534,1914,2009,1776,1966,1911,1992,2019,1532,1789,1856,1951,1910,1964,2005,2018,1903,1760,1950,1787,1977,1528,1908,2003,1960,1902,1997,1786,1948,1023,2002,1783,1973,1887,1520,1900,1995,1728,1022,1782,1944,1971,1886,1533,1913,1994,1775,1965,1896,1991,1020,1780,1970,1504,1884,1531,1774,1855,1936,1909,1963,1990,2017,1016,1530,1664,1759,1854,1949,1772,1880,1962,1527,1907,1988,1959,1901,1758,1472,1785,1852,1947,1526,1906,1008,2001,1768,1958,1872,1519,1899,1756,1946,1727,1021,1524,1781,1848,1943,1956,1885,1518,1898,1993,1726,992,1895,1752,1019,1942,1779,1969,1408,1503,1883,1516,1773,1840,1935,1894,1724,1989,1018,1778,1940,1502,1015,1882,1529,1663,1744,1853,1934,1771,1879,1961,1512,1892,1987,960,1720,1014,1500,1662,1757,1824,1471,1770,1851,1878,1932,1525,1905,1007,1986,1767,1957,1871,1012,1280,1470,1660,1755,1850,1945,1496,1712,1876,1006,1523,1766,1847,1928,1955,1870,1517,1897,1754,1468,1725,896,991,1522,1656,1751,1846,1004,1941,1764,1954,1407,1488,1868,1515,1839,1696,990,1893,1723,1750,1017, 1464,1777,1844,1939,1406,1501,1000,1881,1514,1648,1743,1838,1933,1864,1722,1511,988,1891,1748,959,1938,1719,1013,1404,1499,1661,1742,1823,1456,1769,1836,1877,1931,1510,1890,768,1985,958,1718,984,1498,1632,1011,1279,1822,1469,1659,1740,1849,1400,1930,1495,1711,1875,1005,1508,1765,1832,1927,956,1716,1869,1010,1278,1440,1658,1753,1820,1467,1494,1710,895,1874,976,1521,1655,1736,1845,1003,1926,1763,1953,1392,1487,1867,952,1276,1466,1600,1695,894,989,1492,1654,1708,1749,1816,1002,1463,1762,1843,1924,1405,1486,999,1866,1513,1647,1837,1694,512,1863,1721,892,1272,987,1462,1652,1747,1842,944,1937,1376,1704,998,1403,1484,1646,1741,1808,1455,1835,1862,1692,1509,986,1889,767,1746,957,1460,1717,888,983,1402,1497,1631,996,1264,1821,1454,1644,1739,1834,1399,1929,1480,1860,766,1507,928,1831,1688,955,982,1715,1630,1009,1277,1344,1439,1657,1738,1819,1398,1452,1493,1709,880,1873,975,1506,1640,1735,1830,764,1925,954,1714,1391,980,1248,1438,1628,951,1275,1818,1465,1599,1680,893,1396,974,1491,1653,1707,1734,1815,1001,1448,1761,1828,1923,1390,1485,760,1865,950,1274,1436,1598,1693,864,511,1490,1624,1706,891,1271,1814,972,1461,1651,1732,1841,943,1922,1375,1703,997,1388,1483,1645,1807,948,1216,510,1596,1861,1691,890,1270,985,1432,1650,752,1745,1812,942,1459,1374,1702,887,968,1401,1482,1616,995,1263,1806,1453,1643,1833,1384,1690,1479,508,1859,765,832,1268,927,1458,1592,1687,886,940,981,1372,1700,1629,994,1262,1343,1424,1642,1737,1804,1397,1451,1478,879,1858,736,1505,1639,926,1829,763,1686,953,504,1713,884,1152,979,1247,1342,1437,1627,936,1260,1817,1368,1450,1584,1679,878,1395,973,1476,1638,1733,1800,762,1447,924,1827,1684,1389,978,1246,759,1626,949,1273,1340,1435,1597,1678,863,1394,496,1489,1623,1705,876,1256,1813,971,1446,1636,1731,1826,704,1921,1360,758,1387,920,1244,1434,1568,947,1215,862,509,1595,1622,1676,889,1269,1336,970,1431,1649,751,1730,1811,941,1444,1373,1701,872,967,1386,1481,1615,756,1805,946,1214,480,1594,1383,1689,860,1240,507,1430,1620,750,831,1267,1810,912,1457,1591,1672,885,939,966,1371,1699,1614,993,1261,1328,1423,1641,1803,1382,1212,1477,506,640,1857,735,830,1266,925,1428,1590,748,1685,856,938,503,1370,1698,883,1151,964,1232,1341,1422,1612,935,1259,1802,1367,1449,1583,877,1380,734,1475,1637,448,1799,761,828,1208,923,502,1588,1683,882,1150,977,1245,1312,744,1625,934,1258,1339,1366,1420,1582,1677,848,1393,495,1474,1608,875,1255,1798,732,1445,1635,922,1825,703,1682,1359,500,757,824,1148,919,1243,1338,1433,1567,932,1200,861,1364,494,1580,1621,1675,874,1254,1335,969,1416,1634,1729,1796,702,1443,1358,871,728,1385,918,1242,755,1566,945,1213,384,479,1593,1144,1674,859,1239,1334,492,1429,1619,749,816,1252,1809,911,1442,1576,1671,870,700,965,1356,1613,754,1327,916,1184,478,1564,1381,1211,858,1238,505,639,1618,720,829,1265,1332,910,1427,1589,747,1670,855,937,488,1369,1697,868,1136,963,1231,1326,1421,1611,696,1801,1352,1210,476,638,1379,733,800,1236,447,1426,1560,746,827,1207,854,908,501,1587,1668,881,1149,962,1230,1311,743,1610,933,1257,1324,1365,1419,1581,847,1378,256,1473,1607,446,636,1797,731,826,1206,921,472,1586,688,1681,852,1120,499,1310,742,823,1147,904,1228,1337,1418,1552,931,1199,846,1363,493,1579,1606,873,1253,1320,730,1415,1633,444,1795,701,1204,1357,498,632,727,822,1146,917,1241,1308,740,1565,930,1198,383,1362,464,1578,1143,1673,844,1224,1333,491,1414,1604,815,1251,1794,672,1441,1575,869,699,726,1355,440,753,820,1088,915,1183,382,477,1563,1142,1196,857,1237,1304,490,624,1617,719,814,1250,1331,909,1412,1574,1669,840,698,487,1354,867,1135,724,1325,914,1182,695,1562,1351,1209,380,475,637,1140,718,799,1235,1330,432,1425,1559,745,812,1192,853,907,486,1572,1667,866,1134,961,1229,1296,1609,694,1323,1350,1180,474,608,1377,255,798,1234,445,635,1558,716,825,1205,376,906,471,1585,687,1666,851,1119,484,1309,741,808,1132,903,1227,1322,1417,1551,692,845,1348,254,1605,416,634,1319,729,796,1176,443,470,1556,686,1203,850,1118,497,631,712,821,1145,902,1226,1307,739,1550,929,1197,368,1361,463,1577,1128,843,1223,1318,252,1413,1603,442,576,1793,671,1202,468,630,684,725,792,1116,439,1306,738,819,1087,900,1168,381,462,1548,1141,1195,842,1222,1303,489,623,1602,813,1249,1316,670,1411,1573,839,697,248,1353,438,628,723,818,1086,913,1181,352,680,1561,1112,1194,379,1302,460,622,1139,717,784,1220,1329,431,1410,1544,811,1191,838,668,485,1571,865,1133,722,1295,436,693,1084,1349,1179,378,473,607,1138,240,797,1233,1300,430,620,1557,715,810,1190,375,905,456,1570,1665,836,1104,483,1294,807,1131,664,1321,1178,691,606,1347,253,320,415,633,1080,714,795,1175,374,428,469,1555,685,1188,849,1117,482,616,711,806,1130,901,1225,1292,1549,690,367,1346,224,1127,414,604,1317,251,794,1174,441,575,1554,656,1201,372,467,629,683,710,791,1115,424,1305,737,804,1072,899,1167,366,461,1547,1126,841,1221,1288,250,1601,412,574,1315,669,1172,466,600,682,247,790,1114,437,627,708,817,1085,898,1166,351,679,1546,1111,1193,364,1301,459,621,1124,783,1219,1314,192,1409,1543,572,837,667,246,408,626,721,788,1056,435,350,678,1083,1110,1164,377,458,592,1137,239,782,1218,1299,429,619,1542,809,1189,360,666,455,1569,835,1103,244,1293,434,568,663,1082,1177,348,676,605,1108,238,319,1298,400,618,1079,713,780,1160,373,427,454,1540,1187,834,1102,481,615,805,1129,662,1291,689,128,1345,223,318,413,603,1078,236,793,1173,344,426,560,1553,655,1186,371,452,614,709,776,1100,423,1290,803,1071,660,365,222,1125,602,1287,249,316,411,573,1076,654,1171,370,465,599,681,232,789,1113,42 2,612,707,802,1070,897,1165,336,1545,1096,363,1286,220,1123,410,544,1313,191,1170,571,598,652,245,312,407,625,706,787,1055,420,349,677,1068,1109,1163,362,457,591,1122,781,1217,1284,190,1541,570,359,665,216,406,596,243,786,1054,433,567,648,1081,1162,347,675,590,1107,237,304,1297,399,617,1064,779,1159,358,188,453,1539,833,1101,242,404,566,661,1052,346,674,127,1106,208,317,398,588,1077,235,778,1158,343,425,559,1538,1185,356,451,613,775,1099,184,1289,564,659,126,221,288,601,1048,234,315,342,396,558,1075,653,1156,369,450,584,231,774,1098,421,611,801,1069,658,335,1095,124,1285,219,314,409,543,1074,176,1169,340,556,597,651,230,311,392,610,705,772,1040,419,334,1067,1094,361,218,1121,542,1283,189,569,120,650,215,310,405,595,228,785,1053,418,552,647,1066,1161,332,589,1092,303,1282,160,1063,540,357,187,214,594,241,308,403,565,646,1051,345,673,112,1105,207,302,397,587,1062,777,1157,328,186,1537,355,212,402,536,183,1050,563,644,125,206,287,586,1047,233,300,341,395,557,1060,1155,354,449,583,773,1097,182,562,657,96,286,123,1046,204,313,394,528,1073,175,1154,339,555,582,229,296,391,609,771,1039,180,333,1093,122,217,284,541,1044,174,338,554,119,649,200,309,390,580,227,770,1038,417,551,1065,331,1091,64,1281,159,539,118,172,213,280,593,226,307,388,550,645,1036,330,111,1090,301,158,1061,538,327,185,116,211,306,401,535,168,1049,548,643,110,205,272,585,1032,299,326,156,1059,353,210,534,181,561,642,95,285,108,1045,203,298,393,527,1058,1153,324,581,295,152,532,179,94,121,202,283,526,1043,173,337,553,104,199,294,389,579,769,1037,178,92,282,63,1042,144,524,117,171,198,279,578,225,292,387,549,1035,329,1089,62,157,537,88,170,278,115,196,305,386,520,167,1034,547,109,271,1031,60,325,155,114,209,276,533,166,546,641,80,270,107,1030,297,154,1057,323,56,151,531,164,93,106,201,268,525,1028,322,103,293,150,530,177,91,281,48,1041,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,1033,32,59,86,140,113,194,275,518,165,545,79,269,1029,58,153,84,274,55,136,516,163,78,105,267,1027,321,54,149,529,162,76,266,47,1026,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,1025,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝4096，所述第一极化权重向量为下列极化权重向量：
    4096,4095,4094,4092,4088,4080,4093,4064,4091,4090,4087,4032,4086,4079,4084,4078,3968,4063,4076,4062,4089,4072,4060,4031,4085,3840,4030,4056,4083,4077,4028,4082,3967,4048,4075,4024,3966,4061,4074,4071,3584,3964,4059,4016,4070,4058,3839,4029,3960,4055,4068,3838,4000,4027,4054,4081,3952,4047,3836,4026,4052,4023,3965,4046,4073,3072,3832,4022,3936,3583,3963,4044,4015,4069,4020,3582,3962,4057,3824,4014,3959,4040,4067,3580,3837,3904,3999,3958,4012,4053,4066,3951,3808,3998,3835,4025,3576,3956,4051,4008,3950,4045,3834,3996,3071,4050,3831,4021,2048,3935,3568,3948,4043,3776,3070,3830,3992,4019,3934,3581,3961,4042,3823,4013,3944,4039,3068,3828,4018,3552,3932,3579,3822,3903,3984,3957,4011,4038,4065,3064,3578,3712,3807,3902,3997,3820,3928,4010,3575,3955,4036,4007,3949,3806,3520,3833,3900,3995,3574,3954,3056,4049,3816,4006,2047,3920,3567,3947,3804,3994,3775,3069,3572,3829,3896,3991,2046,4004,3933,3566,3946,4041,3774,3040,3943,3800,3067,3990,3827,4017,3456,3551,2044,3931,3564,3821,3888,3983,3942,3772,4037,3066,3826,3988,3550,3063,3930,3577,3711,3792,3901,3982,2040,3819,3927,4009,3560,3940,4035,3008,3768,3062,3548,3710,3805,3872,3519,3818,3899,3926,3980,3573,3953,3055,4034,3815,4005,2032,3919,3060,3328,3518,3708,3803,3898,3993,3544,3760,3924,3054,3571,3814,3895,3976,2045,4003,3918,3565,3945,3802,3516,3773,2944,3039,3570,3704,3799,3894,3052,3989,3812,2016,4002,3455,3536,2043,3916,3563,3887,3744,3038,3941,3771,3798,3065,3512,3825,3892,3987,3454,3549,2042,3048,3929,3562,3696,3791,3886,3981,2039,3912,3770,3559,3036,3939,3796,3007,3986,3767,3061,3452,3547,3709,1984,3790,3871,3504,2038,3817,3884,3925,3979,3558,3938,2816,4033,3006,3766,3032,2031,3546,3680,3059,3327,3870,3517,3707,3788,3897,3448,3978,3543,2036,3759,3923,3053,3556,3813,3880,3975,3004,2030,3764,3917,3058,3326,3488,3706,3801,3868,3515,3542,3758,2943,3922,3024,3569,3703,3784,3893,3051,3974,1920,3811,2015,4001,3440,3535,2028,3915,3000,3324,3514,3648,3743,2942,3037,3540,3702,3756,3797,3864,3050,3511,3810,3891,2014,3972,3453,3534,2041,3047,3914,3561,3695,3885,3742,2024,2560,3911,3769,2940,3320,3035,3510,3700,3795,3890,2992,3985,3424,3752,2012,3046,3451,3532,3694,1983,3789,3856,3503,2037,3883,3910,3740,3557,3034,3937,2815,3794,3005,3508,3765,2936,3031,3450,1792,3545,3679,1982,3044,3312,3869,3502,3692,2008,3787,3882,3447,3977,3528,2035,3908,2814,3555,2976,3879,3736,3003,3030,2029,3763,3678,3057,3325,3392,3487,3705,1980,3786,3867,3446,3500,3541,2034,3757,2928,3921,3023,3554,3688,3783,3878,2812,3973,3002,1919,2000,3762,3439,3028,3296,2027,3486,3676,2999,3323,3866,3513,3647,3728,2941,3444,3022,3539,3701,1976,3755,3782,3863,3049,3496,1918,3809,3876,2013,3971,3438,3533,2026,2808,3913,2998,3322,3484,3646,3741,2912,2023,2559,3538,3672,3754,2939,3319,3862,3020,3509,3699,3780,3889,1536,2991,3970,3423,1916,3751,2011,3045,3436,3531,3693,1968,3855,2996,3264,2022,2558,3644,39 09,3739,2938,3318,3033,3480,3698,2800,3793,3860,2990,3507,3422,3750,2935,2010,3016,3449,1791,3530,3664,1981,3043,3311,3854,1912,3501,3691,2007,3881,3432,3738,3527,2020,2556,3907,2813,2880,3316,2975,3506,3640,3735,2934,2988,3029,3420,1790,3748,3677,1952,3042,3310,3391,3472,3690,1979,2006,3785,3852,3445,3499,3526,2033,2927,3906,2784,3553,3687,2974,3877,2811,3734,3001,1904,2552,1999,3761,2932,3200,3027,3295,3390,1788,3485,3675,1978,2984,3308,3865,3416,3498,3632,2004,3727,2926,3443,3021,3524,3686,1975,3781,3848,2810,3495,2972,1917,3875,1998,3732,3437,3026,3294,2025,2807,3674,2997,3321,3388,3483,3645,1024,3726,2911,3442,1784,2544,3537,3671,1974,3753,2924,3304,3861,3019,3494,3684,1888,3779,3874,1535,2752,3969,3408,1915,1996,2806,3435,2968,3292,1967,3482,3616,2995,3263,2910,2021,2557,3643,3670,3724,2937,3317,3384,3018,3479,3697,1972,2799,3778,3859,1534,2989,3492,3421,1914,3749,2920,2009,3015,3434,1776,3529,3663,1966,2804,3853,2994,1911,3262,1992,2528,3642,3431,3737,2908,3288,2019,2555,3478,3668,2798,2879,3315,3858,2960,3505,3639,3720,2933,1532,2987,3014,3419,1789,1856,3747,3662,1951,3041,3309,3376,1910,3471,3689,1964,2005,3851,3430,3260,3525,2018,2554,2688,3905,2783,2878,3314,2973,3476,3638,2796,3733,2904,2986,1903,2551,3418,1760,3746,2931,3199,1950,3012,3280,3389,1787,3470,3660,1977,1528,2983,3307,3850,3415,1908,3497,3631,2003,2925,3428,2782,3523,3685,1960,2496,3847,2809,2876,3256,2971,1902,2550,3636,1997,3731,2930,3198,3025,3293,3360,1786,2792,3673,1948,2982,3306,3387,3414,3468,3630,1023,2002,3725,2896,3441,1783,2543,3522,3656,1973,2923,3303,3846,2780,3493,3683,2970,1887,3873,1520,2751,3730,3407,1900,2548,1995,2805,2872,3196,2967,3291,3386,1728,3481,3615,1022,2980,3248,2909,3412,1782,2542,3628,3669,1944,3723,2922,3302,3383,3017,3464,3682,1971,1886,3777,3844,1533,2750,3491,3406,1913,2919,1994,2776,3433,1775,2966,3290,1965,2803,3614,2993,1896,3261,2432,1991,2527,3641,1020,3192,3722,2907,3287,3382,1780,2540,3477,3667,1970,2797,2864,3300,3857,1504,2959,3490,3624,1884,3719,2918,1531,2748,3013,3404,1774,1855,3661,1936,2802,3375,2964,1909,3232,1963,1990,2526,3612,3429,3259,2906,3286,2017,2553,2687,3666,2768,2877,3313,3380,2958,3475,3637,1016,2795,3718,2903,1530,2985,1664,2536,3417,1759,1854,3745,2916,3184,1949,3011,3279,3374,1772,1880,3469,3659,1962,1527,2744,3849,3400,1907,3258,1988,2524,2686,3427,2781,2848,3284,1959,2495,3474,3608,2794,2875,3255,2902,2956,1901,2549,3635,1758,3716,2929,3197,1472,3010,3278,3359,1785,1852,2791,3658,1947,1526,2981,3305,3372,3413,1906,3467,3629,1008,2001,2895,3426,1768,2304,3521,3655,1958,2494,2684,3845,2779,2874,3254,2969,1872,2520,3634,1519,2736,3729,2900,3168,1899,2547,3358,1756,2790,2871,3195,1946,2952,3276,3385,1727,3466,3600,1021,1524,2979,3247,2894,3411,1781,1848,2541,3627,3654,1943,2921,3301,3368,2778,3463,3681,1956,2492,1885,3843,1518,2749,3252,3405,1898,2546,2680,1993,2775,2870,3194,2965,3289,3356,1726,2788,3613,992,2978,1895,3246,2431,3410,1752,2512,3626,1019,3191,1942,3721,2892,3272,3381,1779,2539,3462,3652,1969,1408,2863,3299,3842,1503,2720,3489,3623,1883,2917,1516,2747,2774,3403,1773,1840,2488,1935,2801,2868,3136,2963,1894,3231,2430,1724,1989,2525,3611,1018,3190,3244,2905,3285,3352,1778,2538,2672,3665,1940,2767,2862,3298,3379,1502,2957,3460,3622,1015,1882,3717,2888,1529,2746,1663,2535,3402,1744,1853,2915,3183,1934,2772,3373,1771,2962,1879,3230,1961,1512,2743,3610,3399,1892,3257,2428,1987,2523,2685,960,3188,2766,2847,3283,3378,1720,2480,3473,3607,1014,2793,2860,3240,2901,1500,2955,1662,2534,3620,1757,1824,3715,2914,3182,1471,3009,3277,3344,1770,1851,1878,3657,1932,1525,2742,3371,3398,1905,3228,1007,1986,2522,2656,3425,1767,2303,2846,3282,1957,2493,2683,3606,2764,2873,3253,2424,2954,1871,2519,3633,1012,1280,2735,3714,2899,3167,1470,1660,2532,3357,1755,1850,2789,2856,3180,1945,1496,2951,3275,3370,1712,1876,3465,3599,1006,1523,2740,2893,3396,1766,1847,2302,3653,1928,2464,2682,3367,2777,2844,3224,1955,2491,1870,2518,3604,1517,2734,3251,2898,3166,1897,2545,2679,1754,2760,2869,3193,1468,2950,3274,3355,1725,896,2787,3598,991,1522,2977,1656,3245,2416,3409,1751,1846,2511,3625,1004,3176,1941,2891,3271,3366,1764,2300,3461,3651,1954,2490,1407,2624,3841,1488,2719,3250,1868,2516,2678,1515,2732,2773,2840,3164,1839,2487,3354,1696,2786,2867,3135,990,2948,1893,3216,2429,1723,1750,2510,3596,1017,3189,1464,3243,2890,3270,3351,1777,1844,2537,2671,3650,1939,1406,2861,3297,3364,1501,2718,3459,3621,1000,1881,2887,1514,2745,1648,2296,3401,1743,1838,2486,2676,1933,2771,2866,3134,2961,1864,3229,2400,1722,1511,2728,3609,988,3160,1891,3242,2427,3350,1748,2508,2670,959,3187,1938,2765,2832,3268,3377,1719,2479,3458,3592,1013,1404,2859,3239,2886,1499,2716,1661,2533,3619,1742,1823,2913,3181,1456,2770,3343,1769,1836,2484,1877,1931,1510,2741,3132,3397,1890,3227,2426,768,1985,2521,2655,958,3186,2288,2845,3281,3348,1718,2478,2668,3605,984,2763,2858,3238,2423,1498,2953,1632,2504,3618,1011,1279,1822,3713,2884,3152,1469,1659,2531,3342,1740,1849,1400,2855,3179,1930,1495,2712,3369,1711,1875,3226,1005,1508,2739,2654,3395,1765,1832,2301,2368,1927,2463,2681,956,3128,2762,2843,3223,2422,1716,2476,1869,2517,3603,1010,1278,2733,3236,2897,3165,1440,1658,2530,2664,1753,1820,2759,2854,3178,1467,1494,2949,3273,3340,1710,895,1874,3597,976,1521,2738,1655,2415,3394,1736,1845,2272,1003,3175,1926,2462,2652,3365,1763,2299,2842,3222,1953,2489,1392,2623,3602,1487,2 704,3249,2420,1867,2515,2677,952,1276,2731,2758,2839,3163,1466,1600,2472,3353,1695,894,2785,2852,3120,989,1492,2947,1654,3215,2414,1708,1749,1816,2509,3595,1002,3174,1463,2889,3269,3336,1762,1843,2298,3649,1924,2460,1405,2622,3363,1486,2717,3220,999,1866,2514,2648,1513,2730,1647,2295,2838,3162,1837,2485,2675,1694,2756,2865,3133,512,2946,1863,3214,2399,1721,892,1272,2727,3594,987,3159,1462,1652,3241,2412,3349,1747,1842,2507,2669,944,3172,1937,1376,2831,3267,3362,1704,2240,3457,3591,998,1403,2620,2885,1484,2715,1646,2294,1741,1808,2456,2674,1455,2769,2836,3104,1835,2483,1862,2398,1692,1509,2726,3131,986,3158,1889,3212,2425,767,1746,2506,2640,957,3185,1460,2287,2830,3266,3347,1717,888,2477,2667,3590,983,1402,2857,3237,2408,1497,2714,1631,2503,3617,996,1264,1821,2883,3151,1454,1644,2292,3341,1739,1834,2482,1399,2616,1929,1480,2711,3130,1860,3225,2396,766,1507,2724,2653,928,3156,1831,2286,2367,3346,1688,2448,2666,955,3127,982,2761,2828,3208,2421,1715,2475,1630,2502,3588,1009,1277,1344,3235,2882,3150,1439,1657,2529,2663,1738,1819,1398,2853,3177,1452,1493,2710,3339,1709,880,1873,975,1506,2737,1640,2176,3393,1735,1830,2271,2366,764,1925,2461,2651,954,3126,2284,2841,3221,2392,1714,2474,1391,2608,3601,980,1248,2703,3234,2419,1438,1628,2500,2662,951,1275,1818,2757,2824,3148,1465,1599,2471,3338,1680,893,1396,2851,3119,974,1491,2708,1653,2413,1707,1734,1815,2270,1001,3173,1448,2650,3335,1761,1828,2297,2364,1923,2459,1390,2621,3124,1485,2702,3219,2418,760,1865,2513,2647,950,1274,2729,2280,2837,3161,1436,1598,2470,2660,1693,864,2755,2850,3118,511,1490,2945,1624,3213,2384,1706,891,1271,1814,3593,972,3144,1461,1651,2411,3334,1732,1841,2268,943,3171,1922,2458,1375,2592,3361,1703,2239,3218,997,1388,2619,2646,1483,2700,1645,2293,2360,1807,2455,2673,948,1216,2754,2835,3103,510,1596,2468,1861,2397,1691,890,1270,2725,3116,985,3157,1432,1650,3211,2410,752,1745,1812,2505,2639,942,3170,1459,1374,2829,3265,3332,1702,887,2238,3589,968,1401,2618,2407,1482,2713,1616,2264,995,1263,1806,2454,2644,1453,1643,2291,2834,3102,1833,2481,1384,2615,1690,1479,2696,3129,508,1859,3210,2395,765,832,1268,2723,2638,927,3155,1458,1592,2285,2352,3345,1687,886,2447,2665,940,3112,981,1372,2827,3207,2406,1700,2236,1629,2501,3587,994,1262,1343,2881,3149,1424,1642,2290,1737,1804,2452,1397,2614,1451,1478,2709,3100,879,1858,2394,736,1505,2722,1639,2175,926,3154,1829,2256,2365,763,1686,2446,2636,953,3125,504,2283,2826,3206,2391,1713,884,2473,1152,2607,3586,979,1247,1342,3233,2404,1437,1627,2499,2661,936,1260,1817,1368,2823,3147,1450,1584,2232,3337,1679,878,1395,2612,973,1476,2707,1638,2174,1733,1800,2269,2336,762,1447,2649,924,3096,1827,2282,2363,2390,1684,2444,1389,2606,3123,978,1246,2701,3204,2417,759,1626,2498,2632,949,1273,1340,2279,2822,3146,1435,1597,2469,2659,1678,863,1394,2849,3117,496,1489,2706,1623,2383,1705,876,1256,1813,971,3143,1446,1636,2172,3333,1731,1826,2267,2362,704,1921,2457,1360,2591,3122,2224,3217,2388,758,1387,2604,2645,920,1244,2699,2278,2359,1434,1568,2440,2658,947,1215,862,2753,2820,3088,509,1595,2467,1622,2382,1676,889,1269,1336,3115,970,3142,1431,1649,2409,751,1730,1811,2266,941,3169,1444,1373,2590,3331,1701,872,2237,967,1386,2617,2168,1481,2698,1615,2263,2358,756,1805,2453,2643,946,1214,2276,2833,3101,480,1594,2466,1383,2600,1689,860,1240,2695,3114,507,1430,1620,3209,2380,750,831,1267,1810,2637,912,3140,1457,1591,2351,3330,1672,885,2208,939,3111,966,1371,2588,2405,1699,2235,1614,2262,993,1261,1328,2642,1423,1641,2289,2356,1803,2451,1382,2613,1212,1477,2694,3099,506,640,1857,2393,735,830,1266,2721,2160,925,3153,1428,1590,2255,2350,748,1685,856,2445,2635,938,3110,503,1370,2825,3205,2376,1698,883,2234,1151,3585,964,1232,1341,2403,1422,1612,2260,935,1259,1802,2450,1367,2584,1449,1583,2231,3098,877,1380,2611,734,1475,2692,1637,2173,448,1799,2254,2335,761,828,1208,2634,923,3095,502,1588,2281,2348,2389,1683,882,2443,1150,2605,3108,977,1245,1312,3203,2402,744,1625,2497,2631,934,1258,1339,1366,2821,3145,1420,1582,2230,1677,848,1393,2610,495,1474,2705,1608,2144,875,1255,1798,2334,732,1445,1635,2171,922,3094,1825,2252,2361,703,1682,2442,1359,2576,3121,500,2223,3202,2387,757,824,1148,2603,2630,919,1243,1338,2277,2344,1433,1567,2439,2657,932,1200,861,1364,2819,3087,494,1580,2228,1621,2381,1675,874,1254,1335,969,3141,1416,1634,2170,1729,1796,2265,2332,702,1443,1358,2589,3092,871,2222,2386,728,1385,2602,2167,918,1242,2697,2248,2357,755,1566,2438,2628,945,1213,384,2275,2818,3086,479,1593,2465,1144,2599,1674,859,1239,1334,3113,492,1429,1619,2379,749,816,1252,1809,911,3139,1442,1576,2112,3329,1671,870,2207,700,965,1356,2587,2166,2220,1613,2261,2328,754,1327,2641,916,1184,2274,2355,478,1564,2436,1381,2598,1211,858,1238,2693,3084,505,639,1618,2378,720,829,1265,1332,2159,910,3138,1427,1589,2349,747,1670,855,2206,937,3109,488,1369,2586,2375,1697,868,2233,1136,963,1231,1326,2164,1421,1611,2259,2354,696,1801,2449,1352,2583,1210,2216,3097,476,638,1379,2596,733,800,1236,2691,2158,447,1426,1560,2253,2320,746,827,1207,854,2633,908,3080,501,1587,2347,2374,1668,881,2204,1149,3107,962,1230,1311,2401,743,1610,2258,933,1257,1324,1365,2582,1419,1581,2229,847,1378,2609,256,1473,2690,1607,2143,446,636,1797,2333,731,826,1206,2156,921,3093,472,1586,2251,2346,688,1681,852,2441,1120,2575,3106,499,1310,3201,2372,742,823,1147,2629,904,1228,1337,2343,1418,1552,2200,931,1199,846,1363,2580,493,1579,2227,1606,2142,873,125 3,1320,730,1415,1633,2169,444,1795,2250,2331,701,1204,1357,2574,3091,498,632,2221,2385,727,822,1146,2601,2152,917,1241,1308,2247,2342,740,1565,2437,2627,930,1198,383,1362,2817,3085,464,1578,2226,1143,1673,844,1224,1333,491,1414,1604,2140,815,1251,1794,2330,672,1441,1575,2111,3090,869,2192,699,726,1355,2572,2165,440,2219,2246,2327,753,820,1088,2626,915,1183,382,2273,2340,477,1563,2435,1142,2597,1196,857,1237,1304,3083,490,624,1617,2377,719,814,1250,1331,909,3137,1412,1574,2110,1669,840,2205,698,487,1354,2585,2136,867,2218,1135,2326,724,1325,2163,914,1182,2244,2353,695,1562,2434,1351,2568,1209,380,2215,3082,475,637,1140,2595,718,799,1235,1330,2157,432,1425,1559,2319,745,812,1192,853,907,3079,486,1572,2108,2373,1667,866,2203,1134,961,1229,1296,2162,1609,2257,2324,694,1323,1350,2581,1180,2214,474,608,1377,2594,255,798,1234,2689,2128,445,635,1558,2318,716,825,1205,376,2155,906,3078,471,1585,2345,687,1666,851,2202,1119,3105,484,1309,2371,741,808,1132,903,1227,1322,2104,1417,1551,2199,692,845,1348,2579,254,2212,1605,2141,416,634,1319,729,796,1176,2154,443,470,1556,2249,2316,686,1203,850,1118,2573,3076,497,631,2370,712,821,1145,2151,902,1226,1307,2341,739,1550,2198,929,1197,368,1361,2578,463,1577,2225,1128,843,1223,1318,252,1413,1603,2139,442,576,1793,2329,671,1202,2096,3089,468,630,2191,684,725,792,1116,2571,2150,439,1306,2245,2312,738,819,1087,2625,900,1168,381,2339,462,1548,2196,1141,1195,842,1222,1303,489,623,1602,2138,813,1249,1316,670,1411,1573,2109,839,2190,697,248,1353,2570,2135,438,628,2217,2325,723,818,1086,2148,913,1181,352,2243,2338,680,1561,2433,1112,2567,1194,379,1302,3081,460,622,1139,717,784,1220,1329,431,1410,1544,2080,811,1191,838,668,485,1571,2107,2134,865,2188,1133,722,1295,2161,436,2242,2323,693,1084,1349,2566,1179,378,2213,473,607,1138,2593,240,797,1233,1300,2127,430,620,1557,2317,715,810,1190,375,905,3077,456,1570,2106,1665,836,2201,1104,483,1294,2132,807,1131,2322,664,1321,2103,1178,2184,691,606,1347,2564,253,320,2211,2126,415,633,1080,714,795,1175,374,2153,428,469,1555,2315,685,1188,849,1117,3075,482,616,2369,711,806,1130,901,1225,1292,2102,1549,2197,690,367,1346,2577,224,2210,1127,414,604,1317,251,794,1174,2124,441,575,1554,2314,656,1201,372,2095,3074,467,629,683,710,791,1115,2149,424,1305,2311,737,804,1072,899,1167,366,2100,461,1547,2195,1126,841,1221,1288,250,1601,2137,412,574,1315,669,1172,2094,466,600,2189,682,247,790,1114,2569,2120,437,627,2310,708,817,1085,2147,898,1166,351,2337,679,1546,2194,1111,1193,364,1301,459,621,1124,783,1219,1314,192,1409,1543,2079,572,837,667,246,2092,2133,408,626,2187,721,788,1056,2146,435,350,2241,2308,678,1083,1110,2565,1164,377,458,592,1137,239,782,1218,1299,429,619,1542,2078,809,1189,360,666,455,1569,2105,835,2186,1103,244,1293,2131,434,568,2321,663,1082,2088,1177,348,2183,676,605,1108,2563,238,319,1298,2125,400,618,1079,713,780,1160,373,427,454,1540,2076,1187,834,1102,481,615,2130,805,1129,662,1291,2101,2182,689,128,1345,2562,223,318,2209,413,603,1078,236,793,1173,344,2123,426,560,1553,2313,655,1186,371,3073,452,614,709,776,1100,423,1290,2072,803,1071,660,365,2099,222,2180,1125,602,1287,249,316,2122,411,573,1076,654,1171,370,2093,465,599,681,232,789,1113,2119,422,612,2309,707,802,1070,897,1165,336,2098,1545,2193,1096,363,1286,220,1123,410,544,1313,191,1170,2064,571,598,652,245,312,2091,2118,407,625,706,787,1055,2145,420,349,2307,677,1068,1109,1163,362,457,591,1122,781,1217,1284,190,1541,2077,570,359,665,216,2090,406,596,2185,243,786,1054,2116,433,567,2306,648,1081,2087,1162,347,675,590,1107,237,304,1297,399,617,1064,779,1159,358,188,453,1539,2075,833,1101,242,2129,404,566,661,1052,2086,346,2181,674,127,1106,2561,208,317,398,588,1077,235,778,1158,343,425,559,1538,2074,1185,356,451,613,775,1099,184,1289,2071,564,659,126,2084,221,288,2179,601,1048,234,315,342,2121,396,558,1075,653,1156,369,450,584,231,774,1098,421,611,2070,801,1069,658,335,2097,2178,1095,124,1285,219,314,409,543,1074,176,1169,340,2063,556,597,651,230,311,2117,392,610,705,772,1040,419,334,2068,1067,1094,361,218,1121,542,1283,189,2062,569,120,650,215,310,2089,405,595,228,785,1053,2115,418,552,2305,647,1066,1161,332,589,1092,303,1282,160,1063,540,357,187,214,2060,594,241,308,2114,403,565,646,1051,2085,345,673,112,1105,207,302,397,587,1062,777,1157,328,186,1537,2073,355,212,402,536,183,1050,2056,563,644,125,2083,206,287,586,1047,233,300,341,395,557,1060,1155,354,449,583,773,1097,182,2069,562,657,96,2082,286,2177,123,1046,204,313,394,528,1073,175,1154,339,555,582,229,296,391,609,771,1039,180,333,2067,1093,122,217,284,541,1044,174,338,2061,554,119,649,200,309,390,580,227,770,1038,417,551,2066,1065,331,1091,64,1281,159,539,118,172,213,280,2059,593,226,307,2113,388,550,645,1036,330,111,1090,301,158,1061,538,327,185,2058,116,211,306,401,535,168,1049,2055,548,643,110,205,272,585,1032,299,326,156,1059,353,210,534,181,2054,561,642,95,2081,285,108,1045,203,298,393,527,1058,1153,324,581,295,152,532,179,94,2052,121,202,283,526,1043,173,337,553,104,199,294,389,579,769,1037,178,2065,92,282,63,1042,144,524,117,171,198,279,578,225,292,387,549,1035,329,1089,62,157,537,88,170,278,2057,115,196,305,386,520,167,1034,547,109,271,1031,60,325,155,114,209,276,533,166,2053,546,641,80,270,107,1030,297,154,1057,323,56,151,531,164,93,2051,106,201,268,525,1028,322,103,293,150,530,177,2050,91,281,48,1041,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,1033,32,59,86,140,113,194,275,518,165,545,7 9,269,1029,58,153,84,274,55,136,516,163,78,105,267,1027,321,54,149,529,162,2049,76,266,47,1026,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,1025,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1。
  34. 如权利要求33所述的设备，当所述第一极化权重向量的最小序号为0时，所述第一极化权重向量中的每个序号依次减1。
  35. 如权利要求19-34中任一权利要求所述的设备，第一极化信道的极化权重大于第二极化信道时，在所述第一极化权重向量中，第一极化信道在第二极化信道之前。
  36. 如权利要求33所述的设备，所述极化信道按极化权重从大到小排序时，所述第一极化权重向量为所述极化权重向量按逆序依次读取形成的向量。
  37. 一种通信装置，其特征在于，包括：
    存储器，用于存储执行操作的指令；
    处理器，与所述存储器耦合，根据所述指令用于：确定N个待编码比特，所述N个待编码比特中包含信息比特和固定比特，N为正整数；获取包含N个极化信道的极化权重的第一极化权重向量，所述极化权重是选择信息比特的依据，所述N个待编码比特对应所述N个极化信道；根据所述第一极化权重向量确定所述信息比特的位置；对所述N个待编码比特进行Polar编码，获得Polar编码后的比特。
  38. 根据权利要求37所述的通信装置，其特征在于，Polar码的目标码长M等于2的正整数次幂，N为正整数，所述处理器用于：
    确定N等于M，所述Polar码的目标码长为Polar码的输出码长；
    计算所述N个极化信道的极化权重，得到所述第一极化权重向量。
  39. 根据权利要求38所述的通信装置，其特征在于，所述处理器用于：
    根据如下公式计算所述N个极化信道的极化权重Wi，得到所述第一极化权重向量：
    Figure PCTCN2017090359-appb-100041
    其中，
    Figure PCTCN2017090359-appb-100042
    i为信道索引，Bn-1Bn-2…B0为i的二进制表示，其中Bn-1为最高位，B0为最低位，Bj∈{0,1}，j∈{0,1,···,n-1}，i∈{0,1,···,N-1}，N＝2n，φ与α为根据Polar码的目标码长和码率预设的参数，n为正整数。
  40. 根据权利要求38所述的通信装置，其特征在于，所述处理器用于：
    根据如下公式通过递归计算得到所述第一极化权重向量W0 N-1：
    βi＝(2i-1+φ)α；
    Figure PCTCN2017090359-appb-100043
    Figure PCTCN2017090359-appb-100044
    其中，
    Figure PCTCN2017090359-appb-100045
    其中，i∈{1,···,N-1}，βi为与信道索引i有关的中间变量，φ与α为根据Polar码的目标码长和码率预设的参数，W0为任意常数。
  41. 根据权利要求37所述的通信装置，其特征在于，Polar码的目标码长M等于2的正整数次幂，所述处理器用于：
    从预先存储的第二极化权重向量中获取所述第一极化权重向量，所述第二极化权重向量包含Nmax个极化信道的极化权重，Nmax为预设的通信系统支持的最大码长所对应的母码码长，母码码长为2的正整数次幂。
  42. 根据权利要求41所述的通信装置，其特征在于，
    Polar码的目标码长M＜＝Nmax时，所述第一极化权重向量中的元素集合为所述 第二极化权重向量中的元素集合的子集；
    Polar码的目标码长M＞＝Nmax时，信道索引小于或等于Nmax的极化信道的极化权重与所述第二极化权重向量中的极化权重一一对应，信道索引大于Nmax的极化信道的极化权重等于对应的所述信道索引小于或等于Nmax的极化信道的极化权重加上权重增量
    Figure PCTCN2017090359-appb-100046
    其中，φ与α为根据Polar码的目标码长和码率预设的参数。
  43. 根据权利要求42所述的通信装置，其特征在于，Polar码的目标码长M不等于2的正整数次幂，所述第一确定模块具体用于：
    确定
    Figure PCTCN2017090359-appb-100047
    符号
    Figure PCTCN2017090359-appb-100048
    表示向下取整。
  44. 根据权利要求43所述的通信装置，其特征在于，所述处理器还用于：
    在获取包含N个极化信道的极化权重的第一极化权重向量之前，确定所述N个待编码比特中要删除的N-M个比特的位置；
    根据所述第三确定模块确定的结果计算包含N个待编码比特对应的极化权重的修正系数集合，所述修正系数用于表征删除的比特对每一极化权重的修正量；
    根据所述修正系数集合计算所述N个极化信道的极化权重，得到所述第一极化权重向量。
  45. 根据权利要求44所述的通信装置，其特征在于，所述处理器用于：
    确定所述N个极化信道的信道索引序列
    Figure PCTCN2017090359-appb-100049
    对所述信道索引序列中的每一个索引，进行如下操作：
    将每一索引对应的二进制数进行比特逆序，再转化为十进制数，得到新的信道索引序列
    Figure PCTCN2017090359-appb-100050
    对新的信道索引序列
    Figure PCTCN2017090359-appb-100051
    中的索引排序；
    按照从小到大的顺序选择所述信道索引序列
    Figure PCTCN2017090359-appb-100052
    中的N-M个为要删除的比特索引。
  46. 根据权利要求45所述的通信装置，其特征在于，
    所述修正系数集合
    Figure PCTCN2017090359-appb-100053
    所述处理器用于按照如下公式计算所述修正系数集合g中的每一项g(i,j)：
    Figure PCTCN2017090359-appb-100054
    Figure PCTCN2017090359-appb-100055
    其中，i∈{0,1,···,N-1}，j∈{0,1,···,n-1}，N＝2n，pi为信道索引为i的极化信道对应的比特是否要被删除的标识，pi∈{0,1}。
  47. 根据权利要求43～46任一项所述的通信装置，其特征在于，所述处理器用于：
    根据如下公式计算所述N个极化信道的极化权重Wi，得到所述第一极化权重向量：
    Figure PCTCN2017090359-appb-100056
    其中，
    Figure PCTCN2017090359-appb-100057
    i为信道索引，Bn-1Bn-2…B0为i的二进制表示，其中Bn-1为最高位，B0为最低位，Bj∈{0,1}，j∈{0,1,···,n-1}，i∈{0,1,···,N-1}，N＝2n，g(i,j)为修正系数集合g中第i行第j列的元素,φ与α为根据Polar码的目标码长和码率预设的参数。
  48. 根据权利要求43～46任一项所述的通信装置，其特征在于，所述处理器用于：
    根据如下公式通过递归计算得到所述第一极化权重向量W0 N-1：
    βi＝(2i-1+φ)α；
    Figure PCTCN2017090359-appb-100058
    Figure PCTCN2017090359-appb-100059
    其中，
    Figure PCTCN2017090359-appb-100060
    其中，i∈{1,···,N-1}，βi为与信道索引i有关的中间变量，φ与α为根据Polar码的目标码长和码率预设的参数，g(i,j)为修正系数集合g中第i行第j列的元素，W0为任意常数。
  49. 根据权利要求39或40或42或47或48所述的通信装置，其特征在于，φ＝0，α＝1/4。
  50. 根据权利要求37所述的通信装置，其特征在于，所述处理器用于：
    将所述第一极化权重向量中的极化权重从大到小进行排序，选择前K个极化权重对应的比特作为所述信息比特。
  51. 根据权利要求37-50中任一权利要求所述的通信装置，其特征在于，当所述第一极化权重向量中的极化信道按极化权重从大到小排序且所述极化信道的序号最小值为1时：
    若N＝16，所述第一极化权重向量为下列极化权重向量：
    16,15,14,12,8,13,11,10,7,6,4,9,5,3,2,1；或
    若N＝32，所述第一极化权重向量为下列极化权重向量：
    32,31,30,28,24,16,29,27,26,23,22,15,20,14,12,25,8,21,19,13,18,11,10,7,6,4,17,9,5,3,2,1；或
    若N＝64，所述第一极化权重向量为下列极化权重向量：
    64,63,62,60,56,48,61,32,59,58,55,54,47,52,46,31,44,30,57,40,28,53,24,51,45,50,16,43,29,42,39,27,38,26,23,36,22,49,15,20,14,41,12,37,25,8,35,21,34,19,13,18,11,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝128，所述第一极化权重向量为下列极化权重向量：
    128,127,126,124,120,112,125,96,123,122,119,64,118,111,116,110,95,108,94,121,104,92,63,117,62,88,115,109,60,114,80,107,56,93,106,103,91,48,102,90,61,87,100,32,59,86,113,79,58,84,55,78,105,54,76,47,101,52,89,46,72,99,31,44,85,98,30,57,83,40,77,28,82,53,75,24,51,74,45,71,50,16,43,70,97,29,42,68,39,27,81,38,26,23,36,73,22,49,15,69,20,14,41,67,12,66,37,25,8,35,21,34,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝256，所述第一极化权重向量为下列极化权重向量：
    256,255,254,252,248,240,253,224,251,250,247,192,246,239,244,238,128,223,236,222,249,232,220,191,245,190,216,243,237,188,242,127,208,235,184,126,221,234,231,124,219,176,230,218,189,120,215,228,160,187,214,241,112,207,186,212,183,125,206,233,182,96,123,204,175,229,180,122,217,174,119,200,227,64,159,118,172,213,226,111,158,185,116,211,168,110,205,156,210,181,95,108,203,152,179,94,121,202,173,104,199,178,92,63,144,117,171,198,225,62,157,88,170,115,196,167,109,60,155,114,209,166,80,107,154,56,151,164,93,106,201,103,150,177,91,48,143,102,197,148,90,61,142,87,169,100,195,32,59,86,140,113,194,165,79,58,153,84,55,136,163,78,105,54,149,162,76,47,101,52,147,89,46,141,72,99,146,31,44,85,139,98,193,30,57,138,83,40,135,77,28,82,53,134,161,75,24,51,132,74,45,71,50,145,16,43,70,97,29,42,137,68,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝512，所述第一极化权重向量为下列极化权重向量：
    512,511,510,508,504,496,509,480,507,506,503,448,502,495,500,494,384,479,492,478,505,488,476,447,501,256,446,472,499,493,444,498,383,464,491,440,382,477,490,487,380,475,432,486,474,255,445,376,471,484,254,416,443,470,497,368,463,252,442,468,439,381,462,489,248,438,352,379,460,431,485,436,378,473,240,430,375,456,483,253,320,415,374,428,469,482,367,224,414,251,441,372,467,424,366,461,250,412,466,247,437,351,364,459,192,246,408,435,350,377,458,239,429,360,455,244,434,348,238,319,400,373,427,454,481,128,223,318,413,236,344,426,371,452,423,365,222,249,316,411,370,465,232,422,336,363,220,410,191,245,312,407,420,349,362,457,190,359,216,406,243,433,347,237,304,399,358,188,453,242,404,346,127,208,317,398,235,343,425,356,451,184,126,221,288,234,315,342,396,369,450,231,421,335,124,219,314,409,176,340,230,311,392,419,334,361,218,189,120,215,310,405,228,418,332,303,160,357,187,214,241,308,403,345,112,207,302,397,328,186,355,212,402,183,125,206,287,233,300,341,395,354,449,182,96,286,123,204,313,394,175,339,229,296,391,180,333,122,217,284,174,338,119,200,309,390,227,417,331,64,159,118,172,213,280,226,307,388,330,111,301,158,327,185,116,211,306,401,168,110,205,272,299,326,156,353,210,181,95,285,108,203,298,393,324,295,152,179,94,121,202,283,173,337,104,199,294,389,178,92,282,63,144,117,171,198,279,225,292,387,329,62,157,88,170,278,115,196,305,386,167,109,271,60,325,155,114,209,276,166,80,270,107,297,154,323,56,151,164,93,106,201,268,322,103,293,150,177,91,281,48,143,102,197,264,291,148,90,61,142,87,169,277,100,195,290,385,32,59,86,140,113,194,275,165,79,269,58,153,84,274,55,136,163,78,105,267,321,54,149,162,76,266,47,101,263,52,147,89,46,141,72,262,99,289,146,31,44,85,139,98,193,260,30,57,138,83,273,40,135,77,28,82,53,134,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝1024，所述第一极化权重向量为下列极化权重向量：
    1024,1023,1022,1020,1016,1008,1021,992,1019,1018,1015,960,1014,1007,1012,1006,896,991,1004,990,1017,1000,988,959,1013,768,958,984,1011,1005,956,1010,895,976,1003,952,894,989,1002,999,512,892,987,944,998,986,767,957,888,983,996,766,928,955,982,1009,880,975,764,954,980,951,893,974,1001,760,950,864,511,891,972,943,997,948,510,890,985,752,942,887,968,995,508,765,832,927,886,940,981,994,879,736,926,763,953,504,884,979,936,878,973,762,924,978,759,949,863,496,876,971,704,758,920,947,862,509,889,970,751,941,872,967,756,946,480,860,507,750,831,912,885,939,966,993,506,640,735,830,925,748,856,938,503,883,964,935,877,734,448,761,828,923,502,882,977,744,934,848,495,875,732,922,703,500,757,824,919,932,861,494,874,969,702,871,728,918,755,945,384,479,859,492,749,816,911,870,700,965,754,916,478,858,505,639,720,829,910,747,855,937,488,868,963,696,476,638,733,800,447,746,827,854,908,501,881,962,743,933,847,256,446,636,731,826,921,472,688,852,499,742,823,904,931,846,493,873,730,444,701,498,632,727,822,917,740,930,383,464,844,491,815,672,869,699,726,440,753,820,915,382,477,857,490,624,719,814,909,840,698,487,867,724,914,695,380,475,637,718,799,432,745,812,853,907,486,866,961,694,474,608,255,798,445,635,716,825,376,906,471,687,851,484,741,808,903,692,845,254,416,634,729,796,443,470,686,850,497,631,712,821,902,739,929,368,463,843,252,442,576,671,468,630,684,725,792,439,738,819,900,381,462,842,489,623,813,670,839,697,248,438,628,723,818,913,352,680,379,460,622,717,784,431,811,838,668,485,865,722,436,693,378,473,607,240,797,430,620,715,810,375,905,456,836,483,807,664,691,606,253,320,415,633,714,795,374,428,469,685,849,482,616,711,806,901,690,367,224,414,604,251,794,441,575,656,372,467,629,683,710,791,424,737,804,899,366,461,841,250,412,574,669,466,600,682,247,790,437,627,708,817,898,351,679,364,459,621,783,192,572,837,667,246,408,626,721,788,435,350,678,377,458,592,239,782,429,619,809,360,666,455,835,244,434,568,663,348,676,605,238,319,400,618,713,780,373,427,454,834,481,615,805,662,689,128,223,318,413,603,236,793,344,426,560,655,371,452,614,709,776,423,803,660,365,222,602,249,316,411,573,654,370,465,599,681,232,789,422,612,707,802,897,336,363,220,410,544,191,571,598,652,245,312,407,625,706,787,420,349,677,362,457,591,781,190,570,359,665,216,406,596,243,786,433,567,648,347,675,590,237,304,399,617,779,358,188,453,833,242,404,566,661,346,674,127,208,317,398,588,235,778,343,425,559,356,451,613,775,184,564,659,126,221,288,601,234,315,342,396,558,653,369,450,584,231,774,421,611,801,658,335,124,219,314,409,543,176,340,556,597,651,230,311,392,610,705,772,419,334,361,218,542,189,569,120,650,215,310,405,595,228,785,418,552,647,332,589,303,160,540,357,187,214,594,241,308,403,565,646,345,673,112,207,302,397,587,777,328,186,355,212,402,536,183,563,644,125,206,287,586,233,300,341,395,557,354,449,583,773,182,562,657,96,286,123,204,313,394,528,175,339,555,582,229,296,391,609,771,180,333,122,217,284,541,174,338,554,119,649,200,309,390,580,227,770,417,551,331,64,159,539,118,172,213,280,593,226,307,388,550,645,330,111,301,158,538,327,185,116,211,306,401,535,168,548,643,110,205,272,585,299,326,156,353,210,534,181,561,642,95,285,108,203,298,393,527,324,581,295,152,532,179,94,121,202,283,526,173,337,553,104,199,294,389,579,769,178,92,282,63,144,524,117,171,198,279,578,225,292,387,549,329,62, 157,537,88,170,278,115,196,305,386,520,167,547,109,271,60,325,155,114,209,276,533,166,546,641,80,270,107,297,154,323,56,151,531,164,93,106,201,268,525,322,103,293,150,530,177,91,281,48,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,32,59,86,140,113,194,275,518,165,545,79,269,58,153,84,274,55,136,516,163,78,105,267,321,54,149,529,162,76,266,47,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝2048，所述第一极化权重向量为下列极化权重向量：
    2048,2047,2046,2044,2040,2032,2045,2016,2043,2042,2039,1984,2038,2031,2036,2030,1920,2015,2028,2014,2041,2024,2012,1983,2037,1792,1982,2008,2035,2029,1980,2034,1919,2000,2027,1976,1918,2013,2026,2023,1536,1916,2011,1968,2022,2010,1791,1981,1912,2007,2020,1790,1952,1979,2006,2033,1904,1999,1788,1978,2004,1975,1917,1998,2025,1024,1784,1974,1888,1535,1915,1996,1967,2021,1972,1534,1914,2009,1776,1966,1911,1992,2019,1532,1789,1856,1951,1910,1964,2005,2018,1903,1760,1950,1787,1977,1528,1908,2003,1960,1902,1997,1786,1948,1023,2002,1783,1973,1887,1520,1900,1995,1728,1022,1782,1944,1971,1886,1533,1913,1994,1775,1965,1896,1991,1020,1780,1970,1504,1884,1531,1774,1855,1936,1909,1963,1990,2017,1016,1530,1664,1759,1854,1949,1772,1880,1962,1527,1907,1988,1959,1901,1758,1472,1785,1852,1947,1526,1906,1008,2001,1768,1958,1872,1519,1899,1756,1946,1727,1021,1524,1781,1848,1943,1956,1885,1518,1898,1993,1726,992,1895,1752,1019,1942,1779,1969,1408,1503,1883,1516,1773,1840,1935,1894,1724,1989,1018,1778,1940,1502,1015,1882,1529,1663,1744,1853,1934,1771,1879,1961,1512,1892,1987,960,1720,1014,1500,1662,1757,1824,1471,1770,1851,1878,1932,1525,1905,1007,1986,1767,1957,1871,1012,1280,1470,1660,1755,1850,1945,1496,1712,1876,1006,1523,1766,1847,1928,1955,1870,1517,1897,1754,1468,1725,896,991,1522,1656,1751,1846,1004,1941,1764,1954,1407,1488,1868,1515,1839,1696,990,1893,1723,1750,1017,1464,1777,1844,1939,1406,1501,1000,1881,1514,1648,1743,1838,1933,1864,1722,1511,988,1891,1748,959,1938,1719,1013,1404,1499,1661,1742,1823,1456,1769,1836,1877,1931,1510,1890,768,1985,958,1718,984,1498,1632,1011,1279,1822,1469,1659,1740,1849,1400,1930,1495,1711,1875,1005,1508,1765,1832,1927,956,1716,1869,1010,1278,1440,1658,1753,1820,1467,1494,1710,895,1874,976,1521,1655,1736,1845,1003,1926,1763,1953,1392,1487,1867,952,1276,1466,1600,1695,894,989,1492,1654,1708,1749,1816,1002,1463,1762,1843,1924,1405,1486,999,1866,1513,1647,1837,1694,512,1863,1721,892,1272,987,1462,1652,1747,1842,944,1937,1376,1704,998,1403,1484,1646,1741,1808,1455,1835,1862,1692,1509,986,1889,767,1746,957,1460,1717,888,983,1402,1497,1631,996,1264,1821,1454,1644,1739,1834,1399,1929,1480,1860,766,1507,928,1831,1688,955,982,1715,1630,1009,1277,1344,1439,1657,1738,1819,1398,1452,1493,1709,880,1873,975,1506,1640,1735,1830,764,1925,954,1714,1391,980,1248,1438,1628,951,1275,1818,1465,1599,1680,893,1396,974,1491,1653,1707,1734,1815,1001,1448,1761,1828,1923,1390,1485,760,1865,950,1274,1436,1598,1693,864,511,1490,1624,1706,891,1271,1814,972,1461,1651,1732,1841,943,1922,1375,1703,997,1388,1483,1645,1807,948,1216,510,1596,1861,1691,890,1270,985,1432,1650,752,1745,1812,942,1459,1374,1702,887,968,1401,1482,1616,995,1263,1806,1453,1643,1833,1384,1690,1479,508,1859,765,832,1268,927,1458,1592,1687,886,940,981,1372,1700,1629,994,1262,1343,1424,1642,1737,1804,1397,1451,1478,879,1858,736,1505,1639,926,1829,763,1686,953,504,1713,884,1152,979,1247,1342,1437,1627,936,1260,1817,1368,1450,1584,1679,878,1395,973,1476,1638,1733,1800,762,1447,924,1827,1684,1389,978,1246,759,1626,949,1273,1340,1435,1597,1678,863,1394,496,1489,1623,1705,876,1256,1813,971,1446,1636,1731,1826,704,1921,1360,758,1387,920,1244,1434,1568,947,1215,862,509,1595,1622,1676,889,1269,1336,970,1431,1649,751,1730,1811,941,1444,1373,1701,872,967,1386,1481,1615,756,1805,946,1214,480,1594,1383,1689,860,1240,507,1430,1620,750,831,1267,1810,912,1457,1591,1672,885,939,966,1371,1699,1614,993,1261,1328,1423,1641,1803,1382,1212,1477,506,640,1857,735,830,1266,925,1428,1590,748,1685,856,938,503,1370,1698,883,1151,964,1232,1341,1422,1612,935,1259,1802,1367,1449,1583,877,1380,734,1475,1637,448,1799,761,828,1208,923,502,1588,1683,882,1150,977,1245,1312,744,1625,934,1258,1339,1366,1420,1582,1677,848,1393,495,1474,1608,875,1255,1798,732,1445,1635,922,1825,703,1682,1359,500,757,824,1148,919,1243,1338,1433,1567,932,1200,861,1364,494,1580,1621,1675,874,1254,1335,969,1416,1634,1729,1796,702,1443,1358,871,728,1385,918,1242,755,1566,945,1213,384,479,1593,1144,1674,859,1239,1334,492,1429,1619,749,816,1252,1809,911,1442,1576,1671,870,700,965,1356,1613,754,1327,916,1184,478,1564,1381,1211,858,1238,505,639,1618,720,829,1265,1332,910,1427,1589,747,1670,855,937,488,1369,1697,868,1136,963,1231,1326,1421,1611,696,1801,1352,1210,476,638,1379,733,800,1236,447,1426,1560,746,827,1207,854,908,501,1587,1668,881,1149,962,1230,1311,743,1610,933,1257,1324,1365,1419,1581,847,1378,256,1473,1607,446,636,1797,731,826,1206,921,472,1586,688,1681,852,1120,499,1310,742,823,1147,904,1228,1337,1418,1552,931,1199,846,1363,493,1579,1606 ,873,1253,1320,730,1415,1633,444,1795,701,1204,1357,498,632,727,822,1146,917,1241,1308,740,1565,930,1198,383,1362,464,1578,1143,1673,844,1224,1333,491,1414,1604,815,1251,1794,672,1441,1575,869,699,726,1355,440,753,820,1088,915,1183,382,477,1563,1142,1196,857,1237,1304,490,624,1617,719,814,1250,1331,909,1412,1574,1669,840,698,487,1354,867,1135,724,1325,914,1182,695,1562,1351,1209,380,475,637,1140,718,799,1235,1330,432,1425,1559,745,812,1192,853,907,486,1572,1667,866,1134,961,1229,1296,1609,694,1323,1350,1180,474,608,1377,255,798,1234,445,635,1558,716,825,1205,376,906,471,1585,687,1666,851,1119,484,1309,741,808,1132,903,1227,1322,1417,1551,692,845,1348,254,1605,416,634,1319,729,796,1176,443,470,1556,686,1203,850,1118,497,631,712,821,1145,902,1226,1307,739,1550,929,1197,368,1361,463,1577,1128,843,1223,1318,252,1413,1603,442,576,1793,671,1202,468,630,684,725,792,1116,439,1306,738,819,1087,900,1168,381,462,1548,1141,1195,842,1222,1303,489,623,1602,813,1249,1316,670,1411,1573,839,697,248,1353,438,628,723,818,1086,913,1181,352,680,1561,1112,1194,379,1302,460,622,1139,717,784,1220,1329,431,1410,1544,811,1191,838,668,485,1571,865,1133,722,1295,436,693,1084,1349,1179,378,473,607,1138,240,797,1233,1300,430,620,1557,715,810,1190,375,905,456,1570,1665,836,1104,483,1294,807,1131,664,1321,1178,691,606,1347,253,320,415,633,1080,714,795,1175,374,428,469,1555,685,1188,849,1117,482,616,711,806,1130,901,1225,1292,1549,690,367,1346,224,1127,414,604,1317,251,794,1174,441,575,1554,656,1201,372,467,629,683,710,791,1115,424,1305,737,804,1072,899,1167,366,461,1547,1126,841,1221,1288,250,1601,412,574,1315,669,1172,466,600,682,247,790,1114,437,627,708,817,1085,898,1166,351,679,1546,1111,1193,364,1301,459,621,1124,783,1219,1314,192,1409,1543,572,837,667,246,408,626,721,788,1056,435,350,678,1083,1110,1164,377,458,592,1137,239,782,1218,1299,429,619,1542,809,1189,360,666,455,1569,835,1103,244,1293,434,568,663,1082,1177,348,676,605,1108,238,319,1298,400,618,1079,713,780,1160,373,427,454,1540,1187,834,1102,481,615,805,1129,662,1291,689,128,1345,223,318,413,603,1078,236,793,1173,344,426,560,1553,655,1186,371,452,614,709,776,1100,423,1290,803,1071,660,365,222,1125,602,1287,249,316,411,573,1076,654,1171,370,465,599,681,232,789,1113,422,612,707,802,1070,897,1165,336,1545,1096,363,1286,220,1123,410,544,1313,191,1170,571,598,652,245,312,407,625,706,787,1055,420,349,677,1068,1109,1163,362,457,591,1122,781,1217,1284,190,1541,570,359,665,216,406,596,243,786,1054,433,567,648,1081,1162,347,675,590,1107,237,304,1297,399,617,1064,779,1159,358,188,453,1539,833,1101,242,404,566,661,1052,346,674,127,1106,208,317,398,588,1077,235,778,1158,343,425,559,1538,1185,356,451,613,775,1099,184,1289,564,659,126,221,288,601,1048,234,315,342,396,558,1075,653,1156,369,450,584,231,774,1098,421,611,801,1069,658,335,1095,124,1285,219,314,409,543,1074,176,1169,340,556,597,651,230,311,392,610,705,772,1040,419,334,1067,1094,361,218,1121,542,1283,189,569,120,650,215,310,405,595,228,785,1053,418,552,647,1066,1161,332,589,1092,303,1282,160,1063,540,357,187,214,594,241,308,403,565,646,1051,345,673,112,1105,207,302,397,587,1062,777,1157,328,186,1537,355,212,402,536,183,1050,563,644,125,206,287,586,1047,233,300,341,395,557,1060,1155,354,449,583,773,1097,182,562,657,96,286,123,1046,204,313,394,528,1073,175,1154,339,555,582,229,296,391,609,771,1039,180,333,1093,122,217,284,541,1044,174,338,554,119,649,200,309,390,580,227,770,1038,417,551,1065,331,1091,64,1281,159,539,118,172,213,280,593,226,307,388,550,645,1036,330,111,1090,301,158,1061,538,327,185,116,211,306,401,535,168,1049,548,643,110,205,272,585,1032,299,326,156,1059,353,210,534,181,561,642,95,285,108,1045,203,298,393,527,1058,1153,324,581,295,152,532,179,94,121,202,283,526,1043,173,337,553,104,199,294,389,579,769,1037,178,92,282,63,1042,144,524,117,171,198,279,578,225,292,387,549,1035,329,1089,62,157,537,88,170,278,115,196,305,386,520,167,1034,547,109,271,1031,60,325,155,114,209,276,533,166,546,641,80,270,107,1030,297,154,1057,323,56,151,531,164,93,106,201,268,525,1028,322,103,293,150,530,177,91,281,48,1041,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,1033,32,59,86,140,113,194,275,518,165,545,79,269,1029,58,153,84,274,55,136,516,163,78,105,267,1027,321,54,149,529,162,76,266,47,1026,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,1025,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1；或
    若N＝4096，所述第一极化权重向量为下列极化权重向量：
    4096,4095,4094,4092,4088,4080,4093,4064,4091,4090,4087,4032,4086,4079,4084,4078,3968,4063,4076,4062,4089,4072,4060,4031,4085,3840,4030,4056,4083,4077,4028,4082,3967,4048,4075,4024,3966,4061,4074,4071,3584,3964,4059,4016,4070,4058,3839,4029,3960,4055,4068,3838,4000,4027,4054,4081,3952,4047,3836,4026,4052,4023,3965,4046,4073,3072,3832,4022,3936,3583,3963,4044,4015,4069,4020,3582,3962,4057,3824,4014,3959,4040,4067,3580,3837,3904,3999,3958,4012,4053,4066,3951,3808,3998,3835,4025,3576,3956,4051,4008,3950,4045,3834,3996,3071,4050,3831,4021,2048,3935,3568,3948,4043,3776,3070,3830,3992,4019,3934,3581,3961,4042,3823,4013,3944,4039,3068,3828 ,4018,3552,3932,3579,3822,3903,3984,3957,4011,4038,4065,3064,3578,3712,3807,3902,3997,3820,3928,4010,3575,3955,4036,4007,3949,3806,3520,3833,3900,3995,3574,3954,3056,4049,3816,4006,2047,3920,3567,3947,3804,3994,3775,3069,3572,3829,3896,3991,2046,4004,3933,3566,3946,4041,3774,3040,3943,3800,3067,3990,3827,4017,3456,3551,2044,3931,3564,3821,3888,3983,3942,3772,4037,3066,3826,3988,3550,3063,3930,3577,3711,3792,3901,3982,2040,3819,3927,4009,3560,3940,4035,3008,3768,3062,3548,3710,3805,3872,3519,3818,3899,3926,3980,3573,3953,3055,4034,3815,4005,2032,3919,3060,3328,3518,3708,3803,3898,3993,3544,3760,3924,3054,3571,3814,3895,3976,2045,4003,3918,3565,3945,3802,3516,3773,2944,3039,3570,3704,3799,3894,3052,3989,3812,2016,4002,3455,3536,2043,3916,3563,3887,3744,3038,3941,3771,3798,3065,3512,3825,3892,3987,3454,3549,2042,3048,3929,3562,3696,3791,3886,3981,2039,3912,3770,3559,3036,3939,3796,3007,3986,3767,3061,3452,3547,3709,1984,3790,3871,3504,2038,3817,3884,3925,3979,3558,3938,2816,4033,3006,3766,3032,2031,3546,3680,3059,3327,3870,3517,3707,3788,3897,3448,3978,3543,2036,3759,3923,3053,3556,3813,3880,3975,3004,2030,3764,3917,3058,3326,3488,3706,3801,3868,3515,3542,3758,2943,3922,3024,3569,3703,3784,3893,3051,3974,1920,3811,2015,4001,3440,3535,2028,3915,3000,3324,3514,3648,3743,2942,3037,3540,3702,3756,3797,3864,3050,3511,3810,3891,2014,3972,3453,3534,2041,3047,3914,3561,3695,3885,3742,2024,2560,3911,3769,2940,3320,3035,3510,3700,3795,3890,2992,3985,3424,3752,2012,3046,3451,3532,3694,1983,3789,3856,3503,2037,3883,3910,3740,3557,3034,3937,2815,3794,3005,3508,3765,2936,3031,3450,1792,3545,3679,1982,3044,3312,3869,3502,3692,2008,3787,3882,3447,3977,3528,2035,3908,2814,3555,2976,3879,3736,3003,3030,2029,3763,3678,3057,3325,3392,3487,3705,1980,3786,3867,3446,3500,3541,2034,3757,2928,3921,3023,3554,3688,3783,3878,2812,3973,3002,1919,2000,3762,3439,3028,3296,2027,3486,3676,2999,3323,3866,3513,3647,3728,2941,3444,3022,3539,3701,1976,3755,3782,3863,3049,3496,1918,3809,3876,2013,3971,3438,3533,2026,2808,3913,2998,3322,3484,3646,3741,2912,2023,2559,3538,3672,3754,2939,3319,3862,3020,3509,3699,3780,3889,1536,2991,3970,3423,1916,3751,2011,3045,3436,3531,3693,1968,3855,2996,3264,2022,2558,3644,3909,3739,2938,3318,3033,3480,3698,2800,3793,3860,2990,3507,3422,3750,2935,2010,3016,3449,1791,3530,3664,1981,3043,3311,3854,1912,3501,3691,2007,3881,3432,3738,3527,2020,2556,3907,2813,2880,3316,2975,3506,3640,3735,2934,2988,3029,3420,1790,3748,3677,1952,3042,3310,3391,3472,3690,1979,2006,3785,3852,3445,3499,3526,2033,2927,3906,2784,3553,3687,2974,3877,2811,3734,3001,1904,2552,1999,3761,2932,3200,3027,3295,3390,1788,3485,3675,1978,2984,3308,3865,3416,3498,3632,2004,3727,2926,3443,3021,3524,3686,1975,3781,3848,2810,3495,2972,1917,3875,1998,3732,3437,3026,3294,2025,2807,3674,2997,3321,3388,3483,3645,1024,3726,2911,3442,1784,2544,3537,3671,1974,3753,2924,3304,3861,3019,3494,3684,1888,3779,3874,1535,2752,3969,3408,1915,1996,2806,3435,2968,3292,1967,3482,3616,2995,3263,2910,2021,2557,3643,3670,3724,2937,3317,3384,3018,3479,3697,1972,2799,3778,3859,1534,2989,3492,3421,1914,3749,2920,2009,3015,3434,1776,3529,3663,1966,2804,3853,2994,1911,3262,1992,2528,3642,3431,3737,2908,3288,2019,2555,3478,3668,2798,2879,3315,3858,2960,3505,3639,3720,2933,1532,2987,3014,3419,1789,1856,3747,3662,1951,3041,3309,3376,1910,3471,3689,1964,2005,3851,3430,3260,3525,2018,2554,2688,3905,2783,2878,3314,2973,3476,3638,2796,3733,2904,2986,1903,2551,3418,1760,3746,2931,3199,1950,3012,3280,3389,1787,3470,3660,1977,1528,2983,3307,3850,3415,1908,3497,3631,2003,2925,3428,2782,3523,3685,1960,2496,3847,2809,2876,3256,2971,1902,2550,3636,1997,3731,2930,3198,3025,3293,3360,1786,2792,3673,1948,2982,3306,3387,3414,3468,3630,1023,2002,3725,2896,3441,1783,2543,3522,3656,1973,2923,3303,3846,2780,3493,3683,2970,1887,3873,1520,2751,3730,3407,1900,2548,1995,2805,2872,3196,2967,3291,3386,1728,3481,3615,1022,2980,3248,2909,3412,1782,2542,3628,3669,1944,3723,2922,3302,3383,3017,3464,3682,1971,1886,3777,3844,1533,2750,3491,3406,1913,2919,1994,2776,3433,1775,2966,3290,1965,2803,3614,2993,1896,3261,2432,1991,2527,3641,1020,3192,3722,2907,3287,3382,1780,2540,3477,3667,1970,2797,2864,3300,3857,1504,2959,3490,3624,1884,3719,2918,1531,2748,3013,3404,1774,1855,3661,1936,2802,3375,2964,1909,3232,1963,1990,2526,3612,3429,3259,2906,3286,2017,2553,2687,3666,2768,2877,3313,3380,2958,3475,3637,1016,2795,3718,2903,1530,2985,1664,2536,3417,1759,1854,3745,2916,3184,1949,3011,3279,3374,1772,1880,3469,3659,1962,1527,2744,3849,3400,1907,3258,1988,2524,2686,3427,2781,2848,3284,1959,2495,3474,3608,2794,2875,3255,2902,2956,1901,2549,3635,1758,3716,2929,3197,1472,3010,3278,3359,1785,1852,2791,3658,1947,1526,2981,3305,3372,3413,1906,3467,3629,1008,2001,2895,3426,1768,2304,3521,3655,1958,2494,2684,3845,2779,2874,3254,2969,1872,2520,3634,1519,2736,3729,2900,3168,1899,2547,3358,1756,2790,2871,3195,1946,2952,3276,3385,1727,3466,3600,1021,1524,2979,3247,2894,3411,1781,1848,2541,3627,3654,1943,2921,3301,3368,2778,3463,3681,1956,2492,1885,3843,1518,2749,3252,3405,1898,2546,2680,1993,2775,2870,3194,2965,3289,3356,1726,2788,3613,992,2978,1895,3246,2431,3410,1752,2512,3626,1019,3191,1942,3721,2892,3272,3381,1779,2539,3462,3652,1969,1408,2863,3299,3842,1503,2720,3489,3623,1883,2917,1516,2747,2774,3403,1773,1840,2488,1935,2801,2868,3136,2963,1894,3231,2430,1724,1 989,2525,3611,1018,3190,3244,2905,3285,3352,1778,2538,2672,3665,1940,2767,2862,3298,3379,1502,2957,3460,3622,1015,1882,3717,2888,1529,2746,1663,2535,3402,1744,1853,2915,3183,1934,2772,3373,1771,2962,1879,3230,1961,1512,2743,3610,3399,1892,3257,2428,1987,2523,2685,960,3188,2766,2847,3283,3378,1720,2480,3473,3607,1014,2793,2860,3240,2901,1500,2955,1662,2534,3620,1757,1824,3715,2914,3182,1471,3009,3277,3344,1770,1851,1878,3657,1932,1525,2742,3371,3398,1905,3228,1007,1986,2522,2656,3425,1767,2303,2846,3282,1957,2493,2683,3606,2764,2873,3253,2424,2954,1871,2519,3633,1012,1280,2735,3714,2899,3167,1470,1660,2532,3357,1755,1850,2789,2856,3180,1945,1496,2951,3275,3370,1712,1876,3465,3599,1006,1523,2740,2893,3396,1766,1847,2302,3653,1928,2464,2682,3367,2777,2844,3224,1955,2491,1870,2518,3604,1517,2734,3251,2898,3166,1897,2545,2679,1754,2760,2869,3193,1468,2950,3274,3355,1725,896,2787,3598,991,1522,2977,1656,3245,2416,3409,1751,1846,2511,3625,1004,3176,1941,2891,3271,3366,1764,2300,3461,3651,1954,2490,1407,2624,3841,1488,2719,3250,1868,2516,2678,1515,2732,2773,2840,3164,1839,2487,3354,1696,2786,2867,3135,990,2948,1893,3216,2429,1723,1750,2510,3596,1017,3189,1464,3243,2890,3270,3351,1777,1844,2537,2671,3650,1939,1406,2861,3297,3364,1501,2718,3459,3621,1000,1881,2887,1514,2745,1648,2296,3401,1743,1838,2486,2676,1933,2771,2866,3134,2961,1864,3229,2400,1722,1511,2728,3609,988,3160,1891,3242,2427,3350,1748,2508,2670,959,3187,1938,2765,2832,3268,3377,1719,2479,3458,3592,1013,1404,2859,3239,2886,1499,2716,1661,2533,3619,1742,1823,2913,3181,1456,2770,3343,1769,1836,2484,1877,1931,1510,2741,3132,3397,1890,3227,2426,768,1985,2521,2655,958,3186,2288,2845,3281,3348,1718,2478,2668,3605,984,2763,2858,3238,2423,1498,2953,1632,2504,3618,1011,1279,1822,3713,2884,3152,1469,1659,2531,3342,1740,1849,1400,2855,3179,1930,1495,2712,3369,1711,1875,3226,1005,1508,2739,2654,3395,1765,1832,2301,2368,1927,2463,2681,956,3128,2762,2843,3223,2422,1716,2476,1869,2517,3603,1010,1278,2733,3236,2897,3165,1440,1658,2530,2664,1753,1820,2759,2854,3178,1467,1494,2949,3273,3340,1710,895,1874,3597,976,1521,2738,1655,2415,3394,1736,1845,2272,1003,3175,1926,2462,2652,3365,1763,2299,2842,3222,1953,2489,1392,2623,3602,1487,2704,3249,2420,1867,2515,2677,952,1276,2731,2758,2839,3163,1466,1600,2472,3353,1695,894,2785,2852,3120,989,1492,2947,1654,3215,2414,1708,1749,1816,2509,3595,1002,3174,1463,2889,3269,3336,1762,1843,2298,3649,1924,2460,1405,2622,3363,1486,2717,3220,999,1866,2514,2648,1513,2730,1647,2295,2838,3162,1837,2485,2675,1694,2756,2865,3133,512,2946,1863,3214,2399,1721,892,1272,2727,3594,987,3159,1462,1652,3241,2412,3349,1747,1842,2507,2669,944,3172,1937,1376,2831,3267,3362,1704,2240,3457,3591,998,1403,2620,2885,1484,2715,1646,2294,1741,1808,2456,2674,1455,2769,2836,3104,1835,2483,1862,2398,1692,1509,2726,3131,986,3158,1889,3212,2425,767,1746,2506,2640,957,3185,1460,2287,2830,3266,3347,1717,888,2477,2667,3590,983,1402,2857,3237,2408,1497,2714,1631,2503,3617,996,1264,1821,2883,3151,1454,1644,2292,3341,1739,1834,2482,1399,2616,1929,1480,2711,3130,1860,3225,2396,766,1507,2724,2653,928,3156,1831,2286,2367,3346,1688,2448,2666,955,3127,982,2761,2828,3208,2421,1715,2475,1630,2502,3588,1009,1277,1344,3235,2882,3150,1439,1657,2529,2663,1738,1819,1398,2853,3177,1452,1493,2710,3339,1709,880,1873,975,1506,2737,1640,2176,3393,1735,1830,2271,2366,764,1925,2461,2651,954,3126,2284,2841,3221,2392,1714,2474,1391,2608,3601,980,1248,2703,3234,2419,1438,1628,2500,2662,951,1275,1818,2757,2824,3148,1465,1599,2471,3338,1680,893,1396,2851,3119,974,1491,2708,1653,2413,1707,1734,1815,2270,1001,3173,1448,2650,3335,1761,1828,2297,2364,1923,2459,1390,2621,3124,1485,2702,3219,2418,760,1865,2513,2647,950,1274,2729,2280,2837,3161,1436,1598,2470,2660,1693,864,2755,2850,3118,511,1490,2945,1624,3213,2384,1706,891,1271,1814,3593,972,3144,1461,1651,2411,3334,1732,1841,2268,943,3171,1922,2458,1375,2592,3361,1703,2239,3218,997,1388,2619,2646,1483,2700,1645,2293,2360,1807,2455,2673,948,1216,2754,2835,3103,510,1596,2468,1861,2397,1691,890,1270,2725,3116,985,3157,1432,1650,3211,2410,752,1745,1812,2505,2639,942,3170,1459,1374,2829,3265,3332,1702,887,2238,3589,968,1401,2618,2407,1482,2713,1616,2264,995,1263,1806,2454,2644,1453,1643,2291,2834,3102,1833,2481,1384,2615,1690,1479,2696,3129,508,1859,3210,2395,765,832,1268,2723,2638,927,3155,1458,1592,2285,2352,3345,1687,886,2447,2665,940,3112,981,1372,2827,3207,2406,1700,2236,1629,2501,3587,994,1262,1343,2881,3149,1424,1642,2290,1737,1804,2452,1397,2614,1451,1478,2709,3100,879,1858,2394,736,1505,2722,1639,2175,926,3154,1829,2256,2365,763,1686,2446,2636,953,3125,504,2283,2826,3206,2391,1713,884,2473,1152,2607,3586,979,1247,1342,3233,2404,1437,1627,2499,2661,936,1260,1817,1368,2823,3147,1450,1584,2232,3337,1679,878,1395,2612,973,1476,2707,1638,2174,1733,1800,2269,2336,762,1447,2649,924,3096,1827,2282,2363,2390,1684,2444,1389,2606,3123,978,1246,2701,3204,2417,759,1626,2498,2632,949,1273,1340,2279,2822,3146,1435,1597,2469,2659,1678,863,1394,2849,3117,496,1489,2706,1623,2383,1705,876,1256,1813,971,3143,1446,1636,2172,3333,1731,1826,2267,2362,704,1921,2457,1360,2591,3122,2224,3217,2388,758,1387,2604,2645,920,1244,2699,2278,2359,1434,1568,2440,2658,947,1215,862,2753,2820,3088,509,1595,2467,1622,2382,1676,889,1269,1336,3115,970,3142,1431,1649,2409,751,1730,1811,2266,941,3169,1444,1373,2590,333 1,1701,872,2237,967,1386,2617,2168,1481,2698,1615,2263,2358,756,1805,2453,2643,946,1214,2276,2833,3101,480,1594,2466,1383,2600,1689,860,1240,2695,3114,507,1430,1620,3209,2380,750,831,1267,1810,2637,912,3140,1457,1591,2351,3330,1672,885,2208,939,3111,966,1371,2588,2405,1699,2235,1614,2262,993,1261,1328,2642,1423,1641,2289,2356,1803,2451,1382,2613,1212,1477,2694,3099,506,640,1857,2393,735,830,1266,2721,2160,925,3153,1428,1590,2255,2350,748,1685,856,2445,2635,938,3110,503,1370,2825,3205,2376,1698,883,2234,1151,3585,964,1232,1341,2403,1422,1612,2260,935,1259,1802,2450,1367,2584,1449,1583,2231,3098,877,1380,2611,734,1475,2692,1637,2173,448,1799,2254,2335,761,828,1208,2634,923,3095,502,1588,2281,2348,2389,1683,882,2443,1150,2605,3108,977,1245,1312,3203,2402,744,1625,2497,2631,934,1258,1339,1366,2821,3145,1420,1582,2230,1677,848,1393,2610,495,1474,2705,1608,2144,875,1255,1798,2334,732,1445,1635,2171,922,3094,1825,2252,2361,703,1682,2442,1359,2576,3121,500,2223,3202,2387,757,824,1148,2603,2630,919,1243,1338,2277,2344,1433,1567,2439,2657,932,1200,861,1364,2819,3087,494,1580,2228,1621,2381,1675,874,1254,1335,969,3141,1416,1634,2170,1729,1796,2265,2332,702,1443,1358,2589,3092,871,2222,2386,728,1385,2602,2167,918,1242,2697,2248,2357,755,1566,2438,2628,945,1213,384,2275,2818,3086,479,1593,2465,1144,2599,1674,859,1239,1334,3113,492,1429,1619,2379,749,816,1252,1809,911,3139,1442,1576,2112,3329,1671,870,2207,700,965,1356,2587,2166,2220,1613,2261,2328,754,1327,2641,916,1184,2274,2355,478,1564,2436,1381,2598,1211,858,1238,2693,3084,505,639,1618,2378,720,829,1265,1332,2159,910,3138,1427,1589,2349,747,1670,855,2206,937,3109,488,1369,2586,2375,1697,868,2233,1136,963,1231,1326,2164,1421,1611,2259,2354,696,1801,2449,1352,2583,1210,2216,3097,476,638,1379,2596,733,800,1236,2691,2158,447,1426,1560,2253,2320,746,827,1207,854,2633,908,3080,501,1587,2347,2374,1668,881,2204,1149,3107,962,1230,1311,2401,743,1610,2258,933,1257,1324,1365,2582,1419,1581,2229,847,1378,2609,256,1473,2690,1607,2143,446,636,1797,2333,731,826,1206,2156,921,3093,472,1586,2251,2346,688,1681,852,2441,1120,2575,3106,499,1310,3201,2372,742,823,1147,2629,904,1228,1337,2343,1418,1552,2200,931,1199,846,1363,2580,493,1579,2227,1606,2142,873,1253,1320,730,1415,1633,2169,444,1795,2250,2331,701,1204,1357,2574,3091,498,632,2221,2385,727,822,1146,2601,2152,917,1241,1308,2247,2342,740,1565,2437,2627,930,1198,383,1362,2817,3085,464,1578,2226,1143,1673,844,1224,1333,491,1414,1604,2140,815,1251,1794,2330,672,1441,1575,2111,3090,869,2192,699,726,1355,2572,2165,440,2219,2246,2327,753,820,1088,2626,915,1183,382,2273,2340,477,1563,2435,1142,2597,1196,857,1237,1304,3083,490,624,1617,2377,719,814,1250,1331,909,3137,1412,1574,2110,1669,840,2205,698,487,1354,2585,2136,867,2218,1135,2326,724,1325,2163,914,1182,2244,2353,695,1562,2434,1351,2568,1209,380,2215,3082,475,637,1140,2595,718,799,1235,1330,2157,432,1425,1559,2319,745,812,1192,853,907,3079,486,1572,2108,2373,1667,866,2203,1134,961,1229,1296,2162,1609,2257,2324,694,1323,1350,2581,1180,2214,474,608,1377,2594,255,798,1234,2689,2128,445,635,1558,2318,716,825,1205,376,2155,906,3078,471,1585,2345,687,1666,851,2202,1119,3105,484,1309,2371,741,808,1132,903,1227,1322,2104,1417,1551,2199,692,845,1348,2579,254,2212,1605,2141,416,634,1319,729,796,1176,2154,443,470,1556,2249,2316,686,1203,850,1118,2573,3076,497,631,2370,712,821,1145,2151,902,1226,1307,2341,739,1550,2198,929,1197,368,1361,2578,463,1577,2225,1128,843,1223,1318,252,1413,1603,2139,442,576,1793,2329,671,1202,2096,3089,468,630,2191,684,725,792,1116,2571,2150,439,1306,2245,2312,738,819,1087,2625,900,1168,381,2339,462,1548,2196,1141,1195,842,1222,1303,489,623,1602,2138,813,1249,1316,670,1411,1573,2109,839,2190,697,248,1353,2570,2135,438,628,2217,2325,723,818,1086,2148,913,1181,352,2243,2338,680,1561,2433,1112,2567,1194,379,1302,3081,460,622,1139,717,784,1220,1329,431,1410,1544,2080,811,1191,838,668,485,1571,2107,2134,865,2188,1133,722,1295,2161,436,2242,2323,693,1084,1349,2566,1179,378,2213,473,607,1138,2593,240,797,1233,1300,2127,430,620,1557,2317,715,810,1190,375,905,3077,456,1570,2106,1665,836,2201,1104,483,1294,2132,807,1131,2322,664,1321,2103,1178,2184,691,606,1347,2564,253,320,2211,2126,415,633,1080,714,795,1175,374,2153,428,469,1555,2315,685,1188,849,1117,3075,482,616,2369,711,806,1130,901,1225,1292,2102,1549,2197,690,367,1346,2577,224,2210,1127,414,604,1317,251,794,1174,2124,441,575,1554,2314,656,1201,372,2095,3074,467,629,683,710,791,1115,2149,424,1305,2311,737,804,1072,899,1167,366,2100,461,1547,2195,1126,841,1221,1288,250,1601,2137,412,574,1315,669,1172,2094,466,600,2189,682,247,790,1114,2569,2120,437,627,2310,708,817,1085,2147,898,1166,351,2337,679,1546,2194,1111,1193,364,1301,459,621,1124,783,1219,1314,192,1409,1543,2079,572,837,667,246,2092,2133,408,626,2187,721,788,1056,2146,435,350,2241,2308,678,1083,1110,2565,1164,377,458,592,1137,239,782,1218,1299,429,619,1542,2078,809,1189,360,666,455,1569,2105,835,2186,1103,244,1293,2131,434,568,2321,663,1082,2088,1177,348,2183,676,605,1108,2563,238,319,1298,2125,400,618,1079,713,780,1160,373,427,454,1540,2076,1187,834,1102,481,615,2130,805,1129,662,1291,2101,2182,689,128,1345,2562,223,318,2209,413,603,1078,236,793,1173,344,2123,426,560,1553,2313,655,1186,371,3073,452,614,709,776,1100,423,1290,2072,803,1071,660,365,2099,222,2180,1125,602,1287,249,316,2122,411,573,1076,654,1171,370,2093,465,599,681,232,78 9,1113,2119,422,612,2309,707,802,1070,897,1165,336,2098,1545,2193,1096,363,1286,220,1123,410,544,1313,191,1170,2064,571,598,652,245,312,2091,2118,407,625,706,787,1055,2145,420,349,2307,677,1068,1109,1163,362,457,591,1122,781,1217,1284,190,1541,2077,570,359,665,216,2090,406,596,2185,243,786,1054,2116,433,567,2306,648,1081,2087,1162,347,675,590,1107,237,304,1297,399,617,1064,779,1159,358,188,453,1539,2075,833,1101,242,2129,404,566,661,1052,2086,346,2181,674,127,1106,2561,208,317,398,588,1077,235,778,1158,343,425,559,1538,2074,1185,356,451,613,775,1099,184,1289,2071,564,659,126,2084,221,288,2179,601,1048,234,315,342,2121,396,558,1075,653,1156,369,450,584,231,774,1098,421,611,2070,801,1069,658,335,2097,2178,1095,124,1285,219,314,409,543,1074,176,1169,340,2063,556,597,651,230,311,2117,392,610,705,772,1040,419,334,2068,1067,1094,361,218,1121,542,1283,189,2062,569,120,650,215,310,2089,405,595,228,785,1053,2115,418,552,2305,647,1066,1161,332,589,1092,303,1282,160,1063,540,357,187,214,2060,594,241,308,2114,403,565,646,1051,2085,345,673,112,1105,207,302,397,587,1062,777,1157,328,186,1537,2073,355,212,402,536,183,1050,2056,563,644,125,2083,206,287,586,1047,233,300,341,395,557,1060,1155,354,449,583,773,1097,182,2069,562,657,96,2082,286,2177,123,1046,204,313,394,528,1073,175,1154,339,555,582,229,296,391,609,771,1039,180,333,2067,1093,122,217,284,541,1044,174,338,2061,554,119,649,200,309,390,580,227,770,1038,417,551,2066,1065,331,1091,64,1281,159,539,118,172,213,280,2059,593,226,307,2113,388,550,645,1036,330,111,1090,301,158,1061,538,327,185,2058,116,211,306,401,535,168,1049,2055,548,643,110,205,272,585,1032,299,326,156,1059,353,210,534,181,2054,561,642,95,2081,285,108,1045,203,298,393,527,1058,1153,324,581,295,152,532,179,94,2052,121,202,283,526,1043,173,337,553,104,199,294,389,579,769,1037,178,2065,92,282,63,1042,144,524,117,171,198,279,578,225,292,387,549,1035,329,1089,62,157,537,88,170,278,2057,115,196,305,386,520,167,1034,547,109,271,1031,60,325,155,114,209,276,533,166,2053,546,641,80,270,107,1030,297,154,1057,323,56,151,531,164,93,2051,106,201,268,525,1028,322,103,293,150,530,177,2050,91,281,48,1041,143,523,102,197,264,577,291,148,90,61,142,522,87,169,277,100,195,290,385,519,1033,32,59,86,140,113,194,275,518,165,545,79,269,1029,58,153,84,274,55,136,516,163,78,105,267,1027,321,54,149,529,162,2049,76,266,47,1026,101,263,52,147,89,46,141,521,72,262,99,289,146,31,44,85,139,98,193,260,517,30,57,138,83,273,40,135,515,77,28,82,53,134,514,161,75,265,1025,24,51,132,74,45,71,261,50,145,16,43,70,97,259,29,42,137,68,258,39,27,81,38,133,513,26,23,36,131,73,22,49,130,15,69,20,14,41,67,257,12,66,37,25,8,35,21,34,129,19,13,18,11,65,10,7,6,33,4,17,9,5,3,2,1。
  52. 如权利要求51所述的通信装置，当所述第一极化权重向量的最小序号为0时，所述第一极化权重向量中的每个序号依次减1。
  53. 如权利要求37-52中任一权利要求所述的通信装置，第一极化信道的极化权重大于第二极化信道时，在所述第一极化权重向量中，第一极化信道在第二极化信道之前。
  54. 如权利要求51所述的通信装置，所述极化信道按极化权重从大到小排序时，所述第一极化权重向量为所述极化权重向量按逆序依次读取形成的向量。
  55. 一种计算机存储介质，其特征在于，所述计算机存储介质存储有计算机可执行指令，所述计算机可执行指令在被计算机调用时，使所述计算机执行如权利要求1至18任一权利要求所述的方法。
PCT/CN2017/090359 2016-07-29 2017-06-27 编码方法、设备和装置 WO2018019073A1 (zh)

Priority Applications (6)

Application Number Priority Date Filing Date Title
BR112019001775-5A BR112019001775A2 (pt) 2016-07-29 2017-06-27 método e dispositivo de codificação, e aparelho
JP2019504681A JP6797281B2 (ja) 2016-07-29 2017-06-27 符号化方法およびデバイスならびに装置
EP21152711.4A EP3879729A1 (en) 2016-07-29 2017-06-27 Encoding method and device, and apparatus
EP17833376.1A EP3474472B1 (en) 2016-07-29 2017-06-27 Encoding method, device, and apparatus
US16/261,220 US10879932B2 (en) 2016-07-29 2019-01-29 Encoding method and device, and apparatus
US17/135,061 US11444640B2 (en) 2016-07-29 2020-12-28 Encoding method and device, and apparatus

Applications Claiming Priority (4)

Application Number Priority Date Filing Date Title
CN201610619696.5A CN107666370B (zh) 2016-07-29 2016-07-29 编码方法和设备
CN201610619696.5 2016-07-29
PCT/CN2017/088023 WO2018019044A1 (zh) 2016-07-29 2017-06-13 编码方法和设备
CNPCT/CN2017/088023 2017-06-13

Related Parent Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2017/088023 Continuation WO2018019044A1 (zh) 2016-07-29 2017-06-13 编码方法和设备

Related Child Applications (1)

Application Number Title Priority Date Filing Date
US16/261,220 Continuation US10879932B2 (en) 2016-07-29 2019-01-29 Encoding method and device, and apparatus

Publications (1)

Publication Number Publication Date
WO2018019073A1 true WO2018019073A1 (zh) 2018-02-01

Family

ID=61015651

Family Applications (2)

Application Number Title Priority Date Filing Date
PCT/CN2017/088023 WO2018019044A1 (zh) 2016-07-29 2017-06-13 编码方法和设备
PCT/CN2017/090359 WO2018019073A1 (zh) 2016-07-29 2017-06-27 编码方法、设备和装置

Family Applications Before (1)

Application Number Title Priority Date Filing Date
PCT/CN2017/088023 WO2018019044A1 (zh) 2016-07-29 2017-06-13 编码方法和设备

Country Status (6)

Country Link
US (2) US10879932B2 (zh)
EP (2) EP3879729A1 (zh)
JP (1) JP6797281B2 (zh)
CN (1) CN107666370B (zh)
BR (1) BR112019001775A2 (zh)
WO (2) WO2018019044A1 (zh)

Families Citing this family (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US10637607B2 (en) 2016-09-15 2020-04-28 Huawei Technologies Co., Ltd. Method and apparatus for encoding data using a polar code
US10554223B2 (en) 2016-12-23 2020-02-04 Huawei Technologies Co., Ltd. Apparatus and methods for polar code construction
WO2018127183A1 (en) * 2017-01-09 2018-07-12 Mediatek Inc. Broadcast channel enhancement with polar code
CN108540260B (zh) 2017-03-02 2019-12-24 华为技术有限公司 用于确定Polar码编解码的方法、装置和可存储介质
CN108809486B (zh) * 2017-05-03 2020-09-04 华为技术有限公司 Polar码编译码方法及装置
CN110612681B (zh) * 2017-05-08 2022-09-06 相干逻辑公司 用于传输极性编码的数据的方法和装置
CN110708079B (zh) * 2019-10-25 2021-05-07 北京邮电大学 一种极化码构造方法及装置
CN111698060B (zh) * 2020-06-24 2023-10-20 京信网络系统股份有限公司 编码方法、装置、设备及存储介质
CN111988614B (zh) * 2020-08-14 2022-09-13 深圳前海微众银行股份有限公司 哈希编码优化方法、设备及可读存储介质
CN112737735A (zh) * 2021-01-29 2021-04-30 中山大学 基于极化权重的可见光通信信道的极化编码方法和系统
CN118157687A (zh) * 2022-12-06 2024-06-07 中兴通讯股份有限公司 数据处理方法、设备和存储介质

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2014092502A1 (en) * 2012-12-14 2014-06-19 Samsung Electronics Co., Ltd. Encoding method and apparatus using crc code and polar
CN104079382A (zh) * 2014-07-25 2014-10-01 北京邮电大学 一种基于概率计算的极化码译码器和极化码译码方法
CN105680883A (zh) * 2015-12-23 2016-06-15 华中科技大学 一种极化码和多比特偶校验码级联的纠错编码方法

Family Cites Families (17)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP5374156B2 (ja) * 2005-11-07 2013-12-25 エージェンシー フォー サイエンス， テクノロジー アンド リサーチ データを復号化及び符号化するための装置及び方法
CN102164025B (zh) 2011-04-15 2013-06-05 北京邮电大学 基于重复编码和信道极化的编码器及其编译码方法
CN106899311B (zh) * 2012-09-24 2023-11-03 华为技术有限公司 混合极性码的生成方法和生成装置
CN104079370B (zh) * 2013-03-27 2018-05-04 华为技术有限公司 信道编译码方法及装置
US9768915B2 (en) * 2013-08-20 2017-09-19 Lg Electronics Inc. Method for transmitting data by using polar coding in wireless access system
WO2015180187A1 (zh) * 2014-05-30 2015-12-03 华为技术有限公司 一种打孔的极化码的构造方法和装置
CN105811998B (zh) * 2016-03-04 2019-01-18 深圳大学 一种基于密度演进的极化码构造方法及极化码编译码系统
CN107370560B (zh) * 2016-05-12 2020-04-21 华为技术有限公司 一种极化码的编码和速率匹配方法、装置及设备
US10903857B2 (en) * 2016-06-14 2021-01-26 Lg Electronics Inc. Data retransmission method for polar code, and device therefor
US10291264B2 (en) * 2016-06-17 2019-05-14 Huawei Technologies Co., Ltd. Systems and methods for rate matching when using general polar codes
US10579452B2 (en) * 2016-06-17 2020-03-03 Huawei Technologies Co., Ltd. Systems and methods for rate matching via a heterogeneous kernel when using general polar codes
US10361717B2 (en) * 2016-06-17 2019-07-23 Huawei Technologies Co., Ltd. Apparatus and methods for error detection coding
EP3273602B1 (en) * 2016-07-19 2022-01-26 MediaTek Inc. Low complexity rate matching design for polar codes
US10389484B2 (en) * 2016-07-29 2019-08-20 Lg Electronics Inc. Method for performing polar coding and apparatus therefor
US10049764B2 (en) * 2016-12-13 2018-08-14 Macronix International Co., Ltd. Control method for memory device and memory controller
CN108282259B (zh) * 2017-01-05 2021-02-09 华为技术有限公司 一种编码方法及装置
CN108631916B (zh) * 2017-03-24 2020-03-31 华为技术有限公司 极化Polar码的速率匹配方法和装置、通信装置

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2014092502A1 (en) * 2012-12-14 2014-06-19 Samsung Electronics Co., Ltd. Encoding method and apparatus using crc code and polar
CN104079382A (zh) * 2014-07-25 2014-10-01 北京邮电大学 一种基于概率计算的极化码译码器和极化码译码方法
CN105680883A (zh) * 2015-12-23 2016-06-15 华中科技大学 一种极化码和多比特偶校验码级联的纠错编码方法

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
ARIKAN, E.: "Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels", IEEE TRANSACTION ON INFORMATION THEORY, vol. 55, no. 7, 31 July 2009 (2009-07-31), pages 3051 - 3073, XP011262510 *

Also Published As

Publication number Publication date
US10879932B2 (en) 2020-12-29
JP6797281B2 (ja) 2020-12-09
EP3474472A4 (en) 2019-06-19
US20190165813A1 (en) 2019-05-30
US11444640B2 (en) 2022-09-13
BR112019001775A2 (pt) 2019-05-07
JP2019530269A (ja) 2019-10-17
US20220103189A9 (en) 2022-03-31
CN107666370A (zh) 2018-02-06
EP3474472A1 (en) 2019-04-24
CN107666370B (zh) 2023-09-22
EP3879729A1 (en) 2021-09-15
WO2018019044A1 (zh) 2018-02-01
EP3474472B1 (en) 2021-03-17
US20210194504A1 (en) 2021-06-24

Similar Documents

Publication Publication Date Title
WO2018019073A1 (zh) 编码方法、设备和装置
JP7026763B2 (ja) レートマッチング方法、符号化装置、および通信装置
RU2716739C1 (ru) Способ, аппаратура и устройство полярного кодирования
EP3444980B1 (en) Encoding and rate matching method, apparatus and device for polar code
JP2022066220A (ja) Ｐｏｌａｒ符号符号化方法および装置
WO2018166423A1 (zh) 极化码编码的方法和装置
WO2018157853A1 (zh) 用于确定Polar码编解码的方法、装置和设备
JP6910434B2 (ja) 符号化方法および装置
TWI794260B (zh) 確定傳輸塊大小的方法、裝置及設備
WO2018171401A1 (zh) 一种信息处理方法、装置及设备
WO2019024842A1 (zh) 一种Polar码编码方法及装置
WO2018137552A1 (zh) 一种调整Polar码的方法、装置及编译码装置
JP2018152887A (ja) 改善されたファイルの圧縮及び暗号化
CN114598331A (zh) Polar码的编码方法、编译码方法及装置
WO2018127140A1 (zh) 数据编码及译码的方法和装置
JP6426212B2 (ja) 制限されたキャリー演算による算術コーディングを遂行するための方法及び装置
WO2018161847A1 (zh) 数据处理方法、数据处理装置和通信设备
WO2018228589A1 (zh) 一种编码方法、无线设备和芯片
WO2022057582A1 (zh) 编码方法和装置
WO2019029748A1 (zh) 极化码编码的方法和装置
Wei et al. An improved complementary matching pursuit algorithm for compressed sensing signal reconstruction
US9722921B2 (en) Encoding method and decoding method for a list of identifiers, associated computer program products, transmitter and receiver applying said methods
JPH01136425A (ja) スタック型遂次復号方式

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 17833376

Country of ref document: EP

Kind code of ref document: A1

ENP Entry into the national phase

Ref document number: 2019504681

Country of ref document: JP

Kind code of ref document: A

NENP Non-entry into the national phase

Ref country code: DE

ENP Entry into the national phase

Ref document number: 2017833376

Country of ref document: EP

Effective date: 20190118

REG Reference to national code

Ref country code: BR

Ref legal event code: B01A

Ref document number: 112019001775

Country of ref document: BR

ENP Entry into the national phase

Ref document number: 112019001775

Country of ref document: BR

Kind code of ref document: A2

Effective date: 20190129