WO2018141212A1 - 一种信息的传输方法、译码方法和装置 - Google Patents

一种信息的传输方法、译码方法和装置 Download PDF

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Publication number
WO2018141212A1
WO2018141212A1 PCT/CN2018/073229 CN2018073229W WO2018141212A1 WO 2018141212 A1 WO2018141212 A1 WO 2018141212A1 CN 2018073229 W CN2018073229 W CN 2018073229W WO 2018141212 A1 WO2018141212 A1 WO 2018141212A1
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check
bits
bit
sequence
information
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PCT/CN2018/073229
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English (en)
French (fr)
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张华滋
李榕
乔云飞
罗禾佳
张公正
陈莹
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华为技术有限公司
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Priority to EP18747486.1A priority Critical patent/EP3614589B1/en
Publication of WO2018141212A1 publication Critical patent/WO2018141212A1/zh
Priority to US16/529,514 priority patent/US11133894B2/en

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    • 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
    • H03M13/05—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
    • H03M13/09—Error detection only, e.g. using cyclic redundancy check [CRC] codes or single parity bit
    • 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
    • H03M13/11—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 using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148—Structural properties of the code parity-check or generator matrix
    • H03M13/1174—Parity-check or generator matrices built from sub-matrices representing known block codes such as, e.g. Hamming codes, e.g. generalized LDPC 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
    • H03M13/05—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
    • H03M13/15—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes
    • H03M13/151—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes using error location or error correction polynomials
    • H03M13/157—Polynomial evaluation, i.e. determination of a polynomial sum at a given value
    • 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
    • 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
    • H04L1/0061—Error detection codes
    • 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
    • H04L1/0061—Error detection codes
    • H04L1/0063—Single parity check

Definitions

  • the present application relates to communication technologies, and in particular, to a method, a decoding method and a device for transmitting information.
  • Polar Codes is a new type of channel coding proposed by E. Arlkan in 2008.
  • the polarization code is designed based on Channel Polarization and is the first constructive coding scheme that can prove channel capacity through rigorous mathematical methods.
  • the Polar code is a linear block code. Its generator matrix is G N and its encoding process is among them Is a binary line vector of length N (ie code length); G N is an N ⁇ N matrix, and Here Defined as the Kronecker product of log 2 N matrices F 2 .
  • Some of the bits are used to carry information, called information bits.
  • the set of indexes of these bits is denoted as A; the other part of the bits is set to a fixed value pre-agreed by the transceiver (referred to as fixed bits), and the index is used as a set of indexes.
  • a complementary set a represents C.
  • these fixed bits are usually set to 0, only need to be pre-agreed by the transceiver, and the fixed bit sequence can be arbitrarily set.
  • u A is In the information bit set, u A is the row vector of length K, ie
  • K,
  • the construction process of the Polar code that is, the selection process of the set A, determines the performance of the Polar code.
  • the commonly used information transmission method is to perform Polar coding on the information block to be transmitted to obtain a coding block, and then transmit the data.
  • the error rate of data transmission in this mode is relatively high, and the transmission reliability is low.
  • the present application provides a method and apparatus for information transmission, which is used to solve the commonly used information transmission method, that is, the data to be transmitted, that is, the information block is Polar coded to obtain a coding block, and then transmitted, but the data transmission in this manner The problem of high error rate and low transmission reliability.
  • the first aspect of the present application provides a method for information transmission, including:
  • the sending device encodes the sequence to be encoded according to the preset parameter pair to obtain a coded sequence; the parameter includes the number of check bits, the position of the check bit, and a check equation; the sequence to be encoded The length is K, and the K is an integer greater than 0;
  • the transmitting device transmits the encoded sequence to a receiving device.
  • the number of the check bits is pre-configured, or the number of the check bits is determined according to the length of the list of the decoder, or the number of the check bits is determined according to the code length and the code rate. Or, the number of the check bits is determined according to a pre-configured number of bits, a list length of the decoder, a code length, and a code rate.
  • the number of check bits can be specified by the protocol or configured as 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 , 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 40, 44, 48, 52, 56, 60, 64, and the like.
  • the size of the possible list (also called length) L is 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, and the number of parity bits corresponding to the size L of the list F1 It is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
  • the number of parity bits can also be a combination of the numbers obtained in the above several ways.
  • parity bit is a Parity Check (PC) bit:
  • the number of check bits can be configured as: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 , 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 40, 44, 48, 52, 56, 60, 64, and the like.
  • the size of the possible list (also called length) L is 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, and the number of parity bits corresponding to the size L of the list F1 It is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
  • 2 ))” or “F 2 ceil(log 2 (M))” where a is a coefficient greater than 0, usually 0.75, 1, 1.25, 1.5, etc., where N is the length of the mother code (after encoding) Before the rate matching, K represents the sequence length of the coded (also called the information bit length), M represents the code length (after encoding, after rate matching), F 2 represents the number of check bits, and the function ceil represents rounding up. In practical applications, the rounding may be rounded down, or it may be rounded off. In addition, the number of parity bits may also be a combination of the numbers obtained by the above several methods.
  • the position of the CRC bit is: a bit position selected from a new generation matrix; the new generation matrix is through a CRC
  • the generator matrix performs row-column conversion, and replaces the CRC bits in which only part of the information bits are dependent on the sub-channels having smaller sequence numbers.
  • the parity bit is a PC bit
  • the location of the PC bit is:
  • Presetting a position of the PC bit corresponding to a position of any one bit in the sequence to be encoded, or a position corresponding to a plurality of bits of the sequence to be encoded, where at least two bits of the plurality of bits are discontinuous;
  • said parameter includes the position information and a threshold value Z I Z P at least check threshold;
  • Z I the threshold value information used to represent all of the information sub-subchannels lowest reliability corresponding to reliability;
  • the threshold value Z P is used to indicate the reliability of the subchannel corresponding to the lowest reliability among the subchannel sets in which the reliability is greater than the information threshold Z I and the row weight is the highest among all the syndrome channels.
  • the check equation is determined according to a check equation table; wherein the check equation table includes at least a PC check bit, information Bits and information bits that participate in the check equation.
  • the check equation table also includes fixed bits, shortened bits.
  • the second aspect of the present application provides a method for transmitting information, including:
  • the receiving device receives the encoded sequence sent by the sending device, and the encoded sequence is obtained by encoding the sequence to be encoded according to a preset parameter, where the length of the sequence to be encoded is K, and the K is greater than 0. Integer
  • the receiving device decodes the encoded sequence according to a preset parameter to obtain a decoded sequence; the parameter includes a number of check bits, a position of the check bit, and a check equation.
  • the number of the check bits is pre-configured, or the number of the check bits is determined according to the length of the list of the decoder, or the number of the check bits is determined according to the code length and the code rate. Or, the number of the check bits is determined according to a pre-configured number of bits, a list length of the decoder, a code length, and a code rate.
  • the number of check bits can be specified by the protocol or configured as 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 , 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 40, 44, 48, 52, 56, 60, 64, and the like.
  • the size of the possible list (also called length) L is 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, and the number of parity bits corresponding to the size L of the list F1 It is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
  • the number of parity bits can also be a combination of the numbers obtained in the above several ways.
  • the number of check bits can be configured as: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 , 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 40, 44, 48, 52, 56, 60, 64, and the like.
  • the size of the possible list (also called length) L is 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, and the number of parity bits corresponding to the size L of the list F1 It is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
  • 2 ))” or “F 2 ceil(log 2 (M))” where a is a coefficient greater than 0, usually 0.75, 1, 1.25, 1.5, etc., where N is the length of the mother code (after encoding) Before the rate matching, K represents the sequence length of the coded (also called the information bit length), M represents the code length (after encoding, after rate matching), F 2 represents the number of check bits, and the function ceil represents rounding up. In practical applications, the rounding may be rounded down, or it may be rounded off. In addition, the number of parity bits may also be a combination of the numbers obtained by the above several methods.
  • the parity bit is a CRC bit
  • the location of the CRC bit is:
  • the parity bit is a PC bit
  • the location of the PC bit is:
  • Presetting a position of the PC bit corresponding to a position of any one bit in the sequence to be encoded, or a position corresponding to a plurality of bits of the sequence to be encoded, where at least two bits of the plurality of bits are discontinuous;
  • said parameter includes the position information and a threshold value Z I Z P at least check threshold;
  • Z I the threshold value information used to represent all of the information sub-subchannels lowest reliability corresponding to reliability;
  • the threshold value Z P is used to indicate the reliability of the subchannel corresponding to the lowest reliability among the subchannel sets in which the reliability is greater than the information threshold Z I and the row weight is the highest among all the syndrome channels.
  • the check equation is determined according to a check equation table; wherein the check equation table includes at least a PC check Bits, information bits, and information bits that participate in the check equation.
  • the check equation table further includes fixed bits and shortened bits.
  • the third aspect of the present application provides an information transmission apparatus, including:
  • a processing module configured to encode, according to a preset parameter pair, a sequence to be encoded, to obtain an encoded sequence;
  • the parameter includes a quantity of a check bit, a position of the check bit, and a check equation;
  • the encoded sequence length is K, and the K is an integer greater than 0;
  • a sending module configured to send the encoded sequence to the receiving device.
  • the parity bit is a CRC bit
  • the location of the CRC bit is:
  • the location of the PC bit is:
  • the location of the PC bit corresponds to a position of any one bit in the sequence to be encoded, or a position corresponding to a plurality of bits of the sequence to be encoded, and at least two of the plurality of bits are non-contiguous;
  • said parameter includes the position information and a threshold value Z I Z P at least check threshold;
  • Z I the threshold value information used to represent all of the information sub-subchannels lowest reliability corresponding to reliability;
  • the threshold value Z P is used to indicate the reliability of the subchannel corresponding to the lowest reliability among the subchannel sets in which the reliability is greater than the information threshold Z I and the row weight is the highest among all the syndrome channels.
  • the check equation is determined according to a check equation table; wherein the check equation table may include a PC check bit, Information bits, fixed bits, shortened bits, and information bits that participate in the check equation.
  • a fourth aspect of the present application provides an information transmission apparatus, including:
  • a receiving module configured to receive a coded sequence sent by the sending device, where the encoded sequence is obtained by encoding a sequence to be encoded according to a preset parameter, where the length of the sequence to be encoded is K, the K Is an integer greater than 0;
  • a processing module configured to decode the encoded sequence according to a preset parameter to obtain a decoded sequence; the parameter includes a quantity of the check bit, a position of the check bit, and a check equation.
  • the location of the CRC bit is:
  • the location of the PC bit is:
  • Presetting a position of the PC bit corresponding to a position of any one bit in the sequence to be encoded, or a position corresponding to a plurality of bits of the sequence to be encoded, where at least two bits of the plurality of bits are discontinuous;
  • the location parameter includes at least an information threshold Z I and a check threshold Z P ;
  • the information threshold Z I is used to indicate reliability corresponding to the lowest reliability subchannel in all information subchannels;
  • Z P inspection threshold is used to represent all of the information sub-channel, the reliability information is greater than the threshold value Z I and the heaviest line subchannel lowest reliability corresponding to reliability of the subchannel set.
  • the check equation is determined according to a check equation table; wherein the check equation table includes a PC check bit and an information bit. , fixed bits, shortened bits, and information bits that participate in the check equation.
  • a fifth aspect of the present application provides a decoding method, where a receiving device receives a bit sequence to be decoded from a sending device, where the bit sequence to be decoded includes at least an information bit and at least one parity bit;
  • the serial cancellation list SCL decoding algorithm sequentially decodes the bits to be decoded, and outputs one candidate path with the best metric value; the value 1 ⁇ l ⁇ L, and the L is the width of the SCL.
  • L is an integer greater than or equal to 1;
  • the T candidate path is checked by using the at least one check bit, and the bit sequence in the first candidate path passed by the check is used as a decoding output; T is an integer, and 1 ⁇ T ⁇ l.
  • the metric value is used to indicate the probability of successful decoding calculation by the decoding end, that is, “starting from the candidate path with the best metric value” refers to the path with the highest probability of successful decoding decoding calculated by the decoding end.
  • a sixth aspect of the present application provides a decoding apparatus, including:
  • a receiving module configured to receive, from a sending device, a bit sequence to be decoded; the bit sequence to be decoded includes at least an information bit and at least one parity bit;
  • a processing module configured to sequentially decode the to-be-decoded bit by using a serial offset list SCL decoding algorithm, and output one candidate path with an optimal metric value; the 1 ⁇ l ⁇ L, the L Is the width of the SCL, and the L is an integer greater than or equal to 1;
  • the processing module is further configured to: start from the candidate path with the best metric value, check the T candidate path among the at least one check bit, and check the bit sequence in the first candidate path that passes the check As a decoding output; the T is an integer, and the value 1 ⁇ T ⁇ l.
  • a seventh aspect of the present application provides a sending device, including:
  • a processor configured to encode a sequence to be encoded according to a preset parameter pair to obtain a coded sequence; the parameter includes a quantity of check bits, a position of the check bit, and a check equation;
  • the encoded sequence length is K, and the K is an integer greater than 0;
  • a transmitter configured to send the encoded sequence to a receiving device.
  • the memory may be further included, and the number of the processors is at least one, and the computer executes the instructions for executing the memory storage.
  • the transmission method of the information provided by the first aspect or the various embodiments of the first aspect is performed by causing the transmitting device to perform data interaction with the receiving device through the communication interface.
  • the memory can be integrated inside the processor.
  • the eighth aspect of the present application provides a receiving device, including:
  • a receiver configured to receive a coded sequence sent by the sending device, where the encoded sequence is obtained by encoding a sequence to be encoded according to a preset parameter, where the length of the sequence to be encoded is K, the K Is an integer greater than 0;
  • a processor configured to decode the encoded sequence according to a preset parameter to obtain a decoded sequence; the parameter includes a quantity of the check bit, a position of the check bit, and a check equation.
  • a memory may be further included, and the number of processors is at least one, and an execution instruction for executing the memory storage is performed. Enabling the receiving device to perform data interaction between the second aspect or the second aspect of the second aspect by performing data interaction between the receiving device and the transmitting device, or causing the receiving device to perform the decoding method provided by the fifth aspect .
  • the memory can also be integrated inside the processor.
  • a ninth aspect of the present application provides a readable storage medium, where an execution instruction is stored, and when at least one processor of the transmitting device executes the execution instruction, the sending device performs the first aspect or the first aspect.
  • a method of transmitting information provided by an embodiment.
  • a tenth aspect of the present application provides a readable storage medium, where an execution instruction is stored, and when the at least one processor of the receiving device executes the execution instruction, the receiving device performs the second aspect or the second aspect.
  • the method for transmitting information provided by the embodiment, or the receiving device performs the decoding method provided by the fifth aspect or the various embodiments of the fifth aspect.
  • a ninth aspect of the present application provides a program product, the program product comprising an execution instruction stored in a readable storage medium.
  • the at least one processor of the transmitting device can read the execution instruction from a readable storage medium, and the at least one processor executes the execution instruction such that the transmitting device implements the transmission method of the information provided by the first aspect or the various embodiments of the first aspect.
  • a tenth aspect of the present application provides a program product, the program product comprising an execution instruction stored in a readable storage medium.
  • At least one processor of the receiving device may read the execution instruction from a readable storage medium, and the at least one processor executes the execution instruction such that the receiving device implements the transmission method of the information provided by the second aspect or the various embodiments of the second aspect Or the receiving device performs the decoding method provided by the fifth aspect or the various embodiments of the fifth aspect.
  • the transmitting device encodes the sequence to be encoded according to the preset parameter pair, and obtains the encoded sequence, where the parameter includes the number of check bits and the position of the check bit.
  • the calibration equation, the parameters of the transmitting device need to be set in advance, and then the sequence to be encoded is pre-coded according to the check bit, then the polar code is encoded, and the encoded sequence is sent to the receiving device, thereby effectively reducing the error rate of data transmission. Improve the reliability of data transmission.
  • 1 is a schematic diagram of a basic flow of wireless communication
  • FIG. 2 is a schematic diagram of coding by means of CA-Polar
  • FIG. 3 is a schematic diagram of coding by using a PC-Polar (Parity-check-Polar) method
  • FIG. 5 is a schematic flowchart diagram of Embodiment 1 of a method for transmitting information provided by the present application
  • Figure 6 is a schematic diagram of a tabular representation of a check equation
  • Figure 7 is a schematic diagram of a polynomial [1, 0, 0, 0, 0] using a shift register
  • Figure 8 is a schematic diagram of a polynomial [1, 0, 1, 0, 0] using a shift register
  • FIG. 9 is a schematic diagram of a decoding process of a decoding method of the present application.
  • FIG. 10 is a schematic structural diagram of an embodiment of a device for transmitting information provided by the present application.
  • FIG. 11 is a schematic structural diagram of Embodiment 2 of an information transmission apparatus provided by the present application.
  • FIG. 12 is a schematic structural diagram of an embodiment of a decoding apparatus provided by the present application.
  • the technical solution of the embodiment of the present application can be applied to a 5G communication system or a future communication system, and can also be used in other various wireless communication systems, such as a Global System of Mobile communication (GSM) system, and code division multiple access (CDMA, Code Division Multiple Access system, Wideband Code Division Multiple Access (WCDMA) system, General Packet Radio Service (GPRS), Long Term Evolution (LTE) system, LTE Frequency Division Duplex (FDD) system, LTE Time Division Duplex (TDD), Universal Mobile Telecommunication System (UMTS), and the like.
  • GSM Global System of Mobile communication
  • CDMA Code Division Multiple Access
  • WCDMA Wideband Code Division Multiple Access
  • GPRS General Packet Radio Service
  • LTE Long Term Evolution
  • FDD Frequency Division Duplex
  • TDD Time Division Duplex
  • UMTS Universal Mobile Telecommunication System
  • FIG. 1 is a schematic diagram of a basic flow of wireless communication.
  • a source is sequentially transmitted after source coding, channel coding, and digital modulation.
  • digital demodulation, channel decoding, and source decoding are sequentially outputted to the sink.
  • the channel coding can use a Polar code, and in the case of channel decoding, SC decoding, SCL decoding, etc. can be used.
  • many techniques have been proposed based on the Polar code, such as CA-Polar code, PC-Polar code, CA+PC-Polar and so on.
  • CA-Polar coding is also known as CRC cascaded Polar coding.
  • CA-SCL CRC-Aided Successive Cancellation List
  • CA-SCL CRC-Aided Successive Cancellation List
  • FIG. 3 is a schematic diagram of coding using a PC-Polar (Parity-Check-Polar) method.
  • PC-Polar parity-Check-Polar
  • the main idea of PC-Polar is to select some check freeze bits, also called parity bits (Parity-check-frozen) or dynamic freeze bits, which are distributed into information blocks. These check freeze bit values.
  • the information bits preceding it are determined according to the check equation.
  • the decoding of PC-Polar can be based on the SCL decoding algorithm.
  • the processing of information bits and static freeze bits is the same as the processing of the SCL decoding algorithm, with the difference being the processing of verifying frozen bits.
  • the process of sorting and pruning is completed in the decoding process by using the check freeze bit, and the PC-SCL decoding finally outputs the most reliable path.
  • PC-Polar is uniquely determined by the following parameters: verifying the number of frozen bits, verifying the position of the frozen bits, and checking the equation.
  • FIG. 4 is a schematic diagram of coding by means of PC+CA-Polar.
  • the encoding process includes: (1) performing a Cyclic Redundancy Check (CRC) encoding on the information block to be encoded; (2) performing PC coding, that is, determining information bits, static freeze bits, and check freeze bits.
  • CRC Cyclic Redundancy Check
  • the value of (3) is then encoded by Polar code to obtain a coded block.
  • the CRC coding matrix is uniquely determined by the following parameters: the number of CRC check bits, the location of the CRC check bits, and the CRC check equation.
  • the PC code is determined by the following parameters: verifying the number of frozen bits, verifying the position of the frozen bits, and checking the equation.
  • the coding matrix can be uniquely determined by the following parameters: the number of check bits, the position of the check bits, Check the selection of the equation. There are many ways to determine these parameters, which will be described in the following embodiments. In the following technical solutions, it should be understood that if the CRC bits and PC bits are not distinguished, the CRC is also applicable to the PC, and the PC is also applicable. In the CRC.
  • FIG. 5 is a schematic flowchart of Embodiment 1 of a method for transmitting information provided by the present application. As shown in FIG. 4 , on the basis of the communication flow diagram shown in FIG. 1 , or between other sending devices and receiving devices that perform information interaction, the method for transmitting information provided by the present application specifically includes the following steps:
  • the transmitting device encodes the sequence to be encoded according to the preset parameter pair to obtain a coded sequence.
  • the parameter includes the number of check bits, the position of the check bit, and the check equation.
  • the above check bits are used to verify the information bits.
  • There are many ways to implement the verification for example, using CA-Polar coding, or PC-Polar coding, or PC+CA-Polar coding, etc., but those skilled in the art can understand that It is not limited to these encoding methods, as long as the information bits are verified by using the check bits in the encoding process.
  • the transmitting device needs to perform encoding processing on the sequence to be sent.
  • the transmitting device and the receiving device need to agree in advance on parameters used in the encoding process, such as check bits.
  • the number, the position of the check bits, and the check equation; or the transmitting device needs to notify the receiving device of these parameters before the receiving device decodes.
  • the above parameters may be specified in the protocol, and are configured on the sending device, or may be negotiated between the sending device and the receiving device, or carried in a notification message sent by other devices. .
  • the method for determining the number of check bits includes at least the following:
  • the number of the check bits is pre-configured; or, the number of check bits is determined according to the length of the list of the decoder; or the number of the check bits is determined according to the code length and the code rate; or The number of the check bits is determined according to a pre-configured number of bits, a list length of the decoder, a code length, and a code rate, that is, the total number obtained by combining the first three methods is used as the number of check bits (also referred to as a check bit).
  • the position of the check bit may be the position where the sequence to be coded is sorted according to the sequence number, and the number of consecutively selected check bits is the same, or the position may be randomly selected, or may be a preset configuration directly, or may be It is the position determined according to the preset position parameter.
  • the manner of determining the position of the check bit includes at least the following methods:
  • the position of the check bit is: the position of the consecutive F P bits selected from the bit of the position number N X in the order of the bit position number of the bit to be coded; or be in accordance with the coding sequence position number of bits in the order from small to large, from a number of bits N X position of the start position of the selected consecutive bits F P; wherein, 0 ⁇ N X ⁇ K, 0 ⁇ Fp ⁇ K, to be
  • the position number of the bit in the coding sequence is any integer greater than or equal to 0 and less than K.
  • the position of the check bit is: a bit position selected from a new generation matrix; the new generation matrix is performed by performing row-column conversion on the check generation matrix, and only relying on partial information bits
  • the parity bit is replaced by the position obtained by the subchannel with a smaller sequence number.
  • the position of the check bit corresponds to the position of any one bit in the sequence to be encoded.
  • the position of the check bit corresponds to a position of a plurality of bits of the sequence to be coded, and the position of at least two of the plurality of bits is discontinuous.
  • the position of the check bit is determined according to a position parameter, the position parameter including at least an information threshold Z I and a check threshold Z P ;
  • the information threshold Z I is used to indicate reliability in all information subchannels Reliability of the lowest subchannel;
  • the check threshold Z P is used to indicate the reliability of the subchannel with the lowest reliability among the subchannel sets whose reliability is greater than the information threshold Z I and the line weight is the highest among all the check subchannels.
  • the check equation can be configured in advance, or determined according to a polynomial or check equation table.
  • the polynomial of the check equation can be performed in any of binary, octal, decimal, hexadecimal, position vector, and the like. Said.
  • the sequence to be encoded is first encoded by the check matrix, and then Polar coded to obtain the encoded sequence.
  • the check matrix may also be combined with the matrix of the Polar code to form a matrix, that is, the coded sequence is obtained by encoding the synthesized matrix to be coded.
  • S102 The sending device sends the encoded sequence to the receiving device.
  • the receiving device decodes the encoded sequence according to the preset parameter or the received parameter, to obtain a decoded sequence; the preset parameter or the received parameter includes the number of check bits, and the check bit. The position and the calibration equation.
  • the sending device sends the encoded sequence to the receiving device, that is, the receiving device receives the encoded sequence sent by the sending device, and the receiving device needs to perform decoding processing to obtain the decoded sequence, so the receiving device also The number of bits to be checked, the position of the check bits, and the check equation are required for decoding.
  • the preset parameters may be specified in the protocol, and configured on the receiving device, or may be negotiated between the sending device and the receiving device, or carried in a notification message sent by the sending device or other device to the receiving device. There is no restriction on this program.
  • the number of check bits used for decoding by the receiving device, the position of the check bits, and the check equation are the same as those of the transmitting device. How these parameters are determined has been described above and will not be described in detail herein.
  • the sending device encodes the sequence to be encoded according to the preset parameter pair to obtain a coded sequence, where the parameter includes the number of check bits, the position of the check bit, and the check equation.
  • the parameters of the sending device need to be set in advance, and then the sequence to be encoded is pre-coded according to the check bit, then the polar code is encoded, and the encoded sequence is sent to the receiving device, thereby effectively reducing the error rate of information transmission and improving information transmission. reliability.
  • the following describes in detail how the parameters used by the transmitting device in the encoding process of information transmission are determined.
  • the CRC check or the PC check as an example, the number of check bits, the position of the check bits, and the determination method of the check equation are specifically described.
  • the method for determining the parameters related to CRC can be applied to both CA-Polar and CA+PC-Polar encoding methods.
  • the method for determining PC-related parameters can be applied to both PC-Polar and CA+PC-Polar encoding. the way.
  • the parameters related to the CRC include: the number of CRC bits, the position of the CRC bits, and the CRC check equation.
  • the parameters related to the PC include: the number of PC bits, the position of the PC bits, and the PC check equation.
  • the number of check bits (also known as the length of the check bits)
  • the number of CRC bits can be determined by any of the following methods:
  • the number of CRC bits is pre-configured, that is, the CRC length is fixed in advance.
  • the number of CRC bits can be determined according to the length of the list of decoders.
  • L represents the size of the list
  • F 1 represents the number of check bits
  • the function ceil represents rounding up, and in actual applications, it can also be rounded down. It can also be rounded.
  • the size of the possible list (also called length) L is 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, and the number of parity bits corresponding to the size L of the list F1 It is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
  • the number of CRC bits may be determined according to the code length and the code rate.
  • the number of CRC bits can be determined according to the number of pre-configured bits, the list length of the decoder, the code length, and the code rate.
  • PC bits also known as parity bits, or parity freeze bits, or dynamic
  • the number of frozen bits can be determined in one of several ways: (1) The number of PC bits can be pre-configured, that is, the number of PCs fixed in advance:
  • the number of PC bits may be determined according to the length of the list of decoders.
  • the number of PC bits P F 1 ;
  • L represents the size of the list
  • F 1 represents the number of check bits
  • the function ceil represents rounding up, and in actual applications, it can also be rounded down. It can also be rounded.
  • the size of the possible list (also called length) L is 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, and the number of parity bits corresponding to the size L of the list F1 It is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
  • the number of PC bits may be determined according to the code length and the code rate.
  • N represents the length of the mother code (before encoding, before rate matching)
  • K represents the length of the sequence to be encoded (also called information bit length)
  • M Indicates the code length (after encoding, after rate matching)
  • F 2 indicates the number of check bits
  • the function ceil indicates rounding up. In actual applications, it can also be rounded down or rounded.
  • the number of PC bits may be determined according to a pre-configured number of bits, a list length of the decoder, a code length, and a code rate.
  • the position of the CRC bit can be determined by any of the following methods:
  • the position number of the bit in the sequence to be encoded is any integer greater than or equal to 0 and less than the length K of the sequence to be encoded, that is, each bit in the coded sequence has a unique sequence number, which is continuous and different in size.
  • the number, then the position of a CRC bit is determined in such a way that the position of consecutive J bits selected from the position number N X can be selected in the sequence to be encoded according to the position number of the bit from the largest to the smallest.
  • the position of the consecutive J bits selected from the bit of the position number N X may be used as the position of the CRC bit in the sequence to be encoded, in the order of the bit position number of the bit from small to large.
  • the position of the CRC bit may be a bit position selected from a new generation matrix; the new generation matrix is a CRC bit in which only part of the information bits are dependent by performing row-column conversion on the CRC generation matrix. Substitution to a subchannel with a smaller sequence number.
  • the CRC bit generation matrix is subjected to basic row and column transformation (such as Gaussian elimination) and/or row and column permutation (such as column rearrangement), and then some CRC bits are only dependent on partial information bits or only related to partial information bits, so This partial CRC bit can be replaced with a sub-channel with a smaller sequence number (for example, the corresponding CRC bit is replaced in the column corresponding to the partial information bit in the CRC generation matrix), and the error is eliminated in advance during decoding. path.
  • basic row and column transformation such as Gaussian elimination
  • row and column permutation such as column rearrangement
  • the last bit of the three CRC bits (corresponding to the sixth column of the generator matrix) is only related to the first two bits, so the corresponding column of the last CRC bit in the CRC generation matrix can be advanced to the third column:
  • the receiving end when the receiving end translates to the third bit, it can be regarded as a check bit, and it is set to the XOR value of the first two bits, and the path that does not satisfy the preset value is cut.
  • the number of check bits is 3 bits as an example. In a specific implementation, the number of check bits is not limited in this solution.
  • the position of the CRC bits can also be determined by other methods, for example, by simplifying the CRC generation matrix by Gaussian elimination, and then advancing the position of the CRC bits that depends only on part of the information bits by row and column permutation.
  • x p (u i + u j +... + u k ), that is, the p-th bit of the CRC codeword is the modulo 2 sum of the information bits of the i, j, ..., k, then the p-th in the CRC bit
  • the bits are forwarded to the first max ⁇ i, j, ..., k ⁇ +1 positions, where x p represents the value of the check bit of the p-th check bit, and u i represents the decoding of the i-th information bit
  • the values, i, j, ... k represent the sequence numbers of the information bits.
  • the position of the PC bit can be determined by any of the following methods:
  • the position number of the bit in the sequence to be coded is any integer greater than or equal to 0 and smaller than the length K of the sequence to be encoded, that is, each bit in the coded sequence has a unique sequence number, and the sequence number is continuous.
  • the specific determination of the position of a PC bit is: in the sequence to be encoded, according to the order of the position number of the bit, from the largest to the smallest, starting from the bit with the position number N X
  • the position of the P bits is taken as the position of the PC bit; or, the position of consecutive P bits selected from the bit of the position number N X may be used as the PC bit in the sequence to be encoded according to the position number of the bit from small to large. s position.
  • 0 ⁇ N X ⁇ K 0 ⁇ P ⁇ K.
  • P consecutive positions before the CRC bit can be selected as the position of the PC bit.
  • the location of any of the PC bits can be preset, and for PC locations that are not regularly traversable, all PC locations can be stored, which is typically used in ultra-short codes.
  • the position of the PC bit corresponds to the position of any one bit in the sequence to be encoded, or the position of multiple bits of the sequence to be encoded, and the position of at least two of the plurality of bits is discontinuous.
  • the location of the PC bit may be determined according to a location parameter, the location parameter including at least an information threshold Z I and a check threshold Z P ; the information threshold Z I is used to represent a least reliable sub-channel in all information subchannels reliability of the corresponding channel; said check threshold Z P subchannels used to represent all the information, the reliability information is greater than the threshold value Z I and the heaviest line subchannel lowest reliability corresponding to reliability of the subchannel set.
  • the specific determination process includes:
  • the sub-channel corresponding row weight RW i is defined as the number of 1s in the row corresponding to the (i-th) sub-channel in the Polar code generation matrix.
  • the number of subchannels define the Hamming weight HW of i: the (i-th) subchannel 2 hexadecimal number, the number of 1s.
  • RW i 2 ⁇ (HW i ) is satisfied for all i. Because HW has a smaller range of values, it is more likely to be represented by HW instead of RW in standards and hardware.
  • Threshold Z I Represents the reliability (or polarization weight) corresponding to the lowest reliability subchannel in all information subchannels (excluding the shortened position).
  • Check threshold Z P indicates the lowest reliability subchannel in all the subchannels (excluding the shortened position), the reliability is greater than the least reliable information bit (>Z I ), and the row weight is in the largest subchannel set. Corresponding reliability.
  • the (optional) check line weight RW P (or check Hamming weight HW P ) represents the line weight (or check Hamming weight) corresponding to the subchannel whose reliability is equal to the check threshold Z P . It can be obtained by unique conversion of Z P or directly as a parameter.
  • the potential PC bit selectable position can be obtained (the shortened position is not within the selectable range) And can be divided into three categories:
  • Class B PC bit position All subchannel positions (Z ⁇ Z I ) whose reliability is lower than the information threshold.
  • (Z ⁇ Z I && RW RW P )
  • (Z>Z P && RW RW P )).
  • the location of the PC bits and the location of other bits in the PC-Polar code can be determined using:
  • Class A check Only class A PC bit positions (high reliability locations) are selected, including:
  • Class B check Only class B PC bit positions (positions with low reliability) are selected, including:
  • Class W check select the location of the W class PC bit
  • Hybrid check The CRC check is concatenated with the check code generated by the position of the PC bit in any of the above.
  • Z i 0,1,2,6,3,8,9,18,4,10,11,21,13,23,25,37,5,12,14,24,16,27, 29,41,19,30,32,43,35,46,48,56,7,15,17,28,20,31,33,44,22,34,36,47,39,49,51, 58,26,38,40,50,42,52,53,59,45,54,55,60,57,61,62,63;
  • Z i 8192: 0, 1, 2, 6, 3, 8, 9, 20, 4, 10, 12, twenty four, 14, 28, 31, 55, 5, 13, 15, 29, 18, 34, 38, 64, twenty one, 39, 44, 73, 50, 82, 90, 138, 7, 17, 19, 37, twenty two, 42, 45, 77, 27, 49, 54, 89, 60, 98, 105, 161, 33, 57, 63, 101, 71, 112, 121, 181, 81, 125, 137, 201, 150, 219, 235, 329, 11, twenty three, 26, 47, 30, 53, 59, 95, 35, 61, 67, 107, 74, 117, 128, 190, 43, 72, 79, 123, 88, 136, 147, 216, 99, 151, 163, 237, 177, 256, 274, 381, 52, 86, 93, 144, 103, 157, 169, 246, 116, 175, 188, 271, 204, 291, 311, 428,
  • Z i 0, 1, 2, 6, 3, 8, 9, 20, 4, 10, 12, twenty four, 14, 28, 31, 55, 5, 13, 15, 29, 18, 34, 38, 64, twenty one, 39, 44, 73, 50, 82, 90, 138, 7, 17, 19, 37, twenty two, 42, 45, 77, 27, 49, 54, 89, 60, 98, 105, 161, 33, 57, 63, 101, 71, 112, 121, 181, 81, 125, 137, 201, 150, 219, 235, 330, 11, twenty three, 26, 47, 30, 53, 59, 95, 35, 61, 67, 107, 74, 117, 128, 190, 43, 72, 79, 123, 88, 136, 147, 216, 99, 151, 163, 237, 177, 256, 274, 382, 52, 86, 93, 144, 103, 157, 169, 246, 116, 175, 188, 271, 204, 291, 311, 429,
  • Z i (32768): 0, 1, 2, 6, 3, 8, 9, 20, 4, 10, 12, twenty four, 14, 28, 31, 55, 5, 13, 15, 29, 18, 34, 38, 64, twenty one, 39, 44, 73, 50, 82, 90, 138, 7, 17, 19, 37, twenty two, 42, 45, 77, 27, 49, 54, 89, 60, 98, 105, 161, 33, 57, 63, 101, 71, 112, 121, 181, 81, 125, 137, 201, 150, 219, 235, 330, 11, twenty three, 26, 47, 30, 53, 59, 95, 35, 61, 67, 107, 74, 117, 128, 190, 43, 72, 79, 123, 88, 136, 147, 216, 99, 151, 163, 237, 177, 256, 274, 382, 52, 86, 93, 144, 103, 157, 169, 246, 116, 175, 188, 271, 204, 291, 311, 429
  • RW_8 1, 2, 2, 4, 2, 4, 4, 8;
  • RW_16 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16;
  • RW_32 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 16, 2, 4, 4, 8, 4, 8, 16, 4,8,8,16,8,16,16,32;
  • RW_64 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 16, 4, 8, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 16, 4, 8, 16, 4, 8, 16, 16, 32, 4, 8,8,16,8,16,16,32,8,16,16,32,16,32,32,64;
  • RW_128 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 8, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 4, 8, 8, 16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,16,32,32,64,32,64,32,64,32,64,64,128;
  • RW_256 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 8, 4, 8, 4, 8, 8, 16, 2, 4, 8, 4, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 4, 8, 8, 16,8,16,16,32,8,16,16,32,16,32,64,8,16,16,32,16,32,32,64,16,32,32,64, 32, 64, 64, 128, 2, 4, 4, 8, 4, 8, 8, 8, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 8, 16, 16, 16, 32, 16, 32, 32, 64, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32,
  • RW_512 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 4, 8, 8, 16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,32,64,16,32,32,64, 32, 64, 64, 128, 2, 4, 4, 8, 4, 8, 8, 8, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 8, 16, 16, 16, 32, 16, 32, 32, 64, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32,
  • RW_1024 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 4, 8, 8, 16,8,16,16,32,8,16,16,32,16,32,64,8,16,16,32,32,64,16,32,32,64,16,32,32,64, 32, 64, 64, 128, 2, 4, 4, 8, 4, 8, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 8, 16, 16, 16, 32, 16, 32, 32, 64, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16,
  • RW_2048 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 4, 8, 8, 16,8,16,16,32,8,16,16,32,16,32,64,8,16,16,32,32,64,16,32,32,64,16,32,32,64, 32, 64, 64, 128, 2, 4, 4, 8, 4, 8, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 8, 16, 16, 16, 32, 16, 32, 32, 64, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 32
  • RW_4096 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 4, 8, 8, 16,8,16,16,32,8,16,16,32,16,32,64,8,16,16,32,32,64,16,32,32,64,16,32,32,64, 32, 64, 64, 128, 2, 4, 4, 8, 4, 8, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 8, 16, 16, 16, 32, 16, 32, 32, 64, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 32
  • RW_8192 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 4, 8, 8, 16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,32,64,16,32,32,64, 32, 64, 64, 128, 2, 4, 4, 8, 4, 8, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 8, 16, 16, 16, 32, 16, 32, 32, 64, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 32
  • RW_16384 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 2, 4, 8, 4, 8, 8, 16, 2, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 2, 4, 4, 8, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 16, 16, 32, 64, 4, 8, 16, 16, 16, 16, 32, 16, 16, 32, 64, 8, 16, 1 6, 32, 16, 32, 32, 64, 16, 32, 32, 64, 32, 64, 64, 128, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 32, 64, 4, 8, 8, 16, 8, 16, 16, 32, 16, 32, 32, 64, 4, 8, 8, 16, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 32, 32, 64, 16, 16, 32, 32, 32, 64, 16, 16, 32,
  • RW_32768 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 64, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 16, 32, 64, 4, 8, 8, 16, 8, 16, 16, 16, 32, 8, 16, 16, 32, 16, 32, 64, 16, 16, 32, 32, 64, 16, 32, 32, 64, 32, 64, 64, 128, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 16, 4, 8, 16, 4, 8, 16, 8, 16, 16, 16, 32, 4, 8, 16, 16, 16, 32, 16, 32, 32, 64, 4, 8, 8, 16, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 16, 16, 32, 32, 64, 16, 16, 32, 32, 64, 16, 16, 32, 32,
  • HW_8 0, 1, 1, 2, 1, 2, 2, 3;
  • HW_16 0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4;
  • HW_32 0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4, 2,3,3,4,3,4,4,5;
  • HW_64 0,1,1,2,1,2,2,3,1,2,2,3,2,3,4,1,2,2,3,2,3,3,4, 2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2, 3,3,4,3,4,4,5,3,4,4,5,5,6;
  • HW_128 0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4, 2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2, 3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3, 3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3, 4,3,4,4,5,3,4,4,5,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6, 5,6,6,7;
  • the check equations can be uniquely determined by the generator polynomial, and the generator polynomial has multiple equivalent representations. For example, it can be expressed in any of binary, octal, decimal, hexadecimal, and position vectors.
  • the CRC polynomial is [1,1,0,0,1,1,1]
  • it can also be equivalently represented as its position vector (the lowest bit starts from 0) [6,5,2,1, 0]; can also be represented by the decimal number corresponding to its binary vector, that is, the decimal representation given below is the decimal value converted into the high and low bits of the binary vector, such as for the polynomial [1, 1, 0 , 0, 1, 1, 1], whose decimal representation is 115.
  • the check equation can generate a polynomial (polynomial generation).
  • generator polynomial can be: (24): 29254851 ;(24):25952259;(19):1005307;(16):67601;(15):57977;(14):31993;(13):16299;(12):7705;(11):3805; 10): 1939; (9): 817; (8): 435; (7): 211; (6): 115; (5): 41; (4): 25; (3): 9;
  • the numerical values in the above brackets indicate the length of the CRC (i.e., the number of CRC bits), and the sequence after the parentheses indicates the polynomial.
  • the polynomial can also be other sequences for each CRC length, and the above examples are only used to aid understanding.
  • the polynomial is expressed in decimal, and other hexadecimal representations may be used in practical applications, and the application does not limit this.
  • Figure 6 is a schematic diagram of the tabular representation of the check equation, as shown in Figure 6 freeze / information / The check/short positions are represented by different paddings respectively.
  • F in the table indicates fixed bits
  • I indicates information bits
  • S indicates shortening bits
  • numbers in other tables represent the first check equations in which they participate.
  • the bits participate in the same check equation, where the most (lowest) bit of the subchannel number is the PC bit.
  • the check equation can be represented by another polynomial, that is, the shift register can be used for representation.
  • Figure 7 is a schematic diagram of a polynomial [1,0,0,0,0] using a shift register. As shown in Figure 7, for a shift register of length 5, the polynomial representation can be [1,0,0,0 , 0] or [4] or a decimal number of 16.
  • FIG. 8 is a schematic diagram of a polynomial [1, 0, 1, 0, 0] using a shift register, as shown in FIG. 8, for a shift register having a length of 5 but having a feedback tap at a third position, a polynomial thereof
  • the representation can be [1,0,1,0,0] or [4,2] or a decimal number of 20.
  • the decimal representation of the polynomial that can be used is: 4; 16; 64; 256; 272; 68; 273; 65552; 65808; 65535; 70661; 1028; 4100; 65540; ; 65604; 21; 69633; 69636; 69648; 69636.
  • PC-Polar can also use the CRC polynomial directly as a polynomial of its check equation.
  • PC bits and CRC bits can use different polynomials to define the check equations and perform precoding independently of each other (for example, using two different sets of shift registers)
  • PC bits and CRC bits use the same polynomial to define the check equation, and at the same time jointly perform precoding (for example, using a set of identical shift registers);
  • PC bits and CRC bits are different
  • the check equation for example, the PC bit uses a table to define a non-polynomial check equation, and the CRC bit uses a shift register to define the check equation.
  • the transmitting end adopts the coding mode of CA-Polar or CA+PC-Polar
  • the corresponding end of the receiving end can adopt the decoding mode of CA+PC-SCL.
  • the CA+PC-Polar coding mode uses check bits (for example, CRC bits) for verification
  • the receiving end needs to decode all the decoding paths in the list during the decoding process (for example, The L decoding paths are all checked using the CRC to determine if the path being checked is correct.
  • each CRC test adds a certain false alarm probability. "false alarm” means: decoding error but passing the CRC bit check. This is because there may be multiple decoding results that have the same CRC check value, but only one of them is the correct decoding result.
  • FIG. 9 is a schematic diagram of a decoding process of the decoding method of the present application, as shown in FIG. A CRC check is performed for each decoding path, thereby improving the efficiency of decoding.
  • the sequence encoded by CA+PC-Polar coding includes four bits, namely: information bits, static freeze bits (or frozen bits, which are optional, that is, in the encoded sequence) It is also possible to exclude static freeze bits, PC bits and CRC bits. Static freeze bit (or frozen bit, this bit is optional, that is, it may not include static freeze bit in the encoded sequence)
  • the receiving end Since the receiving end knows the type, number, and corresponding position of each bit, it is treated differently when decoding. Assume that the coded block outputted by the transmitting end contains N bits, and the width of the decoding list used by the receiving end is L. After receiving each bit, the receiving end performs different processing according to the type of each bit:
  • the path corresponding to the information bit is expanded to two paths of 0 and 1, and the metric values of the two paths, that is, the PM value are respectively calculated;
  • Method 1 Do not extend the path, directly set the value of the bit to the value of the check equation, and calculate the corresponding PM value;
  • the path is expanded in exactly the same way as the information bits, and the PM value of each path is calculated;
  • the parameters that need to be used in the encoding process have been introduced, that is, the number of check bits, the position of the check bits, the check equation, and the receiving end also needs to use these parameters in the process of decoding. . If the above-mentioned CA+PC-SCL decoding method with controllable false alarm probability is adopted, it is necessary to further know the value of the maximum number of times T allowed for the CRC check.
  • the false alarm probability is independent of the decoder list width (the size of L), based on the method for determining the number of CRC bits described above,
  • the number of CRC bits J, T and the maximum false alarm rate FAR can be made to satisfy the following relationship:
  • J(1) is the number of CRC bits that satisfy the requirement in a single CRC detection
  • J(T) is the number of CRC bits that satisfy the requirement for T-time CRC detection.
  • the values of J and T above may be predetermined by a protocol.
  • J and T may be any combination of the following Table xx:
  • J and T may be any combination of the following Table xx:
  • T and P are closely related to the coding method used at the encoding end, for example:
  • the T-th check refers to an error detection of the decoding result corresponding to the path.
  • FIG. 10 is a schematic structural diagram of an embodiment of a device for transmitting information provided by the present application; as shown in FIG. 10, the device 10 for transmitting information includes:
  • the processing module 11 is configured to encode a sequence to be encoded according to a preset parameter pair to obtain a coded sequence; the parameter includes a quantity of check bits, a position of the check bit, and a check equation;
  • the sequence to be encoded has a length of K, and the K is an integer greater than 0;
  • the sending module 12 is configured to send the encoded sequence to the receiving device.
  • the processing module 11 may be one or more processors.
  • the processor can execute the function of the processing module 11 by running the program code.
  • the functions of the above-described processing module 11 can be realized by reading the program code stored in the external memory.
  • the processing module 11 described above can also process circuits.
  • the above sending module 12 can be a transmitter or a transmitting circuit.
  • the information transmission device provided in this embodiment may be used to perform the technical solution on the sending device side in any of the foregoing method embodiments, and the implementation principle and the technical effect are similar to the method embodiments, and details are not described herein again.
  • the embodiment further provides an encoding device, which includes the above processing module 11, an input interface and an output interface; the input interface is used to input the sequence to be encoded to the processing module 11, and the output interface is used for outputting and encoding by the processing module 11. After the sequence.
  • an encoding device which includes the above processing module 11, an input interface and an output interface; the input interface is used to input the sequence to be encoded to the processing module 11, and the output interface is used for outputting and encoding by the processing module 11. After the sequence.
  • the coding device provided in this embodiment may be implemented by using a chip or a circuit, and is used to perform the coding technology solution on the transmitting device side in any of the foregoing method embodiments.
  • the implementation principle and the technical effect are similar to the method embodiment. No longer.
  • FIG. 11 is a schematic structural diagram of Embodiment 2 of an information transmission apparatus provided by the present application; as shown in FIG. 11, the information transmission apparatus 20 includes:
  • the receiving module 21 is configured to receive the encoded sequence sent by the sending device, where the encoded sequence is obtained by encoding a sequence to be encoded according to a preset parameter, where the sequence length to be encoded is K, K is an integer greater than 0;
  • the processing module 22 is configured to decode the encoded sequence according to the preset parameter to obtain a decoded sequence; the parameter includes a quantity of check bits, a position of the check bit, and a calibration Test the equation.
  • the information transmission device provided in this embodiment is used to perform the technical solution on the receiving device side in any of the foregoing method embodiments, and the implementation principle and technical effects thereof are similar, and details are not described herein again.
  • the information transmission apparatus 20 provided in this embodiment may further include an input interface and an output interface; the input interface is used to input the encoded sequence to the processing module 22, and the output interface is used to output the sequence decoded by the processing module 22.
  • the information transmission device provided in this embodiment may be implemented by using a chip or a circuit, and is used to perform a decoding technical solution on the receiving device side in any of the foregoing method embodiments, because the implementation principle and the technical effect are similar to the method embodiment. , will not repeat them here.
  • FIG. 12 is a schematic structural diagram of an embodiment of a decoding apparatus provided by the present application; as shown in FIG. 12, the decoding apparatus 30 includes:
  • the receiving module 31 is configured to receive, from the sending device, a bit sequence to be decoded, where the bit sequence to be decoded includes at least information bits and at least one parity bit;
  • the processing module 32 is configured to sequentially decode the to-be-decoded bits by using a serial offset list SCL decoding algorithm, and output one candidate path with the best metric value; the 1 ⁇ l ⁇ L, L is the width of SCL, and L is an integer greater than or equal to 1;
  • the processing module 32 is further configured to: start from the candidate path with the best metric value, check the T candidate path among the at least one check bit, and check the bit in the first candidate path that passes the check
  • the sequence is output as a decoding; the T is an integer, and 1 ⁇ T ⁇ l.
  • the decoding apparatus provided in this embodiment may further include an input interface and an output interface; the input interface is configured to input the encoded sequence to the processing module 32, and the output interface is configured to output the sequence decoded by the processing module 32.
  • the decoding device provided in this embodiment may be implemented by using a chip or a circuit, and is used to perform the decoding technical solution on the receiving device side in any of the foregoing method embodiments.
  • the implementation principle and the technical effect are similar to the method embodiment. I will not repeat them here.
  • the present application further provides a readable storage medium, where the readable storage medium stores instructions, when the at least one processor of the transmitting device executes the instruction, the transmitting device performs the transmission method of the information provided in any one of the foregoing method embodiments, and Coding method.
  • the present application further provides a readable storage medium, where the readable storage medium stores instructions, when the at least one processor of the receiving device executes the instruction, the receiving device performs the transmission method of the information provided in any one of the foregoing method embodiments, and Decoding method.
  • the application also provides a program product comprising instructions stored in a readable storage medium.
  • At least one processor of the transmitting device can read the instructions from the readable storage medium and execute the instructions such that the transmitting device implements the method of transmitting the information provided in any of the method embodiments and the encoding method.
  • the application also provides a program product comprising instructions stored in a readable storage medium.
  • At least one processor of the receiving device can read the instruction from a readable storage medium and execute the instruction such that the receiving device implements the method of transmitting information and the method of decoding provided in any of the method embodiments described above.
  • the processor may be a central processing unit (English: Central Processing Unit, CPU for short), or other general-purpose processor, digital signal processor (English: Digital Signal) Processor, referred to as DSP, and Application Specific Integrated Circuit (ASIC).
  • the general purpose processor may be a microprocessor or the processor or any conventional processor or the like. The steps of the method disclosed in connection with the present application may be directly embodied by hardware processor execution or by a combination of hardware and software modules in a processor.
  • All or part of the steps of implementing the above method embodiments may be performed by hardware associated with the program instructions.
  • the aforementioned program can be stored in a readable memory.
  • the steps including the foregoing method embodiments are performed; and the foregoing memory (storage medium) includes: read-only memory (English: read-only memory, abbreviation: ROM), RAM, flash memory, hard disk, Solid state drive, magnetic tape (English: magnetic tape), floppy disk (English: floppy disk), optical disc (English: optical disc) and any combination thereof.

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Abstract

本申请提供一种信息的传输方法、译码方法和装置，该方法包括：发送设备根据预设的参数对的待编码的序列进行编码，得到编码后的序列，参数包括校验比特的数量、校验比特的位置以及校验方程，发送设备的参数需要预先进行设置，然后对待编码的序列先按照校验比特进行预编码，再进行polar编码，将编码后的序列发送至接收设备，有效降低数据传输的错误率，提高数据传输的可靠性。

Description

一种信息的传输方法、译码方法和装置
本申请要求于2017年2月3日提交中国专利局、申请号为201710063758.3、申请名称为“一种信息的传输方法、译码方法和装置”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本申请涉及通信技术，尤其涉及一种信息的传输方法、译码方法和装置。
背景技术
极化码(Polar Codes)是2008年由E.Arlkan提出的一种新型信道编码。极化码基于信道极化(Channel Polarization)进行设计，是第一种能够通过严格的数学方法证明达到信道容量的构造性编码方案。Polar码是一种线性块码。其生成矩阵为G N,其编码过程为
Figure PCTCN2018073229-appb-000001
其中
Figure PCTCN2018073229-appb-000002
是一个二进制的行矢量，长度为N(即码长)；G N是一个N×N的矩阵，且
Figure PCTCN2018073229-appb-000003
这里
Figure PCTCN2018073229-appb-000004
Figure PCTCN2018073229-appb-000005
定义为log 2N个矩阵F 2的克罗内克(Kronecker)乘积.
Figure PCTCN2018073229-appb-000006
Figure PCTCN2018073229-appb-000007
Figure PCTCN2018073229-appb-000008
Polar码的编码过程中，
Figure PCTCN2018073229-appb-000009
中的一部分比特用来携带信息，称为信息比特，这些比特的索引的集合记作A；另外的一部分比特置为收发端预先约定的固定值(称之为固定比特)，其索引的集合用A的补集A c表示。不失一般性，这些固定比特通常被设为0，只需要收发端预先约定，固定比特序列可以被任意设置。从而，Polar码的编码输出可简化为：
Figure PCTCN2018073229-appb-000010
这里u A为
Figure PCTCN2018073229-appb-000011
中的信息比特集 合，u A为长度K的行矢量，即|A|＝K，|·|表示集合中元素的个数，K为信息块大小，G N(A)是矩阵G N中由集合A中的索引对应的那些行得到的子矩阵，G N(A)是一个K×N的矩阵。Polar码的构造过程即集合A的选取过程，决定了Polar码的性能。
在提出Polar码之后，常用的信息传输方式是将待发送的信息块进行Polar编码得到编码块，然后进行传输，然而这种方式下的数据传输的错误率比较高，传输可靠性较低。
发明内容
本申请提供一种信息传输的方法和装置，用于解决常用的信息传输方式是将待发送的数据，即信息块进行Polar编码得到编码块，然后进行传输，然而这种方式下的数据传输的错误率比较高，传输可靠性较低的问题。
本申请第一方面提供一种信息传输的方法，包括：
发送设备根据预设的参数对的待编码的序列进行编码，得到编码后的序列；所述参数包括校验比特的数量、所述校验比特的位置以及校验方程；所述待编码的序列长度为K，所述K为大于0的整数；
所述发送设备将所述编码后的序列发送至接收设备。
在上述方案的具体实现中：
所述校验比特的数量是预先配置的，或者，所述校验比特的数量是根据译码器的列表长度确定的，或者，所述校验比特的数量是根据码长和码率确定的，或者，所述校验比特的数量是根据预先配置的比特数、译码器的列表长度、码长和码率确定的。
在上述方案中，校验比特为循环冗余校验(Cyclic Redundancy Check，CRC)比特时：
该校验比特的数量(也称为长度)可以被协议规定或者配置为2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,36,40,44,48,52,56,60,64等。校验比特的数量还可以根据list的大小确定，采用公式F 1＝ceil(log 2(L))，其中，L表示list的大小，F 1表示校验比特的数量，函数ceil表示向上取整，在实际应用中也可以是向下取整，还可以是四舍五入。可能的list的大小(也称为长度)L为1，2，4，8，16，32，64，128，256，512，1024，与该些list的大小L对应的校验比特的数量F1为0，1，2，3，4，5，6，7，8，9，10。该校验比特的数量还可以通过码长和码率确定，其中“F 2＝ceil(log 2(M))”；或，“F 2＝ceil(log 2(K))”；或“F 2＝ceil(a*log 2(N))”，其中，a为系数，K表示带编码的序列长度(也称为信息比特长度)，M表示码长(编码后、速率匹配后)，F 2表示校验比特的数量，函数ceil表示向上取整，在实际应用中也可以是向下取整，还可以是四舍五入。另外也校验比特的数量还可以是上述几种方式得到的数量的组合。
校验比特为奇偶校验(Parity Check，PC)比特时：
该校验比特的数量可以被配置为：2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,36,40,44,48,52,56,60,64等。校验比特的数量还可以根据list的大小确定，采用公式F 1＝ceil(log 2(L))，其中，L表示list的大小，F 1表示校验比特的数量，函数ceil表示向上取整，在实际应用中也可以是向下取整，还可以是四舍五入。可能的list 的大小(也称为长度)L为1，2，4，8，16，32，64，128，256，512，1024，与该些list的大小L对应的校验比特的数量F1为0，1，2，3，4，5，6，7，8，9，10。该校验比特的数量还可以通过码长和码率确定，PC数量＝F p＝F 2”，其中“F 2＝ceil(log 2(N)*(α-|α*(K/M-1/2)| 2))”或“F 2＝ceil(log 2(M))”其中a为大于0的系数，通常可取0.75,1,1.25,1.5等，N表示母码长度(编码后、速率匹配前)，K表示带编码的序列长度(也称为信息比特长度)，M表示码长(编码后、速率匹配后)，F 2表示校验比特的数量，函数ceil表示向上取整，在实际应用中也可以是向下取整，还可以是四舍五入。另外也校验比特的数量还可以是上述几种方式得到的数量的组合。
在一种具体实现方式中，当所述校验比特为CRC比特时，所述CRC比特的位置为：从一个新的生成矩阵中选择出的比特位置；所述新的生成矩阵是通过对CRC的生成矩阵进行行列转换，将其中只依赖部分信息比特的CRC比特置换至序号更小的子信道得到的。
在另一种实施方式中，当所述校验比特为PC比特时，所述PC比特的位置为：
预先设置的；所述PC比特的位置对应待编码序列中任意一个比特的位置，或者对应待编码序列多个比特的位置，所述多个比特中至少有两个比特的位置是非连续的；
或者，
根据位置参数确定的，所述位置参数至少包括信息阈值Z I和校验阈值Z P；所述信息阈值Z I用于表示所有信息子信道中可靠度最低子信道对应的可靠度；所述校验阈值Z P用于表示所有校验子信道中，可靠度大于信息阈值Z I且行重最大的子信道集合中可靠度最低的子信道对应的可靠度。
在上述任一方案的基础上，当所述校验比特为PC比特时，所述校验方程是根据校验方程表格确定的；其中，所述校验方程表格至少包括PC校验比特、信息比特以及参与校验方程的信息比特。在一种具体实现中，校验方程表格还包括固定比特、缩短比特。
本申请第二方面提供一种信息的传输方法，包括：
接收设备接收发送设备发送的编码后的序列；所述编码后的序列是根据预设的参数对待编码的序列进行编码后得到的，所述待编码的序列长度为K，所述K为大于0的整数；
所述接收设备根据预设的参数对所述编码后的序列进行译码，得到译码后的序列；所述参数包括校验比特的数量、所述校验比特的位置以及校验方程。
在上述方案中：
所述校验比特的数量是预先配置的，或者，所述校验比特的数量是根据译码器的列表长度确定的，或者，所述校验比特的数量是根据码长和码率确定的，或者，所述校验比特的数量是根据预先配置的比特数、译码器的列表长度、码长和码率确定的。
在上述方案中，校验比特为CRC比特时：
该校验比特的数量(也称为长度)可以被协议规定或者配置为2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,36,40,44,48,52,56,60,64等。校验比特的数量还可以根据list的大小确定，采用公式F 1＝ceil(log 2(L))，其中，L表示list的大小，F 1表示校验比特的数量，函数ceil表示向上取整，在实际应用中也可以是向下取整，还可以是四舍五入。可能的list的大小(也称为长度)L为1，2，4，8，16，32，64，128，256，512，1024，与该些list的大小L对应的校验比特的数量F1为0，1，2，3，4，5，6，7，8，9，10。该校验比特的数量还可以通过码长和码率确定，其中“F 2＝ceil(log 2(M))”；或，“F 2＝ceil(log 2(K))”；或“F 2＝ceil(a*log 2(N))”，其中，a为系数，K表示带编码的序列长度(也称为信息比特长度)，M表 示码长(编码后、速率匹配后)，F 2表示校验比特的数量，函数ceil表示向上取整，在实际应用中也可以是向下取整，还可以是四舍五入。另外也校验比特的数量还可以是上述几种方式得到的数量的组合。
校验比特为PC比特时：
该校验比特的数量可以被配置为：2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,36,40,44,48,52,56,60,64等。校验比特的数量还可以根据list的大小确定，采用公式F 1＝ceil(log 2(L))，其中，L表示list的大小，F 1表示校验比特的数量，函数ceil表示向上取整，在实际应用中也可以是向下取整，还可以是四舍五入。可能的list的大小(也称为长度)L为1，2，4，8，16，32，64，128，256，512，1024，与该些list的大小L对应的校验比特的数量F1为0，1，2，3，4，5，6，7，8，9，10。该校验比特的数量还可以通过码长和码率确定，PC数量＝F p＝F 2”，其中“F 2＝ceil(log 2(N)*(α-|α*(K/M-1/2)| 2))”或“F 2＝ceil(log 2(M))”其中a为大于0的系数，通常可取0.75,1,1.25,1.5等，N表示母码长度(编码后、速率匹配前)，K表示带编码的序列长度(也称为信息比特长度)，M表示码长(编码后、速率匹配后)，F 2表示校验比特的数量，函数ceil表示向上取整，在实际应用中也可以是向下取整，还可以是四舍五入。另外也校验比特的数量还可以是上述几种方式得到的数量的组合。
在一种具体实施方式中，当所述校验比特为CRC比特时，所述CRC比特的位置为：
从一个新的生成矩阵中选择出的比特位置；所述新的生成矩阵是通过对CRC的生成矩阵进行行列转换，将其中只依赖部分信息比特的CRC比特置换至序号更小的子信道得到的。
在另一种实施方式中，当所述校验比特为PC比特时，所述PC比特的位置为：
预先设置的；所述PC比特的位置对应待编码序列中任意一个比特的位置，或者对应待编码序列多个比特的位置，所述多个比特中至少有两个比特的位置是非连续的；
或者，
根据位置参数确定的，所述位置参数至少包括信息阈值Z I和校验阈值Z P；所述信息阈值Z I用于表示所有信息子信道中可靠度最低子信道对应的可靠度；所述校验阈值Z P用于表示所有校验子信道中，可靠度大于信息阈值Z I且行重最大的子信道集合中可靠度最低的子信道对应的可靠度。
在上述任一方案的基础上，当所述校验比特为奇偶校验PC比特时，所述校验方程是根据校验方程表格确定的；其中，所述校验方程表格至少包括PC校验比特、信息比特以及参与校验方程的信息比特。一种具体实现中，该校验方程表格还包括固定比特、缩短比特。
本申请第三方面提供一种信息的传输装置，包括：
处理模块，用于根据预设的参数对的待编码的序列进行编码，得到编码后的序列；所述参数包括校验比特的数量、所述校验比特的位置以及校验方程；所述待编码的序列长度为K，所述K为大于0的整数；
发送模块，用于将所述编码后的序列发送至接收设备。
在另一种实现方式中，当所述校验比特为CRC比特时，所述CRC比特的位置为：
从一个新的生成矩阵中选择出的比特位置；所述新的生成矩阵是通过对CRC的生成矩阵进行行列转换，将其中只依赖部分信息比特的CRC比特置换至序号更小的子信道得到的。
在另一种实现方式中，当所述校验比特为PC比特时，所述PC比特的位置为：
预先设置的；所述PC比特的位置对应待编码序列中任意一个比特的位置，或者对应待编码序 列多个比特的位置，所述多个比特中至少有两个比特的位置是非连续的；
或者，
根据位置参数确定的，所述位置参数至少包括信息阈值Z I和校验阈值Z P；所述信息阈值Z I用于表示所有信息子信道中可靠度最低子信道对应的可靠度；所述校验阈值Z P用于表示所有校验子信道中，可靠度大于信息阈值Z I且行重最大的子信道集合中可靠度最低的子信道对应的可靠度。
在上述任一实施方式的基础上，当所述校验比特为PC比特时，所述校验方程是根据校验方程表格确定的；其中，所述校验方程表格可包括PC校验比特、信息比特、固定比特、缩短比特以及参与校验方程的信息比特。
本申请第四方面提供一种信息的传输装置，包括：
接收模块，用于接收发送设备发送的编码后的序列；所述编码后的序列是根据预设的参数对待编码的序列进行编码后得到的，所述待编码的序列长度为K，所述K为大于0的整数；
处理模块，用于根据预设的参数对所述编码后的序列进行译码，得到译码后的序列；所述参数包括校验比特的数量、所述校验比特的位置以及校验方程。
在一种实现方式中，当所述校验比特为CRC比特时，所述CRC比特的位置为：
从一个新的生成矩阵中选择出的比特位置；所述新的生成矩阵是通过对CRC的生成矩阵进行行列转换，将其中只依赖部分信息比特的CRC比特置换至序号更小的子信道得到的。
在另一种实现方式中，当所述校验比特为PC比特时，所述PC比特的位置为：
预先设置的；所述PC比特的位置对应待编码序列中任意一个比特的位置，或者对应待编码序列多个比特的位置，所述多个比特中至少有两个比特的位置是非连续的；
或者，
根据位置参数确定的，所述位置参数至少包括信息阈值Z I和校验阈值Z P；所述信息阈值Z I用于表示所有信息子信道中可靠度最低子信道对应的可靠度；所述校验阈值Z P用于表示所有信息子信道中，可靠度大于信息阈值Z I且行重最大的子信道集合中可靠度最低的子信道对应的可靠度。
在上述任一方案的基础上，当所述校验比特为PC比特时，所述校验方程是根据校验方程表格确定的；其中，所述校验方程表格包括PC校验比特、信息比特、固定比特、缩短比特以及参与校验方程的信息比特。
本申请第五方面提供一种译码方法，接收设备从发送设备接收待译码的比特序列；所述待译码的比特序列中至少包括信息比特和至少一个校验比特；所述接收设备采用串行抵消列表SCL译码算法按顺序对所述待译码的比特进行译码，输出度量值最优的l条候选路径；所述1≤l≤L，所述L为SCL的宽度，所述L为大于或等于1的整数；
从度量值最优的候选路径开始，用所述至少一个校验比特对其中的T条候选路径进行校验，将校验通过的第一个候选路径中的比特序列作为译码输出；所述T为整数，所述1≤T≤l。
其中，度量值用于表示译码端计算得到的译码成功的概率，即“从度量值最优的候选路径开始”是指译码端计算得到的译码成功的概率最高的路径开始。
本申请第六方面提供一种译码装置，包括：
接收模块，用于从发送设备接收待译码的比特序列；所述待译码的比特序列中至少包括信息比特和至少一个校验比特；
处理模块，用于采用串行抵消列表SCL译码算法按顺序对所述待译码的比特进行译码，输出 度量值最优的l条候选路径；所述1≤l≤L，所述L为SCL的宽度，所述L为大于或等于1的整数；
所述处理模块还用于从度量值最优的候选路径开始，用所述至少一个校验比特对其中的T条候选路径进行校验，将校验通过的第一个候选路径中的比特序列作为译码输出；所述T为整数，所述1≤T≤l。
本申请第七方面提供一种发送设备，包括：
处理器，用于根据预设的参数对的待编码的序列进行编码，得到编码后的序列；所述参数包括校验比特的数量、所述校验比特的位置以及校验方程；所述待编码的序列长度为K，所述K为大于0的整数；
发送器，用于将所述编码后的序列发送至接收设备。
在上述发送设备的具体实现方式中，还可以包括存储器，处理器的数量为至少一个，用来执行存储器存储的计算机执行指令。使得发送设备通过通信接口与接收设备之间进行数据交互来执行上述第一方面或者第一方面的各种实施方式提供的信息的传输方法。可选的，存储器可以集成在处理器的内部。
本申请第八方面提供一种接收设备，包括：
接收器，用于接收发送设备发送的编码后的序列；所述编码后的序列是根据预设的参数对待编码的序列进行编码后得到的，所述待编码的序列长度为K，所述K为大于0的整数；
处理器，用于根据预设的参数对所述编码后的序列进行译码，得到译码后的序列；所述参数包括校验比特的数量、所述校验比特的位置以及校验方程。
在上述接收设备的具体实现中，还可包括存储器，且处理器的数量为至少一个，用来执行存储器存储的执行指令。使得接收设备通过通信接口与发送设备之间进行数据交互来执行上述第二方面或者第二方面的各种实施方式提供的信息的传输方法，或者使得接收设备执行上述第五方面提供的译码方法。可选的，存储器还可以集成在处理器内部。
本申请第九方面提供一种可读存储介质，可读存储介质中存储有执行指令，当发送设备的至少一个处理器执行该执行指令时，发送设备执行上述第一方面或者第一方面的各种实施方式提供的信息的传输方法。
本申请第十方面提供一种可读存储介质，可读存储介质中存储有执行指令，当接收设备的至少一个处理器执行该执行指令时，接收设备执行上述第二方面或者第二方面的各种实施方式提供的信息的传输方法，或者接收设备执行上述第五方面或者第五方面的各种实施方式提供的译码方法。
本申请第九方面提供一种程序产品，该程序产品包括执行指令，该执行指令存储在可读存储介质中。发送设备的至少一个处理器可以从可读存储介质读取该执行指令，至少一个处理器执行该执行指令使得发送设备实施第一方面或者第一方面的各种实施方式提供的信息的传输方法。
本申请第十方面提供一种程序产品，该程序产品包括执行指令，该执行指令存储在可读存储介质中。接收设备的至少一个处理器可以从可读存储介质读取该执行指令，至少一个处理器执行该执行指令使得接收设备实施上述第二方面或者第二方面的各种实施方式提供的信息的传输方法，或者接收设备执行上述第五方面或者第五方面的各种实施方式提供的译码方法。
本申请提供的信息的传输方法、译码方法和装置，发送设备根据预设的参数对的待编码的序列进行编码，得到编码后的序列，参数包括校验比特的数量、校验比特的位置以及校验方程，发送设备 的参数需要预先进行设置，然后对待编码的序列先按照校验比特进行预编码，再进行polar编码，将编码后的序列发送至接收设备，有效降低数据传输的错误率，提高数据传输的可靠性。
附图说明
图1为无线通信的基本流程示意图；
图2为采用CA-Polar的方式进行编码的示意图；
图3为采用PC-Polar(Parity-check-Polar)的方式进行编码的示意图；
图4为采用PC+CA-Polar的方式进行编码的示意图；
图5为本申请提供的信息的传输方法实施例一的流程示意图；
图6为校验方程的表格表示法的示意图；
图7为多项式[1,0,0,0,0]采用移位寄存器的示意图；
图8为多项式[1,0,1,0,0]采用移位寄存器的示意图；
图9为本申请的译码方法的译码过程示意图；
图10为本申请提供的信息的传输装置实施例的结构示意图；
图11为本申请提供的信息的传输装置实施例二的结构示意图；
图12为本申请提供的译码装置实施例的结构示意图。
具体实施方式
本申请实施例的技术方案可以应用5G通信系统或未来的通信系统，也可以用于其他各种无线通信系统，例如：全球移动通讯(Global System of Mobile communication，GSM)系统、码分多址(CDMA，Code Division Multiple Access)系统、宽带码分多址(Wideband Code Division Multiple Access，WCDMA)系统、通用分组无线业务(General Packet Radio Service，GPRS)、长期演进(Long Term Evolution，LTE)系统、LTE频分双工(Frequency Division Duplex，FDD)系统、LTE时分双工(Time Division Duplex，TDD)、通用移动通信系统(Universal Mobile Telecommunication System，UMTS)等。
图1为无线通信的基本流程示意图，如图1所示，在发送端，信源依次经过信源编码、信道编码、数字调制后发出。在接收端，依次经过数字解调、信道译码、信源解码输出信宿。信道编码可以采用Polar码，而在信道译码的时候，可以采用SC译码、SCL译码等。为了提高Polar码的性能，现在又提出了很多在Polar码的基础上进行改进的技术，例如，CA-Polar码，PC-Polar码，CA+PC-Polar等等。
图2为采用CA-Polar的方式进行编码的示意图，即对待编码的信息块先进行级联循环冗余校验(Cyclic Redundancy Check，CRC)编码，然后再进行Polar码编码得到编码块进行发送，CA-Polar编码也称为CRC级联Polar编码。相应的，译码的时候可以采用CA-SCL(CRC-Aided Successive Cancellation List)译码算法进行译码，即在SCL译码输出的多条候选路径中选择CRC通过的候选路径作为译码输出。采用CA-SCL译码算法，能显著提高Polar码的性能。CA-Polar可以由以下参数唯一确定：CRC校验比特的数量、CRC校验比特的位置和CRC校验方程。
图3为采用PC-Polar(Parity-check-Polar)的方式进行编码的示意图。PC-Polar的主要思想是选择一些校验冻结比特，也称为奇偶校验比特(Parity-check-frozen)或动态冻结(Dynamic Frozen)比特， 分布到信息块中，这些校验冻结比特的值由其前面的信息比特根据校验方程确定。PC-Polar的译码可以基于SCL译码算法。信息比特和静态冻结比特的处理与SCL译码算法的处理一样，不同是校验冻结比特的处理。具体来说是利用校验冻结比特在译码过程中完成排序、剪枝的过程，PC-SCL译码最终输出最可靠的路径。PC-Polar由以下参数唯一确定：校验冻结比特的数量，校验冻结比特的位置和校验方程。
图4为采用PC+CA-Polar的方式进行编码的示意图。编码过程包括：(1)对待编码的信息块先进行级联循环冗余校验(Cyclic Redundancy Check，CRC)编码；(2)进行PC编码，即确定信息比特、静态冻结比特和校验冻结比特的值；(3)然后进行Polar码编码得到编码块。CRC编码矩阵由如下参数唯一确定：CRC校验比特的数量、CRC校验比特的位置和CRC校验方程。而PC编码是由如下参数确定：校验冻结比特的数量，校验冻结比特的位置和校验方程。
综上所述，对于校验级联Polar编码(CA-Polar，PC-Polar或PC+CA-Polar)，编码矩阵可由以下参数唯一决定，即：校验比特的数量、校验比特的位置，校验方程的选择。这些参数的确定有很多种方式，在下面的实施例中将会介绍，后续的技术方案中，应理解：若不区分CRC比特和PC比特的话，则CRC的也适用于PC，PC的也适用于CRC。
图5为本申请提供的信息的传输方法实施例一的流程示意图，如图4所示，在图1所示的通信流程示意图基础上，或者其他进行信息交互的发送设备和接收设备之间，本申请提供的信息的传输方法具体包括以下步骤：
S101：发送设备根据预设的参数对的待编码的序列进行编码，得到编码后的序列；参数包括校验比特的数量、校验比特的位置以及校验方程。
上述校验比特是用于对信息比特进行校验的。能够实现校验的方式可以有很多种，例如，采用CA-Polar编码方式，或者PC-Polar编码方式，或者PC+CA-Polar编码方式等，但是本领域的技术人员可以理解，在实现时可以不限于这些编码方式，只要在编码过程中采用了校验比特对信息比特进行了校验即可。
在本步骤中，发送设备需要对待发送的序列进行编码处理，为了能使接收设备正确解码发送设备发送的编码序列，发送设备和接收设备需要事先约定好编码过程中使用的参数，例如校验比特的数量、校验比特的位置以及校验方程；或者发送设备需要在接收设备译码之前，将这些参数通知给接收设备。上述参数可以是协议中规定好，并且配置在发送设备上的，也可以是发送设备与接收设备之间协商得到的，或者是其他设备发送的通知消息中携带的，对此本方案不做限制。
在该方案的具体实现中，校验比特的数量的确定方式至少包括以下几种：
该校验比特的数量是预先配置的；或者，校验比特的数量是根据译码器的列表长度确定的；或者，所述校验比特的数量是根据码长和码率确定的；或者，所述校验比特的数量是根据预先配置的比特数、译码器的列表长度、码长和码率确定的，即综合前三种方式得到的数量整体作为校验比特的数量(也称为校验比特的长度)；或者，所述校验比特的数量为J，所述J≥log 2(T/FAR)；所述T为允许使用校验比特进行校验的最大次数，所述FAR为使用校验比特进行单次检验的最大虚警概率；或者，所述校验比特的数量为J(T)，所述J(T)＝J(1)+ΔJ＝J(1)+log 2T；其中，所述J(1)为单次校验是需要使用的校验比特的数量，所述J(T)为T次校验需要使用的校验比特的数量，所述T为允许使用校验比特进行校验的最大次数，其中，T＝1时候，一次校验指的是该路径对应的 译码结果的一次检错。
校验比特的位置可以是待编码的序列按照序号大小排序之后，连续选择的与校验比特的数量相同的位置，或者也可以是随机选择出位置，还可以是直接预先设置的配置，还可以是根据预设的位置参数确定的位置。
具体的，校验比特的位置的确定方式至少包括以下几种方式：
第一种方式，校验比特的位置为：在待编码序列中按照比特的位置序号从大到小的顺序，从位置序号为N X的比特开始选择的连续F P个比特的位置；或者在待编码序列中按照比特的位置序号从小到大的顺序，从位置序号为N X的比特开始选择的连续F P个比特的位置；其中，0≤N X≤K，0<Fp<K，待编码序列中比特的位置序号为大于等于0且小于K的任意整数。
第二种方式，校验比特的位置为：从一个新的生成矩阵中选择出的比特位置；所述新的生成矩阵是通过对校验生成矩阵进行行列转换，将其中只依赖部分信息比特的校验比特置换至序号更小的子信道得到的位置。
第三种方式，校验比特的位置对应待编码序列中任意一个比特的位置。
第四种方式，校验比特的位置对应待编码序列多个比特的位置，所述多个比特中至少有两个比特的位置是非连续的。
第五种方式，校验比特的位置是根据位置参数确定的，所述位置参数至少包括信息阈值Z I和校验阈值Z P；所述信息阈值Z I用于表示所有信息子信道中可靠度最低子信道对应的可靠度；所述校验阈值Z P用于表示所有校验子信道中，可靠度大于信息阈值Z I且行重最大的子信道集合中可靠度最低的子信道对应的可靠度
同样的，校验方程可以预先进行配置，或者根据多项式或者校验方程表格进行确定，校验方程的多项式可以采用二进制，八进制，十进制，十六进制，位置向量等中的任一种形式进行表示。
发送设备在得到需要的校验比特的参数之后，对待编码的序列先通过校验矩阵进行编码，然后再进行Polar编码，得到编码后的序列。作为一种可选的实施例，校验矩阵也可以与Polar码的矩阵合成一个矩阵，即对待编码的采用合成后的矩阵进行编码后就得到了编码后的序列。
S102：发送设备将编码后的序列发送至接收设备。
S103：接收设备根据预设的参数或者接收到的参数对编码后的序列进行译码，得到译码后的序列；该预设的参数或者接收到的参数包括校验比特的数量、校验比特的位置以及校验方程。
在上述步骤中，发送设备将编码后的序列发送给接收设备，即接收设备接收到发送设备发送的编码后的序列，接收设备需要进行译码处理得到译码后的序列，因此该接收设备也需要校验比特的数量，校验比特的位置以及校验方程来进行译码。
上述预设的参数可以是协议中规定好，并且配置在接收设备上的，也可以是发送设备与接收设备之间协商得到的，或者是发送设备或其他设备发送给接收设备的通知消息中携带的，对此本方案不做限制。
接收设备译码时采用的校验比特的数量、校验比特的位置和校验方程与发送设备相同，关于这些参数是如何确定的前面已经描述过，此处不再详述。
本实施例提供的信息的传输方法，发送设备根据预设的参数对的待编码的序列进行编码，得到编码后的序列，参数包括校验比特的数量、校验比特的位置以及校验方程，发送设备的参数需要预先进行设置，然后对待编码的序列先按照校验比特进行预编码，再进行polar编码，将编码后的序列发送至 接收设备，有效降低信息传输的错误率，提高信息传输的可靠性。
结合上述实施例，下面具体介绍发送设备在信息传输时的编码过程中使用的参数是如何确定的。以CRC校验或者PC校验为例，对校验比特的数量、校验比特的位置以及校验方程的确定方式进行具体说明。例如：与CRC相关的参数的确定方法可以适用于CA-Polar和CA+PC-Polar两种编码方式，与PC相关的参数的确定方法可以适用于PC-Polar和CA+PC-Polar两种编码方式。与CRC相关的参数包括：CRC比特的数量、CRC比特的位置，CRC校验方程。与PC相关的参数包括：PC比特的数量、PC比特的位置，PC校验方程。
一、校验比特的数量(也称为校验比特的长度)
对于在编码过程中采用CRC比特进行校验的编码方式，例如，CA-Polar或者CA+PC-Polar编码方式，CRC比特的数量可以采用如下几种方式中的任意一种来确定：
(1)、CRC比特的数量是预先配置的，即预先固定CRC长度。
预先在设备中配置CRC比特的长度(即CRC比特的数量)为固定值，或者在协议中规定CRC比特的长度(即CRC比特的数量)为固定值：例如“CRC比特数量J＝F 0”，例如，，F 0＝2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,36,40,44,48,52,56,60,64等。
(2)、CRC比特的数量可以根据译码器的列表(list)长度确定。
例如，CRC比特的数量J＝F 1；
其中，“F 1＝ceil(log 2(L))”，L表示list的大小，F 1表示校验比特的数量，函数ceil表示向上取整，在实际应用中也可以是向下取整，还可以是四舍五入。可能的list的大小(也称为长度)L为1，2，4，8，16，32，64，128，256，512，1024，与该些list的大小L对应的校验比特的数量F1为0，1，2，3，4，5，6，7，8，9，10。
或者，在上述方式(1)的F 0的基础上，再增加一个F 1作为CRC的长度，即CRC比特的数量J＝F 0+F 1。
(3)、CRC比特的数量可以是根据码长和码率确定。
例如：“CRC比特数量J＝F 2”，其中“F 2＝ceil(log 2(M))”或“F 2＝ceil(log 2(K))”或“F 2＝ceil(a*log 2(N))”；其中，a为系数，K表示待编码的序列长度(也称为信息比特长度)，M表示码长(编码后、速率匹配后)，F 2表示校验比特的数量，函数ceil表示向上取整，在实际应用中也可以是向下取整，还可以是四舍五入。一种具体实现中，F 2可以是：3,4,5,6,7,8,9,10,11。
(4)、CRC比特的数量可以根据预先配置的比特数、译码器的列表长度、码长和码率来确定。
例如，校验比特的数量还可以是上述几种方式得到的数量的组合，即CRC比特的数量J＝F 0+F 1+F 2。
对于在编码过程中采用PC比特进行校验的编码方式，例如，PC-Polar或者CA+PC-Polar编码方式，PC比特(也可以称为奇偶校验比特，或者奇偶校验冻结比特，或者动态冻结比特)的数量可以采用如下几种方式中的一种来确定：(1)、PC比特的数量可以是预先配置的，即预先固定PC数量：
预先在设备中配置PC比特的长度(即PC比特的数量)为固定值，或者在协议中规定PC比特的长度(即PC比特的数量)为固定值：例如：“PC比特的数量P＝F 0”，例如，F 0＝2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,36,40,44,48,52,56,60,64等。
(2)、PC比特的数量可以是根据译码器的列表(list)长度确定。
例如，PC比特的数量P＝F 1；
其中，“F 1＝ceil(log 2(L))”，L表示list的大小，F 1表示校验比特的数量，函数ceil表示向上取整，在实际应用中也可以是向下取整，还可以是四舍五入。可能的list的大小(也称为长度)L为1，2，4，8，16，32，64，128，256，512，1024，与该些list的大小L对应的校验比特的数量F1为0，1，2，3，4，5，6，7，8，9，10。
或者，在上述方式(1)的F 0的基础上，再增加一个F 1作为PC的长度，即CRC比特的数量P＝F 0+F 1。
(3)、PC比特的数量可以是根据码长和码率确定的。
例如：PC比特的数量P＝F 2，其中，F 2＝ceil(log 2(N)*(α-|α*(K/M-1/2)| 2))或F 2＝ceil(log 2(M))；
其中a为大于0的系数，通常可取0.75,1,1.25,1.5等，N表示母码长度(编码后、速率匹配前)，K表示待编码的序列长度(也称为信息比特长度)，M表示码长(编码后、速率匹配后)，F 2表示校验比特的数量，函数ceil表示向上取整，在实际应用中也可以是向下取整，还可以是四舍五入。
(4)、PC比特的数量可以是根据预先配置的比特数、译码器的列表长度、码长和码率确定的。
即PC比特的数量为上述参数的组合：如PC比特的数量P＝F 0+F 1+F 2。
二、校验比特的位置
对于在编码过程中采用CRC比特进行校验的编码方式，例如，CA-Polar或者CA+PC-Polar编码方式，CRC比特的位置可以采用如下几种方式中的任意一种来确定：
(1)、CRC比特的位置是连续的
例如，待编码序列中比特的位置序号为大于等于0且小于待编码序列的长度K的任意整数，即带编码序列中的每个比特都有唯一的序号，该序号为连续、且大小不同的数字，那么一种CRC比特的位置的具体确定方式为：可以在待编码序列中按照比特的位置序号从大到小的顺序，从位置序号为N X的比特开始选择的连续J个比特的位置作为CRC比特的位置；或者，可以在待编码序列中按照比特的位置序号从小到大的顺序，从位置序号为N X的比特开始选择的连续J个比特的位置作为CRC比特的位置。其中，0≤N X＜K，0<J<K。例如，选择最靠后的J个连续位置作为CRC比特的位置。
(2)、CRC比特的位置是分散的
该方式中，CRC比特的位置可以为从一个新的生成矩阵中选择出的比特位置；所述新的生成矩阵是通过对CRC的生成矩阵进行行列转换，将其中只依赖部分信息比特的CRC比特置换至序号更小的子信道得到的。
例如：将CRC比特的生成矩阵做基本行列变换(如高斯消元)和/或行列置换(如列重排)，后使得一些CRC比特只依赖于部分信息比特或者只和部分信息比特相关，因此可以将此部分CRC比特置换到序号更小的子信道(例如，将此部分CRC比特在CRC生成矩阵中对应的列与所述部分信息比特后面一列进行置换)，在译码时帮助提前排除错误路径。
以3比特CRC举例，若其生成矩阵如下：
Figure PCTCN2018073229-appb-000012
可以发现，3个CRC比特中的最后一个比特(对应生成矩阵第6列)只和前两个比特相关，因此可以将该最后一个CRC比特在CRC生成矩阵中对应的列提前至第三列：
Figure PCTCN2018073229-appb-000013
这样，当接收端译到第三个比特时，可将其看做一个校验比特，并将其置为前两个比特的异或值，并剪去不满足预设值的路径。
上述实例中是以校验比特的数量是3比特为例进行说明的，具体的实现中，校验比特的数量本方案不做限制。
分散CRC比特的位置还可以通过其它方法来确定，例如，通过高斯消元简化CRC生成矩阵，然后通过行列置换将CRC比特中只依赖于部分信息比特的位置提前，
如x p＝(u i+u j+…+u k)，即CRC码字第p个比特为第i,j,…,k的信息比特的模2和，则将CRC比特中的第p个比特前移到第max{i,j,…,k}+1个位置，其中，x p表示第p个校验比特的校验位的值，u i表示第i个信息比特的译码值,i,j,……k表示信息比特的序号,。
对于在编码过程中采用PC比特进行校验的编码方式，例如，PC-Polar或者CA+PC-Polar编码方式，PC比特的位置可以采用如下几种方式中的任意一种来确定：
(1)、PC比特的位置是连续
该方式的含义是，待编码序列中比特的位置序号为大于等于0且小于待编码序列的长度K的任意整数，即带编码序列中的每个比特都有唯一的序号，该序号为连续、且大小不同的数字，那么一种PC比特的位置的具体确定方式为：可以在在待编码序列中按照比特的位置序号从大到小的顺序，从位置序号为N X的比特开始选择的连续P个比特的位置作为PC比特的位置；或者，可以在待编码序列中按照比特的位置序号从小到大的顺序，从位置序号为N X的比特开始选择的连续P个比特的位置作为PC比特的位置。其中，0≤N X≤K，0<P<K。例如，可以选择CRC比特之前的P个连续位置作为PC比特的位置。
(2)PC比特的位置是任意的
例如，可以预设任一的PC比特的位置，对于没有规律可循的PC位置，可以将所有PC位置存表，该方式通常在超短码中使用。一般来说，PC比特的位置对应待编码序列中任意一个比特的位置，或者对应待编码序列多个比特的位置，所述多个比特中至少有两个比特的位置是非连续的。
(3)PC比特的位置是根据子信道行重选择的
对于长码，存储所有PC比特的位置会带来较大存储开销，可通过一些规律来减少存储开销，以及加速硬件实现。该方案中，PC比特的位置可以根据位置参数确定的，所述位置参数至少包括信息阈值Z I和校验阈值Z P；所述信息阈值Z I用于表示所有信息子信道中可靠度最低子信道对应的可靠度；所述校验阈值Z P用于表示所有信息子信道中，可靠度大于信息阈值Z I且行重最大的子信道集合中可靠度最低的子信道对应的可靠度。具体的确定过程包括：
首先，定义归一化可靠度序列Z i：给定按可靠度从小到大已排序的子信道序号序列Q，以及序列长度N max，则归一化可靠度可唯一定义为：for i from 0 to N max-1,set Z[Q i]＝i；endfor
将子信道对应行重RW i的定义为：Polar码生成矩阵中，该(第i个)子信道对应的行中，1的个数。
将子信道序号的汉明重量HW i的定义为：该(第i个)子信道的序号的2进制表示中，1的个数。例如，第5个子信道的序号用2进制可以表示为101，则HW 5＝2。对于所有i满足RW i＝2^(HW i)。因HW的取值范围更小，因此在标准和硬件中更可能用HW而不是RW来表示。
对于一个PC-Polar码，其信息比特/冻结比特/校验比特位置可由2或3个参数唯一确定：
信息阈值Z I:表示所有信息子信道中(除去缩短位置)，可靠度最低子信道对应的可靠度(或极化权重)。
校验阈值Z P:表示所有校验子信道中(除去缩短位置)，可靠度大于最不可靠信息比特(>Z I)的，且行重在其中最大的子信道集合中，可靠度最低子信道对应的可靠度。
(可选的)校验行重RW P(或校验汉明重HW P)表示可靠度等于校验阈值Z P的子信道对应的行重(或校验汉明重)。其可通过Z P唯一换算得到，也可作为参数直接给出。
给定了(Z I,Z P,RW P)，以及第i个子信道的行重RW i以及行重Z i，即可获得潜在的PC比特可选位置(缩短位置不在可选范围之内)，且可以分为三类：
A类PC比特位置：子信道行重为RW P/2，且可靠度不低于信息阈值的位置(Z≥Z I&&RW＝RW P/2)，以及行重为RW P，且可靠度不低于校验阈值的位置(Z≥Z P&&RW＝RW P)。
B类PC比特位置：所有可靠度低于信息阈值的子信道位置(Z<Z I)。
W类PC比特位置：为以下两种位置的并集(一)所有A类子信道位置，(二)B类子信道位置中，行重为为RW P/2以及行重为RW P的位置。即((RW＝RW P/2)||(Z<Z I&&RW＝RW P)||(Z>Z P&&RW＝RW P))。
给定了上述PC比特的位置分类后，可以使用以下方式来确定PC比特的位置，以及PC-Polar码中其它比特的位置：
(1)A类校验:只选择A类PC比特位置(可靠度较高的位置)，包括：
F(冻结比特):Z i<Z I；
PF(PC比特):(RW i＝＝RW P/2&&Z i>Z I)||(RW i＝＝RW P&&Z i>Z P)；I(信息比特):Z i≥Z I&&I≠(PF||P)。
(2)B类校验：只选择B类PC比特位置(可靠度较低的位置)，包括：
PF(PC比特):Z i<Z I；
I(信息比特):Z i≥Z I&&I≠(PF||P)；
(3)W类校验:选择W类PC比特的位置；
F(冻结比特):Z i<Z I&&RW i≠RWP；
PF(PC比特):(RW i＝＝RW P/2)||(RW i＝＝RW P&&Z i>Z P)||(Z i<Z I&&RW＝＝RW P)；
I(信息比特):Z i≥Z I&&I≠(PF||P)。
(4)全校验:选择所有非信息比特且非缩短子信道的位置，包括：
PF(PC比特):Z i<Z I||(RW i<RW P)||(RW i＝＝RW P&&Z i>Z P)；或者，
I(信息比特):Z i≥Z I&&I≠(PF||P)；或者，
(5)混合校验:将CRC校验与上述任一中PC比特的位置产生的校验码级联。
下面将归一化可靠度序列和子信道行重序列可能的情况进行举例：
(一)、归一化可靠度序列Z i：
Z i(8)：0,1,2,4,3,5,6,7；
Z i(16)：0,1,2,5,3,6,7,11,4,8,9,12,10,13,14,15；
Z i(32)：0,1,2,6,3,7,8,15,4,9,10,17,12,18,20,26,5,11,13,19,14,21,22,27,16,23,24,28，25,29,30,31；
Z i(64)：0,1,2,6,3,8,9,18,4,10,11,21,13,23,25,37,5,12,14,24,16,27,29,41,19,30,32,43，35,46,48,56,7,15,17,28,20,31,33,44,22,34,36,47,39,49,51,58,26,38,40,50,42,52,53,59,45,54,55,60,57,61,62,63；
Z i(128)：0,1,2,6,3,8,9,19,4,10,12,23,14,26,29,46,5,13,15,27,17,31,34,52,20,35,38，56,42,61,65,84,7,16,18,33,21,36,39,58,25,41,45,64,49,68,72,90,30,47,51,70,54,74,77,95,60,79,83,99,87,103,105,116,11,22,24,40,28,44,48,67,32,50,53,73,57,76,80,97,37,55,59,78,63,82,86,102,69,88,91,106,94,109,111,120,43,62,66,85,71,89,92,107,75,93,96,110,100,112,114,122,81,98,101,113,104,115,117,123,108,118,119,124,121,125,126,127；
Z i(256)：0,1,2,6,3,8,9,20,4,10,12,24,14,27,30,51,5,13,15,28,18,33,37,59,21,38,42，65,47,72,78,108,7,17,19,36,22,40,43,68,26,46,50,77,55,83,88,120,32,53,58,86,63,92,97,130,71,100,107,138,114,146,152,182,11,23,25,44,29,49,54,81,34,56,60,89,66,94,101,133,41,64,69,98,76,106,112,144,84,115,121,153,127,160,165,194,48,74,80,110,87,118,124,156,93,126,132,164,139,170,176,203,104,136,142,173,150,180,185,210,159,188,193,216,198,
220,224,239,16,31,35,57,39,62,67,96,45,70,75,105,82,113,119,151,52,79,85,116,91,123,129,162,99,131,137,168,145,175,181,207,61,90,95,128,102,134,140,171,111,143,149,179,157,186,191,214,122,154,161,189,166,195,199,221,174,201,206,226,211,230,232,244,73,103,109,141,117,148,155,184,125,158,163,192,169,197,202,223,135,167,172,200,178,205,209,229,187,212,215,233,219,236,238,248,147,177,183,208,190,213,217,234,196,218,222,237,227,240,242,250,204,225,228,241,231,243,245,251,235,246,247,252,249,253,254,255；
Z i(512)：0,1,2,6,3,8,9,20,4,10,12,24,14,28,31,54,5,13,15,29,18,34,38,63,21,39，43,70,49,78,85,124,7,17,19,37,22,41,44,73,27,48,53,84,59,92,98,141,33,56,62,95,68,103,110,155,77,114,123,168,133,180,190,242,11,23,26,46,30,52,58,90,35,60,65,100,71,107,116,161,42,69,75,112,83,122,131,178,93,134,143,192,152,203,213,267,51,81,88,128,97,139,147,197,106,151,159,211,170,222,232,287,120,165,175,227,188,240,249,303,202,254,265,317,277,329,339,386,16,32,36,61,40,67,72,109,47,76,82,121,91,132,140,189,55,86,94,135,102,145,154,205,113,157,166,217,179,230,241,295,66,101,108,153,117,162,171,223,130,177,187,239,199,251,261,313,144,193,204,256,214,268,278,330,228,282,293,344,304,355,363,407,80,119,127,174,138,186,196,248,150,201,210,264,221,276,286,338,164,215,226,280,238,292,302,353,253,305,316,365,328,375,385,424,184,236,245,299,259,311,320,369,274,326,335,382,348,393,400,437,291,342,351,396,362,406,412,447,374,415,422,454,432,461,466,486,25,45,50,79,57,89,96,137,64,99,105,149,115,160,169,220,74,111,118,163,129,176,185,237,142,191,200,252, 212,266,275,327,87,126,136,183,146,195,206,258,158,209,219,273,231,285,296,347,173,225,235,290,247,301,310,361,263,315,325,373,337,384,392,431,104,148,156,207,167,218,229,283,181,233,243,297,255,307,318,367,198,250,260,312,272,324,334,381,288,340,349,394,358,403,410,445,216,270,281,332,294,345,354,398,306,357,366,409,376,417,425,456,322,371,379,420,390,429,435,464,402,439,444,471,450,475,479,495,125,172,182,234,194,246,257,309,208,262,271,323,284,336,346,391,224,279,289,341,300,352,360,405,314,364,372,414,383,423,430,460,244,298,308,359,319,368,377,418,333,380,389,428,399,436,442,469,350,395,404,440,411,446,451,476,421,453,459,481,465,485,488,500,269,321,331,378,343,388,397,434,356,401,408,443,416,449,455,478,370,413,419,452,427,458,463,484,438,467,470,489,474,492,494,504,387,426,433,462,441,468,472,490,448,473,477,493,482,496,498,506,457,480,483,497,487,499,501,507,491,502,503,508,505,509,510,511；
Z i(1024)：0,1,2,6,3,8,9,20,4,10,12,24,14,28,31,55,5,13,15,29,18,34,38,64,21,39,44，72,50,81,89,133,7,17,19,37,22,42,45,76,27,49,54,88,60,97,103,154,33,57,63,100,70,109,117,171,80,121,132,187,144,202,215,286,11,23,26,47,30,53,59,94,35,61,66,105,73,113,123,177,43,71,78,119,87,131,141,199,98,145,156,217,167,232,245,322,52,85,92,138,102,151,161,224,112,166,175,243,189,258,272,353,129,184,196,266,212,283,297,380,231,304,320,403,338,423,440,530,16,32,36,62,41,69,75,116,48,79,86,130,96,143,153,214,56,90,99,146,108,159,170,235,120,173,185,252,201,270,285,366,67,106,114,168,125,180,191,261,140,198,211,282,227,300,315,398,157,218,233,306,248,325,341,426,267,346,363,449,382,470,487,576,84,128,137,195,150,210,223,295,165,230,242,319,257,337,352,439,183,250,265,344,281,362,378,466,303,384,402,490,422,510,529,617,207,278,291,374,311,393,410,499,334,419,435,525,455,545,561,650,360,446,463,552,483,572,589,675,508,596,614,697,635,716,733,804,25,46,51,83,58,93,101,149,65,104,111,164,122,176,188,256,77,118,127,182,139,197,209,280,155,216,229,302,244,321,336,421,91,136,147,206,160,222,236,310,174,241,254,333,271,351,367,454,194,264,277,359,294,377,392,482,318,401,418,507,438,528,544,634,110,162,172,238,186,253,268,347,203,273,287,369,305,386,404,492,226,299,314,397,332,417,433,523,355,442,458,548,476,566,582,669,251,329,345,430,364,450,468,556,385,474,491,580,511,599,618,700,413,503,519,609,539,629,644,727,564,653,667,749,684,764,777,845,135,193,205,276,221,293,309,391,240,317,331,416,350,437,453,543,263,343,358,445,376,465,481,571,400,489,506,595,527,616,633,715,289,372,387,477,408,497,514,603,432,522,538,628,559,648,662,744,461,551,567,655,587,674,688,768,612,696,711,786,731,803,815,875,328,412,429,518,448,537,554,642,473,563,579,666,598,683,699,776,502,592,608,693,627,710,725,798,652,735,748,819,763,833,844,899,535,624,640,722,658,739,754,823,681,761,774,842,789,854,865,916,707,784,795,860,810,871,881,928,831,889,897,941,908,949,955,983,40,68,74,115,82,126,134,192,95,142,152,213,163,228,239,316,107,158,169,234,181,249,262,342,200,269,284,365,301,383,399,488,124,179,190,260,204,275,288,371,225,298,313,396,330,415,431,521,247,324,340,425,357,444,460,550,381,469,486,575,505,594,611,695,148,208,220,292,237,312,327,411,255,335,349,436,368,456,472,562,279,361,375,464,395,485,501,591,420,509,526,615,546,636,651,734,308,390,407,496,428,517,534,623,452,542,558,647,578,665,680,760,480,570,586,673,607,692,706,783,632,714,730,802,747,818,830,888,178,246,259,339,274,356,370,459,296,379,394,484,414,504,520,610,323,405,424,512,443,532,549,638,467,555,573,659,593,678,694,772,354,441,457,547,475,565,581,668,500,590,606,691,626,709,724, 797,531,619,637,718,654,736,750,820,676,755,770,837,785,851,861,913,389,479,495,585,516,605,622,705,541,631,646,729,664,746,759,829,569,656,672,752,690,769,782,849,713,787,801,863,817,876,887,932,602,687,702,779,721,794,807,868,743,814,826,884,841,896,905,946,767,835,847,901,859,912,919,958,874,922,930,965,940,972,977,998,219,290,307,388,326,409,427,515,348,434,451,540,471,560,577,663,373,462,478,568,498,588,604,689,524,613,630,712,649,732,745,816,406,494,513,601,533,621,639,720,557,645,661,742,679,758,773,840,584,671,686,766,704,781,793,858,728,800,813,873,828,886,895,939,447,536,553,641,574,660,677,756,597,682,698,775,717,790,805,866,625,708,723,796,741,812,825,883,762,832,843,898,855,909,917,956,657,738,753,822,771,838,850,903,788,853,864,915,877,924,933,967,809,870,880,927,893,937,944,975,907,948,954,982,961,987,991,1007,493,583,600,685,620,703,719,792,643,726,740,811,757,827,839,894,670,751,765,834,780,848,857,911,799,862,872,921,885,931,938,971,701,778,791,856,806,867,878,925,824,882,892,936,904,945,952,980,846,900,910,950,918,957,962,988,929,964,970,993,976,997,1000,1012,737,808,821,879,836,891,902,943,852,906,914,953,923,960,966,990,869,920,926,963,935,969,974,996,947,978,981,1001,986,1004,1006,1016,890,934,942,973,951,979,984,1002,959,985,989,1005,994,1008,1010,1018,968,992,995,1009,999,1011,1013,1019,1003,1014,1015,1020,1017,1021,1022,1023；
Z i(2048)：0,1,2,6,3,8,9,20,4,10,12,24,14,28,31,55,5,13,15,29,18,34,38,64,21,39，44,73,50,82,90,137,7,17,19,37,22,42,45,77,27,49,54,89,60,98,105,160,33,57,63,101,71,111,120,178,81,124,136,196,149,213,229,312,11,23,26,47,30,53,59,95,35,61,67,107,74,116,127,186,43,72,79,122,88,135,146,210,99,150,162,231,174,248,264,357,52,86,93,143,103,156,167,239,115,173,184,262,199,279,296,397,133,193,207,288,225,308,326,431,247,334,355,462,377,488,512,641,16,32,36,62,41,70,76,119,48,80,87,134,97,148,158,227,56,91,100,151,110,165,177,251,123,181,194,272,212,293,310,412,68,108,117,175,129,189,202,283,145,209,224,307,242,329,348,455,163,232,249,337,267,360,381,492,289,387,408,524,433,553,578,712,85,132,142,206,155,223,238,324,172,246,260,353,278,376,395,510,192,269,287,384,306,407,429,548,333,437,460,583,487,613,639,779,220,303,320,425,343,449,472,598,372,483,505,634,533,664,690,834,405,519,545,675,573,706,735,879,609,745,774,919,807,954,984,1133,25,46,51,84,58,94,102,154,66,106,114,171,126,185,198,277,78,121,131,191,144,208,222,305,161,230,245,332,263,356,375,486,92,141,152,219,166,237,252,342,182,259,274,371,294,394,414,532,205,286,302,404,323,428,448,572,352,459,482,608,509,638,663,806,112,168,179,254,195,273,290,388,215,297,314,417,336,441,464,588,241,328,346,453,370,481,502,631,399,514,537,668,565,699,725,870,270,365,385,497,409,525,550,681,438,560,585,720,614,752,781,927,475,602,625,766,655,799,824,975,694,838,865,1016,898,1049,1077,1227,140,204,218,301,236,322,341,447,258,351,369,480,393,508,530,661,285,383,403,518,427,547,571,705,458,581,607,743,637,777,805,952,317,422,442,566,469,595,619,759,501,630,654,798,686,830,856,1008,542,673,700,843,732,877,905,1055,771,916,946,1094,981,1130,1159,1303,364,474,496,624,523,653,679,822,559,693,718,863,751,897,925,1075,601,738,765,911,797,945,973,1123,837,987,1015,1165,1048,1199,1226,1369,648,791,817,967,849,1000,1028,1179,890,1041,1068,1219,1103,1251,1278,1419,939,1089,1117,1264,1151,1297,1324,1460,1193,1337,1363,1495,1395,1525,1548,1661,40,69,75,118,83,130,139,203,96,147,157,226,170,244,257,350,109,164,176,250,190,268,284,382,211,291,309,410,331,435,457,580,128,188,200,281,217,300,316,421,240,327,345,452, 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Z 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Z i(16384)：0,1,2,6,3,8,9,20,4,10,12,24,14,28,31,55,5,13,15,29,18,34,38,64,21,39,44，73,50,82,90,138,7,17,19,37,22,42,45,77,27,49,54,89,60,98,105,161,33,57,63,101,71,112,121,181,81,125,137,201,150,219,235,330,11,23,26,47,30,53,59,95,35,61,67,107,74,117,128,190,43,72,79,123,88,136,147,216,99,151,163,237,177,256,274,382,52,86,93,144,103,157,169,246,116,175,188,271,204,291,311,429,134,198,212,301,231,326,346,473,254,355,378,512,405,547,577,759,16,32,36,62,41,70,76,120,48,80,87,135,97,149,159,233,56,91,100,152,111,167,180,259,124,185,199,284,218,308,328,449,68,10 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Z i(32768)：0,1,2,6,3,8,9,20,4,10,12,24,14,28,31,55,5,13,15,29,18,34,38,64,21,39， 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1386,30683,31073,31142,31468,31219,31532,31587,31843,29004,29595,29700,30213,29819,30320,30408,30835,29958,30443,30526,30939,30623,31024,31091,31426,30121,30584,30665,31058,30759,31139,31205,31521,30867,31231,31295,31596,31369,31660,31710,31945,30304,30743,30820,31191,30909,31268,31330,31627,31010,31356,31414,31699,31482,31757,31802,32023,31126,31455,31510,31780,31575,31834,31877,32085,31650,31895,31937,32133,31986,32173,32204,32350,24653,25594,25765,26634,25965,26820,26974,27753,26198,27036,27187,27948,27363,28109,28242,28910,26474,27290,27439,28176,27611,28334,28465,29108,27809,28515,28643,29268,28789,29401,29511,30044,26791,27584,27724,28438,27892,28592,28714,29334,28083,28766,28885,29489,29027,29617,29718,30231,28310,28968,29085,29667,29224,29790,29889,30381,29381,29928,30026,30500,30140,30599,30680,31070,27154,27917,28054,28739,28213,28882,29002,29593,28397,29049,29164,29739,29299,29858,29956,30441,28615,29244,29357,29908,29486,30023,30119,30582,29636,30156,30249,30694,30355,30788,30865,31229,28861,29466,29573,30100,29698,30211,30302,30741,29839,30338,30424,30850,30524,30937,31008,31354,30006,30483,30566,30973,30663,31056,31124,31453,30774,31150,31217,31530,31293,31594,31648,31893,27571,28299,28428,29077,28581,29215,29326,29883,28756,29373,29481,30020,29608,30133,30224,30675,28959,29554,29660,30177,29783,30287,30376,30806,29922,30410,30495,30911,30594,30997,31066,31403,29191,29763,29861,30358,29979,30462,30543,30955,30114,30579,30658,31053,30753,31135,31199,31517,30270,30712,30791,31165,30883,31244,31308,31607,30984,31332,31392,31679,31462,31738,31785,32007,29457,29999,30093,30561,30204,30657,30736,31120,30331,30769,30844,31213,30932,31289,31350,31645,30478,30896,30969,31319,31052,31391,31450,31728,31147,31472,31527,31793,31592,31847,31891,32095,30641,31039,31106,31439,31185,31505,31559,31821,31276,31582,31634,31883,31694,31933,31973,32163,31381,31669,31720,31953,31776,31999,32039,32215,31839,32052,32089,32256,32130,32289,32317,32438,28040,28727,28849,29456,28990,29583,29688,30203,29153,29729,29830,30330,29947,30433,30517,30931,29346,29899,29998,30477,30109,30574,30656,31051,30240,30687,30768,31146,30857,31223,31288,31591,29563,30092,30184,30640,30294,30735,30811,31184,30416,30843,30916,31275,31002,31349,31407,31693,30560,30968,31038,31380,31119,31449,31504,31775,31212,31526,31581,31838,31644,31890,31932,32129,29808,30310,30398,30826,30498,30914,30987,31335,30614,31015,31083,31418,31163,31486,31541,31805,30749,31131,31197,31515,31273,31579,31632,31881,31360,31653,31703,31940,31760,31988,32026,32206,30901,31261,31323,31621,31395,31682,31731,31963,31475,31750,31796,32017,31849,32061,32097,32263,31569,31829,31872,32081,31923,32122,32155,32311,31980,32168,32199,32346,32235,32374,32397,32503,30083,30552,30633,31032,30728,31113,31179,31500,30837,31207,31270,31577,31344,31640,31689,31929,30962,31314,31376,31666,31444,31724,31772,31997,31523,31790,31836,32050,31887,32092,32127,32287,31099,31433,31488,31762,31554,31817,31860,32071,31629,31879,31920,32120,31969,32160,32190,32339,31716,31950,31990,32176,32036,32213,32243,32380,32087,32254,32283,32411,32315,32436,32457,32547,31256,31564,31617,31868,31678,31919,31960,32152,31747,31977,32014,32196,32059,32233,32261,32395,31825,32042,32078,32248,32119,32282,32309,32433,32166,32319,32344,32460,32373,32484,32502,32583,31911,32112,32146,32303,32183,32333,32358,32472,32226,32367,32390,32497,32416,32517,32533,32607,32277,3 2407,32429,32527,32453,32545,32561,32628,32480,32565,32580,32641,32596,32653,32663,32702,25501,26387,26549,27359,26736,27532,27677,28393,26955,27736,27875,28577,28037,28724,28846,29453,27210,27968,28105,28785,28262,28926,29045,29632,28449,29094,29211,29779,29343,29896,29995,30474,27506,28238,28369,29023,28523,29160,29274,29835,28700,29322,29430,29975,29560,30089,30181,30637,28906,29507,29613,30136,29735,30245,30334,30770,29879,30372,30458,30879,30557,30965,31035,31377,27844,28547,28674,29296,28818,29427,29536,30066,28988,29581,29686,30201,29806,30308,30396,30824,29182,29754,29855,30352,29971,30454,30537,30949,30107,30572,30654,31049,30747,31129,31195,31513,29408,29953,30049,30521,30161,30618,30698,31086,30292,30733,30809,31182,30899,31259,31321,31619,30438,30862,30934,31290,31019,31364,31421,31705,31117,31447,31502,31773,31567,31827,31870,32079,28228,28897,29015,29606,29152,29728,29829,30329,29312,29870,29967,30451,30081,30550,30631,31030,29499,30034,30131,30592,30239,30686,30767,31145,30365,30797,30874,31237,30960,31312,31374,31664,29708,30222,30311,30751,30415,30842,30915,31274,30533,30946,31016,31362,31097,31431,31487,31761,30673,31064,31133,31460,31211,31525,31580,31837,31301,31601,31655,31899,31714,31948,31989,32175,29946,30432,30516,30930,30613,31014,31082,31417,30727,31112,31178,31499,31255,31563,31616,31867,30856,31222,31287,31590,31359,31652,31702,31939,31443,31723,31771,31996,31824,32041,32077,32247,31001,31348,31406,31692,31474,31749,31795,32016,31553,31816,31859,32070,31910,32111,32145,32302,31643,31889,31931,32128,31979,32167,32198,32345,32035,32212,32242,32379,32276,32406,32428,32526,28662,29286,29399,29945,29526,30058,30154,30612,29676,30192,30285,30726,30388,30817,30894,31254,29846,30343,30431,30855,30529,30941,31013,31358,30646,31042,31111,31442,31188,31507,31562,31823,30042,30515,30597,31000,30692,31081,31148,31473,30804,31177,31242,31552,31317,31615,31667,31909,30929,31286,31347,31642,31416,31701,31748,31978,31498,31770,31815,32034,31866,32076,32110,32275,30263,30707,30787,31162,30877,31240,31304,31604,30979,31328,31390,31677,31458,31735,31783,32005,31094,31428,31485,31759,31550,31813,31857,32068,31625,31875,31918,32118,31966,32157,32188,32337,31228,31540,31593,31848,31657,31901,31942,32137,31727,31959,31998,32182,32044,32219,32249,32384,31804,32025,32060,32234,32103,32269,32295,32422,32151,32308,32332,32452,32361,32475,32492,32576,30508,30923,30996,31343,31076,31412,31471,31746,31171,31494,31548,31812,31611,31864,31907,32109,31281,31585,31639,31886,31697,31935,31976,32165,31767,31993,32032,32210,32074,32245,32274,32405,31402,31688,31737,31968,31792,32013,32051,32225,31855,32067,32102,32268,32142,32300,32326,32446,31928,32126,32159,32314,32195,32343,32366,32479,32240,32378,32401,32506,32426,32525,32540,32613,31535,31800,31846,32058,31897,32100,32135,32293,31956,32149,32181,32331,32217,32360,32383,32491,32021,32202,32232,32372,32266,32399,32420,32520,32306,32431,32451,32544,32474,32562,32575,32638,32094,32260,32288,32415,32320,32440,32461,32550,32356,32470,32488,32572,32509,32588,32601,32657,32394,32501,32516,32595,32535,32609,32619,32671,32559,32627,32636,32684,32648,32692,32698,32727,29138,29715,29817,30318,29934,30421,30506,30921,30069,30540,30621,31022,30716,31103,31169,31492,30228,30677,30757,31137,30847,31214,31279,31583,30952,31305,31367,31658,31436,31717,31765,31991,30406,30833,30907,31266,30994,31341,31400,31686,31089,31424,31480,3 1755,31546,31810,31853,32065,31203,31519,31573,31832,31637,31884,31926,32124,31708,31943,31984,32171,32030,32208,32238,32376,30604,31006,31075,31411,31154,31478,31534,31799,31247,31557,31610,31863,31671,31913,31955,32148,31352,31646,31696,31934,31753,31982,32020,32201,31819,32037,32073,32244,32114,32278,32305,32430,31470,31745,31791,32012,31845,32057,32093,32259,31906,32108,32141,32299,32180,32330,32355,32469,31975,32164,32194,32342,32231,32371,32393,32500,32273,32404,32425,32524,32450,32543,32558,32626,30827,31198,31262,31570,31336,31633,31683,31924,31419,31704,31751,31981,31806,32027,32062,32236,31516,31784,31830,32045,31882,32088,32123,32284,31941,32136,32169,32321,32207,32352,32375,32485,31622,31873,31915,32116,31964,32156,32186,32336,32018,32200,32229,32370,32264,32398,32418,32519,32082,32250,32280,32409,32312,32434,32455,32546,32347,32462,32482,32567,32504,32584,32597,32654,31741,31972,32010,32193,32054,32228,32258,32392,32105,32271,32297,32424,32328,32448,32468,32557,32162,32316,32341,32458,32369,32481,32499,32581,32403,32507,32523,32599,32542,32614,32625,32675,32223,32365,32387,32495,32414,32515,32531,32605,32444,32539,32553,32622,32571,32635,32645,32689,32478,32564,32578,32640,32594,32652,32661,32701,32612,32665,32673,32709,32683,32716,32721,32742,31068,31405,31464,31740,31528,31794,31840,32053,31605,31858,31902,32104,31951,32144,32177,32327,31691,31930,31971,32161,32015,32197,32227,32368,32069,32241,32270,32402,32301,32427,32447,32541,31787,32009,32047,32222,32090,32257,32285,32413,32138,32296,32323,32443,32353,32467,32486,32570,32192,32340,32364,32477,32391,32498,32514,32593,32423,32522,32538,32611,32556,32624,32634,32682,31892,32096,32131,32290,32170,32322,32348,32463,32214,32357,32381,32489,32408,32510,32528,32602,32262,32396,32417,32518,32442,32537,32552,32621,32471,32560,32573,32637,32589,32649,32658,32699,32318,32439,32459,32549,32483,32568,32582,32643,32508,32587,32600,32656,32615,32667,32676,32711,32534,32608,32618,32670,32632,32680,32687,32719,32647,32691,32697,32726,32705,32731,32735,32751,32006,32189,32220,32362,32255,32389,32412,32513,32294,32421,32441,32536,32466,32555,32569,32633,32338,32456,32476,32563,32496,32579,32592,32651,32521,32598,32610,32664,32623,32674,32681,32715,32385,32493,32511,32590,32530,32604,32616,32668,32551,32620,32631,32679,32644,32688,32695,32724,32577,32639,32650,32693,32660,32700,32706,32732,32672,32708,32714,32737,32720,32741,32744,32756,32437,32532,32548,32617,32566,32630,32642,32686,32586,32646,32655,32696,32666,32704,32710,32734,32606,32662,32669,32707,32678,32713,32718,32740,32690,32722,32725,32745,32730,32748,32750,32760,32629,32677,32685,32717,32694,32723,32728,32746,32703,32729,32733,32749,32738,32752,32754,32762,32712,32736,32739,32753,32743,32755,32757,32763,32747,32758,32759,32764,32761,32765,32766,32767；
(二)、子信道行重序列RW：
RW_8：1,2,2,4,2,4,4,8；
RW_16：1,2,2,4,2,4,4,8,2,4,4,8,4,8,8,16；
RW_32：1,2,2,4,2,4,4,8,2,4,4,8,4,8,8,16,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32；
RW_64：1,2,2,4,2,4,4,8,2,4,4,8,4,8,8,16,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,2,4,4，8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64；
RW_128：1,2,2,4,2,4,4,8,2,4,4,8,4,8,8,16,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,2,4,4,8，4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128；
RW_256：1,2,2,4,2,4,4,8,2,4,4,8,4,8,8,16,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,2,4,4,8，4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256；
RW_512：1,2,2,4,2,4,4,8,2,4,4,8,4,8,8,16,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,2,4,4,8，4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512；
RW_1024：1,2,2,4,2,4,4,8,2,4,4,8,4,8,8,16,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,2,4,4，8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,3 2,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024；
RW_2048：1,2,2,4,2,4,4,8,2,4,4,8,4,8,8,16,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,2,4,4，8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,2,4,4,8,4,8,8,16,4,8,8,1 6,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,2 56,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048；
RW_4096：1,2,2,4,2,4,4,8,2,4,4,8,4,8,8,16,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,2,4，4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,3 2,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64, 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56,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096；
RW_8192：1,2,2,4,2,4,4,8,2,4,4,8,4,8,8,16,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,2,4,4，8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,4,8, 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28,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192；
RW_16384：1,2,2,4,2,4,4,8,2,4,4,8,4,8,8,16,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,2,4，4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,1 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24,2048,2048,4096,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,1024,2048,2048,4096,2048,4096,4096,8192,2048,4096,4096,8192,4096,8192,8192,16384；
RW_32768：1,2,2,4,2,4,4,8,2,4,4,8,4,8,8,16,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,2,4，4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,2,4,4,8,4,8,8,16,4,8,8,16,8,16,16,32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32,64,64,128,32,64,64,128,64,128,128,256,8,16,16,32,16,32,32,64,16,32,32,64,32,64,64,128,16,32,32,64,32, 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256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,1024,2048,2048,4096,2048,4096,4096,8192,2048,4096,4096,8192,4096,8192,8192,16384,32,64,64,128,64,128,128,256,64,128,128,256,128,256,256,512,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,128,256,256,512,256,512,512,1024, 256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,1024,2048,2048,4096,2048,4096,4096,8192,2048,4096,4096,8192,4096,8192,8192,16384,64,128,128,256,128,256,256,512,128,256,256,512,256,512,512,1024,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,1024,2048,2048,4096,2048,4096,4096,8192,2048,4096,4096,8192,4096,8192,8192,16384,128,256,256,512,256,512,512,1024,256,512,512,1024,512,1024,1024,2048,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,1024,2048,2048,4096,2048,4096,4096,8192,2048,4096,4096,8192,4096,8192,8192,16384,256,512,512,1024,512,1024,1024,2048,512,1024,1024,2048,1024,2048,2048,4096,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048, 4096,2048,4096,4096,8192,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,1024,2048,2048,4096,2048,4096,4096,8192,2048,4096,4096,8192,4096,8192,8192,16384,512,1024,1024,2048,1024,2048,2048,4096,1024,2048,2048,4096,2048,4096,4096,8192,1024,2048,2048,4096,2048,4096,4096,8192,2048,4096,4096,8192,4096,8192,8192,16384,1024,2048,2048,4096,2048,4096,4096,8192,2048,4096,4096,8192,4096,8192,8192,16384,2048,4096,4096,8192,4096,8192,8192,16384,4096,8192,8192,16384,8192,16384,16384,32768；
(三)、汉明重量序列HW：
HW_8：0,1,1,2,1,2,2,3；
HW_16：0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4；
HW_32：0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5；
HW_64：0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4，2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6；
HW_128：0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3，4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7；
HW_256：0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3，4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8；
HW_512：0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3，4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9；
HW_1024：0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,1,2,2,3,2,3，3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7, 4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10；
HW_2048：0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3，4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,3,4,4,5,4, 5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11；
HW_4096：0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3，4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,3,4,4,5,4, 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9,10,10,11,10,11,11,12,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,10,11,11,12,11,12,12,13,11,12,12,13,12,13,13,14,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9, 9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,10,11,11,12,11,12,12,13,11,12,12,13,12,13,13,14,5,6,6,7,6,7,7,8,6,7,7,8,7,8,8,9,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,10,11,11,12,11,12,12,13,11,12,12,13,12,13,13,14,6,7,7,8,7,8,8,9,7,8,8,9,8,9,9,10,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,10,11,11,12,11,12,12,13,11,12,12,13,12,13,13,14,7,8,8,9,8,9,9,10,8,9,9,10,9,10,10,11,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,10,11,11,12,11,12,12,13,11,12,12,13,12,13,13,14,8,9,9,10,9,10,10,11,9,10,10,11,10,11,11,12,9,10,10,11,10,11,11, 12,10,11,11,12,11,12,12,13,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,10,11,11,12,11,12,12,13,11,12,12,13,12,13,13,14,9,10,10,11,10,11,11,12,10,11,11,12,11,12,12,13,10,11,11,12,11,12,12,13,11,12,12,13,12,13,13,14,10,11,11,12,11,12,12,13,11,12,12,13,12,13,13,14,11,12,12,13,12,13,13,14,12,13,13,14,13,14,14,15。
三、校验方程
无论是采用哪种编码方式，例如，CA-Polar、PC-Polar或者CA+PC-Polar编码方法，其校验方程都可以由生成多项式唯一确定，而生成多项式又有多种等价的表示方式，例如可以采用二进制，八进制，十进制，十六进制，位置向量中的任一种进行表示。例如：若CRC多项式为[1,1,0,0,1,1,1],其也可以等价表示为其1的位置向量(最低位从0开始)[6,5,2,1,0]；也可以由其2进制向量对应的十进制数表示，即，下文给出的十进制表示为将二进制向量高低位翻转后，转换成的十进制值，如对于多项式为[1,1,0,0,1,1,1],其十进制表示为115。
(1)对于在编码过程中采用CRC比特进行校验的编码方式，校验方程可以生成多项式(polynomial产生)，例如，假设生成多项式采用十进制表示，则这些生成多项式可以是：(24):29254851；(24):25952259；(19):1005307；(16):67601；(15):57977；(14):31993；(13):16299；(12):7705；(11):3805；(10):1939；(9):817；(8):435；(7):211；(6):115；(5):41；(4):25；(3):9；
上述括号中的数值表示CRC的长度(即CRC比特数)，括号后的序列表示多项式。针对每种CRC长度，多项式也可以是其它的序列，上述例子只是用于帮助理解。在上述例子中，多项式是采用十进制表示的，在实际应用中还可以采用其它进制表示，对此本申请不做限制。
(2)对于在编码过程中采用PC比特进行校验的编码方式，校验方程还可以采用表格表示法：图6为校验方程的表格表示法的示意图，如图6所示冻结/信息/校验/缩短位置分别由不同填充表示，表格中的F表示固定比特，I表示信息比特，S表示缩短比特，其他的表格中的数字代表其参与的第几个校验方程，相同数字对应位置的比特参与同一个校验方程，其中子信道序号最大(最靠后)的比特为PC比特。
下面列举几种表格表示的校验方式的实例：
Figure PCTCN2018073229-appb-000014
除了上述的使用多种进制的数字表示多项式，来确定校验方程，或者使用表格表示校验方程之外，还可以通过另一种多项式表示校验方程，即可以使用移位寄存器进行表示。
PC-Polar校验方程的多项式表示法：作为更为简便的校验方程表示方式，每个校验方程只需要1个向量，或一个十进制数表示即可。下面举几个移位寄存器表示多项式的实例。
图7为多项式[1,0,0,0,0]采用移位寄存器的示意图，如图7所示，对于长度为5的移位寄存器，其多项式表示可以为[1,0,0,0,0]或者[4]或者十进制数16。
图8为多项式[1,0,1,0,0]采用移位寄存器的示意图，如图8所示，对于长度为5，但在第3个位置具有反馈抽头的的移位寄存器，其多项式表示可以为[1,0,1,0,0]或者[4,2]或者十进制数20。
此外，对于PC校验方程，可用(但不仅限于)的多项式的十进制表示为：4；16；64；256；272；68；273；65552；65808；65553；70661；1028；4100；65540；1029；65604；21；69633；69636；69648；69636。作为一种可选的方式，PC-Polar也可以使用CRC多项式直接作为其校验方程的多项式。
需要说明的是，对于CA+PC-Polar编码方式：(1)PC比特和CRC比特可以使用不同的多项式来定义校验方程，且相互独立进行预编码(例如，采用两组不同的移位寄存器)；(2)PC比特和CRC比特使用相同的多项式来定义校验方程，且同时联合进行预编码(例如，采用一组相同的移位寄存器)；(3)PC比特和CRC比特采用不同的校验方程，例如，PC比特使用表格的方式来定义非多项式的校验方程，CRC比特使用移位寄存器来定义校验方程。
如果发送端采用CA-Polar或者CA+PC-Polar的编码方式，则接收端对应的可以采用CA+PC-SCL的译码方式。由于CA+PC-Polar的编码方式中采用了校验比特(例如，CRC比特)进行校验，正常情况下，接收端在译码过程中需要对list(列表)中所有的译码路径(例如L条译码路径)都使用CRC进行检验，以确定被检查的路径是否正确。但是本申请人的发明人发现，每次CRC检验都会增加一定的虚警概率。“虚警”是指：译码错误但是使用CRC比特检验通过。这是因为可能存在多个译码结果都具有相同的CRC校验值，但其中只有唯一一个是正确的译码结果。
由此可见，虚警概率和使用CRC比特进行校验的次数密切相关。基于此，本申请的实施例还提供了一种虚警概率可控的译码方法，图9为本申请的译码方法的译码过程示意图，如图9所示，通过此方法，可以不用对每条译码路径都进行CRC检验，由此提高了译码的效率。采用采用CA+PC-Polar编码方式编码后的序列中包括四种比特，即：信息比特、静态冻结比特(或称为冻结比特，此比特为可选，也就是说，在编码后的序列中也有可能不包括静态冻结比特)、PC比特和CRC比特。静态冻结比特(或称为冻结比特，此比特为可选，也就是说，在编码后的序列中也有可能不包括静态冻结比特)
接收端因为知道每种比特的类型、数量以及对应的位置，因此在译码时也会区分对待。假设，发送端经过编码后输出的编码块中包含N个比特，接收端采用的译码列表的宽度为L，接收端收到每个比特后都会根据每个比特的类型进行不同的处理：
(1)对于信息比特，则将该信息比特对应的路径扩展为0和1的两个路径，并分别计算两条路径的度量值,即PM值；
如果扩展后的路径数l≤L，则保留所有路径；
如扩展后路径数l>L，则保留PM值最优(最小)的L条路径；
(2)对于静态冻结比特，则不扩展路径，直接将该比特译码结果置为0，并计算此静态冻结 比特所在路径的PM值；
(3)对于PC比特或者CRC比特，在处理时可以采用如下两种方式中的任意一种：
a.方法一：不扩展路径，直接将该比特的值置为满足校验方程的值，并计算相应的PM值；
如果是CRC比特，则在译到最后一个CRC比特之前，可以按照上述方法一进行处理，如果译到最后一个CRC比特时，可以按照下面的方法二的第ii中方式进行处理。
b.方法二：
i.在译码过程中，例如，译到最后一个CRC比特之前，按照与信息比特完全相同的方法扩展路径，并计算每条路径的PM值；
ii.在译码结束时，例如，译到最后一个CRC比特时，按PM值从好到差(从小到大)依次做最多T次CRC检验，其中T满足1≤T≤L，例如，参见图9所示，列表的宽度L＝16，其中只进行了T＝4次CRC检验。
ii.1若检验次数≤T时，已经找到一条校验通过的路径，则译码成功，并返回CRC通过的那条路径作为译码结果；
ii.2.若检验次数>T时，仍未找到一条校验通过的路径，则译码失败。
在前面的实施例中已经介绍过编码过程中需要使用到的参数，即：校验比特的数量、校验比特的位置，校验方程，接收端在译码的过程中同样需要使用到这些参数。如果是采用上述虚警概率可控的CA+PC-SCL译码方法的话，则还需要进一步知道允许CRC检验的最大次数T的值。
在一个可选的实施例中，为了满足虚警概率可控，且虚警概率与译码器列表宽度(L的大小)无关，在基于前面描述的确定CRC比特数量的方法的基础上，还可以使得CRC比特数量J、T和最大虚警概率FAR(false alarm rate)满足如下关系：
FAR≈2 -J×T
或者所述CRC比特长度至满足：
J≥log 2(T/FAR)
下面通过两个具体的例子来进行说明：
例1，给定单次译码的虚警概率上限为FAR＝10 -5，而当前译码器参数T＝4，则所需的CRC长度至少为J＝ceil(log 2(4/10 -5))＝19比特。
例2，如在T＝1时，J＝16比特已能满足虚警概率不超过设定值FAR，则T＝8时，若仍要满足虚警概率不超过原设定值FAR，则所需的额外CRC比特数应满足ΔJ＝log 2(T)，即
J(T)＝J(1)+ΔJ＝J(1)+log 2T
上式中J(1)为单次CRC检测时满足要求的CRC比特个数，J(T)为T次CRC检测是满足要求的CRC比特个数。
在一个可选的实施例中，上述J和T的值有可能是通过协议预先规定的。
(1)如果单次校验最少需要8个CRC比特，则，J和T的值可以是如下表xx中的任意一种组合：
  组合1 组合2 组合3 组合4 组合5 组合6 组合7 组合8 组合9
J的值 8 9 10 11 12 13 14 15 16
T的值 1 2 4 8 16 32 64 128 256
(2)如果单次校验最少需要16个CRC比特，则J和T的值可以是如下表xx中的任意一种组合：
  组合1 组合2 组合3 组合4 组合5 组合6 组合7 组合8 组合9
J的值 16 17 18 19 20 21 22 23 24
T的值 1 2 4 8 16 32 64 128 256
(3)如果单次校验最少需要24个CRC比特，则J和T的值可以是如下表xx中的任意一种组合：
  组合1 组合2 组合3 组合4 组合5 组合6 组合7 组合8 组合9
J的值 24 25 26 27 28 29 30 31 32
T的值 1 2 4 8 16 32 64 128 256
(4)如果单次校验最少需要32个CRC比特，则，J和T的值可以是如下表xx中的任意一种组合：
  组合1 组合2 组合3 组合4 组合5 组合6 组合7 组合8 组合9
J的值 32 33 34 35 36 37 38 39 40
T的值 1 2 4 8 16 32 64 128 256
在一个可选的实施例中，为了使在各种列表宽度L下，都具有较好的误块率(BLER)性能，需要设定一定数量的A类PC比特，例如，PC比特的数量P的值有可能是如下等号后面所列的多个值中的任意一个：
P＝1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16。
T和P的取值与编码端采用的编码方式息息相关，例如：
情况(1)：如果T＝L,P＝0,则编码端采用的是CA-Polar编码方式，其虚警概率不可控；
情况(2):如果T＝1,P>0,则编码端采用的是PC-Polar编码方式，其虚警概率可控；
情况(3):如果1<T<L且T为不随L变化的常数，且P>0,则编码端采用的是PC+CA-Polar编码方式，其虚警概率可控；
情况(4):如果1<T<L且T为不随L变化的常数，且P＝0,所构造码即为虚警概率可控的CA-Polar码。
在上述方案中，应理解，T＝1时，T次校验指的是该路径对应的译码结果的一次检错。
由于每次检错(CRC检查)都会增加一定的虚警概率，“虚警”的定义为”译码错误但未检测出译码错误(如CRC通过)”，这是因为存在多个译码结果具有相同的检错校验值(如CRC校验值)，但其中只有唯一一个正确译码结果。因此，虚警概率随检错次数(如CRC使用次数)成比例上升。对此， 本申请提出的方案限制了检错次数(如CRC使用次数)，从根本上解决了虚警概率不可控的问题。在传统方法中，列表译码的List越大，则虚警概率越高；而在本申请提出的方案中，虚警概率不随list增大而增大。
图10为本申请提供的信息的传输装置实施例的结构示意图；如图10所示，该信息的传输装置10包括：
处理模块11，用于根据预设的参数对的待编码的序列进行编码，得到编码后的序列；所述参数包括校验比特的数量、所述校验比特的位置以及校验方程；所述待编码的序列长度为K，所述K为大于0的整数；
发送模块12，用于将所述编码后的序列发送至接收设备。
关于校验比特的数量、校验比特的位置以及校验方程的配置或者确定可以参见前面方法实施例中的描述，此处不再赘述。
在实现时上述处理模块11可以是一个或多个处理器，当处理器中存储有程序代码时，该处理器运行该程序代码就可以实现上述处理模块11的功能，当处理器中没有存储有程序代码时，可以通过通过读取外部存储器中存储的程序代码来实现上述处理模块11的功能。上述处理模块11还可以处理电路。上述发送模块12可以是一个发送器或者发送电路。
本实施例中提供的信息的传输装置，可以用于执行前述任一方法实施例中发送设备侧的技术方案，其实现原理和技术效果与方法实施例类似，在此不再赘述。
本实施例还提供了一种编码装置，该装置包括上述处理模块11、输入接口和输出接口；输入接口用于将待编码的序列输入给处理模块11，输出接口用于输出经过处理模块11编码后的序列。
本实施例中提供的编码装置，可以是通过芯片或者电路实现，其用于执行前述任一方法实施例中发送设备侧的编码技术方案，因实现原理和技术效果与方法实施例类似，在此不再赘述。
图11为本申请提供的信息的传输装置实施例二的结构示意图；如图11所示，该信息的传输装置20包括：
接收模块21，用于接收发送设备发送的编码后的序列；所述编码后的序列是根据预设的参数对待编码的序列进行编码后得到的，所述待编码的序列长度为K，所述K为大于0的整数；
处理模块22，用于根据所述预设的参数对所述编码后的序列进行译码，得到译码后的序列；所述参数包括校验比特的数量、所述校验比特的位置以及校验方程。
关于校验比特的数量、校验比特的位置以及校验方程的配置或者确定可以参见前面方法实施例中的描述，此处不再赘述。
本实施例提供的信息的传输装置，用于执行前述任一方法实施例中接收设备侧的技术方案，其实现原理和技术效果类似，在此不再赘述。
本实施例提供的信息的传输装置20，还可包括输入接口和输出接口；输入接口用于将编码后的序列输入给处理模块22，输出接口用于输出经过处理模块22译码后的序列。
本实施例中提供的信息的传输装置，可以是通过芯片或者电路实现，其用于执行前述任一方法实施例中接收设备侧的译码技术方案，因实现原理和技术效果与方法实施例类似，在此不再赘述。
图12为本申请提供的译码装置实施例的结构示意图；如图12所示，该译码装置30包括：
接收模块31，用于从发送设备接收待译码的比特序列；所述待译码的比特序列中至少包括信息比特和至少一个校验比特；
处理模块32，用于采用串行抵消列表SCL译码算法按顺序对所述待译码的比特进行译码，输出度量值最优的l条候选路径；所述1≤l≤L，所述L为SCL的宽度，所述L为大于或等于1的整数；
所述处理模块32还用于从度量值最优的候选路径开始，用所述至少一个校验比特对其中的T条候选路径进行校验，将校验通过的第一个候选路径中的比特序列作为译码输出；所述T为整数，所述1≤T≤l。
本实施例提供的译码装置，还可包括输入接口和输出接口；输入接口用于将编码后的序列输入给处理模块32，输出接口用于输出经过处理模块32译码后的序列。
本实施例中提供的译码装置，可以是通过芯片或者电路实现，其用于执行前述任一方法实施例中接收设备侧的译码技术方案，因实现原理和技术效果与方法实施例类似，在此不再赘述。
本申请还提供一种可读存储介质，可读存储介质中存储有指令，当发送设备的至少一个处理器执行该指令时，发送设备执行上述任一方法实施例中提供的信息的传输方法以及编码方法。
本申请还提供一种可读存储介质，可读存储介质中存储有指令，当接收设备的至少一个处理器执行该指令时，接收设备执行上述任一方法实施例中提供的信息的传输方法以及译码方法。
本申请还提供一种程序产品，该程序产品包括指令，该指令存储在可读存储介质中。发送设备的至少一个处理器可以从可读存储介质读取该指令，并执行该指令使得发送设备实施任一方法实施例中提供的信息的传输方法以及编码方法。
本申请还提供一种程序产品，该程序产品包括指令，该指令存储在可读存储介质中。接收设备的至少一个处理器可以从可读存储介质读取该指令，并执行该指令使得接收设备实施上述任一方法实施例中提供的信息的传输方法以及译码方法。
在发送设备或者接收设备的具体实现中，应理解，处理器可以是中央处理单元(英文：Central Processing Unit，简称：CPU)，还可以是其他通用处理器、数字信号处理器(英文：Digital Signal Processor，简称：DSP)、专用集成电路(英文：Application Specific Integrated Circuit，简称：ASIC)等。通用处理器可以是微处理器或者该处理器也可以是任何常规的处理器等。结合本申请所公开的方法的步骤可以直接体现为硬件处理器执行完成，或者用处理器中的硬件及软件模块组合执行完成。
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可读取存储器中。该程序在执行时，执行包括上述各方法实施例的步骤；而前述的存储器(存储介质)包括：只读存储器(英文：read-only memory，缩写：ROM)、RAM、快闪存储器、硬盘、固态硬盘、磁带(英文：magnetic tape)、软盘(英文：floppy disk)、光盘(英文：optical disc)及其任意组合。
最后应说明的是：以上各实施例仅用以说明本申请的技术方案，而非对其限制。

Claims (43)

  1. 一种信息的传输方法，其特征在于，包括：
    发送设备根据预设的参数对的待编码的序列进行编码，得到编码后的序列；所述参数包括校验比特的数量、所述校验比特的位置以及校验方程；所述待编码的序列长度为K，所述K为大于0的整数；
    所述发送设备将所述编码后的序列发送至接收设备。
  2. 根据权利要求1所述的方法，其特征在于：
    所述校验比特的数量是预先配置的；
    或者，
    所述校验比特的数量是根据译码器的列表长度确定的；
    或者，
    所述校验比特的数量是根据码长和码率确定的；
    或者，
    所述校验比特的数量是根据预先配置的比特数、译码器的列表长度、码长和码率确定的；
    或者，
    所述校验比特的数量为J，所述J≥log 2(T/FAR)；所述T为允许使用校验比特进行校验的最大次数，所述FAR为使用校验比特进行单次检验的最大虚警概率；
    或者，
    所述校验比特的数量为J(T)，所述
    J(T)＝J(1)+ΔJ＝J(1)+log 2T，
    所述J(1)为单次校验是需要使用的校验比特的数量，所述J(T)为T次校验需要使用的校验比特的数量，所述T为允许使用校验比特进行校验的最大次数。
  3. 根据权利要求1或2所述的方法，其特征在于，所述待编码序列中比特的位置序号为大于等于0且小于K的任意整数；
    所述校验比特的位置为：
    在待编码序列中按照比特的位置序号从大到小的顺序，从位置序号为N X的比特开始选择的连续F P个比特的位置；或者在待编码序列中按照比特的位置序号从小到大的顺序，从位置序号为N X的比特开始选择的连续F P个比特的位置；其中，0≤N X≤K，0<Fp<K。
  4. 根据权利要求1或2所述的方法，其特征在于，所述校验比特的位置为：
    从一个新的生成矩阵中选择出的比特位置；所述新的生成矩阵是通过对校验生成矩阵进行行列转换，将其中只依赖部分信息比特的校验比特置换至序号更小的子信道得到的。
  5. 根据权利要求1或2所述的方法，其特征在于，所述校验比特的位置对应待编码序列中任意一个比特的位置；
    或者，
    所述校验比特的位置对应待编码序列多个比特的位置，所述多个比特中至少有两个比特的位置是非连续的；
    或者，
    所述校验比特的位置是根据位置参数确定的，所述位置参数至少包括信息阈值Z I和校验阈值Z P；所述信息阈值Z I用于表示所有信息子信道中可靠度最低子信道对应的可靠度；所述校验阈值Z P用于表示所有校验子信道中，可靠度大于信息阈值Z I且行重最大的子信道集合中可靠度最低的子信道对应的可靠度。
  6. 根据权利要求1至5任一项所述的方法，其特征在于，所述校验方程是根据多项式确定的；其中，所述多项式采用以下任一种形式表示：二进制，八进制，十进制，十六进制，位置向量。
  7. 根据权利要求1至5任一项所述的方法，其特征在于，所述校验方程是根据校验方程表格确定的；其中，所述校验方程表格至少包括校验比特、信息比特以及参与校验方程的信息比特。
  8. 一种信息的传输方法，其特征在于，包括：
    接收设备接收发送设备发送的编码后的序列；所述编码后的序列是根据预设的参数对待编码的序列进行编码后得到的，所述待编码的序列长度为K，所述K为大于0的整数；
    所述接收设备根据所述预设的参数对所述编码后的序列进行译码，得到译码后的序列；所述参数包括校验比特的数量、所述校验比特的位置以及校验方程。
  9. 根据权利要求8所述的方法，其特征在于：
    所述校验比特的数量是预先配置的；
    或者，
    所述校验比特的数量是根据译码器的列表长度确定的；
    或者，
    所述校验比特的数量是根据码长和码率确定的；
    或者，
    所述校验比特的数量是根据预先配置的比特数、译码器的列表长度、码长和码率确定的；
    或者，
    所述校验比特的数量为J，所述J≥log 2(T/FAR)；所述T为允许使用校验比特进行校验的最大次数，所述FAR为使用校验比特进行单次检验的最大虚警概率；
    或者，
    所述校验比特的数量为J(T)，所述
    J(T)＝J(1)+ΔJ＝J(1)+log 2T，
    所述J(1)为单次校验是需要使用的校验比特的数量，所述J(T)为T次校验需要使用的校验比特的数量，所述T为允许使用校验比特进行校验的最大次数。
  10. 根据权利要求8或9所述的方法，其特征在于，所述待编码序列中比特的位置序号为大于等于0且小于K的任意整数；所述校验比特的位置为：
    在待编码序列中按照比特的位置序号从大到小的顺序，从位置序号为N X的比特开始选择的连续F P个比特的位置；或者在待编码序列中按照比特的位置序号从小到大的顺序，从位置序号为N X的比特开始选择的连续F P个比特的位置；其中，0≤N X≤K，0<Fp<K。
  11. 根据权利要求8或9所述的方法，其特征在于，所述校验比特的位置为：
    从一个新的生成矩阵中选择出的比特位置；所述新的生成矩阵是通过对校验生成矩阵进行行列转 换，将其中只依赖部分信息比特的校验比特置换至序号更小的子信道得到的。
  12. 根据权利要求8或9所述的方法，其特征在于，所述校验比特的位置对应待编码序列中任意一个比特的位置；
    或者，
    所述校验比特的位置对应待编码序列多个比特的位置，所述多个比特中至少有两个比特的位置是非连续的；
    或者，
    所述校验比特的位置是根据位置参数确定的，所述位置参数至少包括信息阈值Z I和校验阈值Z P；所述信息阈值Z I用于表示所有信息子信道中可靠度最低子信道对应的可靠度；所述校验阈值Z P用于表示所有校验子信道中，可靠度大于信息阈值Z I且行重最大的子信道集合中可靠度最低的子信道对应的可靠度。
  13. 根据权利要求8至12任一项所述的方法，其特征在于，所述校验方程是根据多项式确定的；其中，所述多项式采用以下任一种形式表示：二进制，八进制，十进制，十六进制，位置向量。
  14. 根据权利要求8至12任一项所述的方法，其特征在于，所述校验方程是根据校验方程表格确定的；其中，所述校验方程表格至少包括校验比特、信息比特以及参与校验方程的信息比特。
  15. 一种信息的传输装置，其特征在于，包括：
    处理模块，用于根据预设的参数对的待编码的序列进行编码，得到编码后的序列；所述参数包括校验比特的数量、所述校验比特的位置以及校验方程；所述待编码的序列长度为K，所述K为大于0的整数；
    发送模块，用于将所述编码后的序列发送至接收设备。
  16. 根据权利要求15所述的装置，其特征在于：
    所述校验比特的数量是预先配置的；
    或者，
    所述校验比特的数量是根据译码器的列表长度确定的；
    或者，
    所述校验比特的数量是根据码长和码率确定的；
    或者，
    所述校验比特的数量是根据预先配置的比特数、译码器的列表长度、码长和码率确定的；
    或者，
    所述校验比特的数量为J，所述J≥log 2(T/FAR)；所述T为允许使用校验比特进行校验的最大次数，所述FAR为使用校验比特进行单次检验的最大虚警概率；
    或者，
    所述校验比特的数量为J(T)，所述
    J(T)＝J(1)+ΔJ＝J(1)+log 2T，
    所述J(1)为单次校验是需要使用的校验比特的数量，所述J(T)为T次校验需要使用的校验比特的数量，所述T为允许使用校验比特进行校验的最大次数。
  17. 根据权利要求15或16所述的装置，其特征在于，所述待编码序列中比特的位置序号为大 于等于0且小于K的任意整数；所述校验比特的位置为：
    在待编码序列中按照比特的位置序号从大到小的顺序，从位置序号为N X的比特开始选择的连续F P个比特的位置；或者在待编码序列中按照比特的位置序号从小到大的顺序，从位置序号为N X的比特开始选择的连续F P个比特的位置；其中，0≤N X≤K，0<Fp<K。
  18. 根据权利要求15或16所述的装置，其特征在于，所述校验比特的位置为：
    从一个新的生成矩阵中选择出的比特位置；所述新的生成矩阵是通过对校验生成矩阵进行行列转换，将其中只依赖部分信息比特的校验比特置换至序号更小的子信道得到的。
  19. 根据权利要求15或16所述的装置，其特征在于，所述校验比特的位置对应待编码序列中任意一个比特的位置；
    或者，
    所述校验比特的位置对应待编码序列多个比特的位置，所述多个比特中至少有两个比特的位置是非连续的；
    或者，
    所述校验比特的位置是根据位置参数确定的，所述位置参数至少包括信息阈值Z I和校验阈值Z P；所述信息阈值Z I用于表示所有信息子信道中可靠度最低子信道对应的可靠度；所述校验阈值Z P用于表示所有校验子信道中，可靠度大于信息阈值Z I且行重最大的子信道集合中可靠度最低的子信道对应的可靠度。
  20. 根据权利要求15至19任一项所述的装置，其特征在于，所述校验方程是根据多项式确定的；其中，所述多项式采用以下任一种形式表示：二进制，八进制，十进制，十六进制，位置向量。
  21. 根据权利要求15至19任一项所述的装置，其特征在于，所述校验方程是根据校验方程表格确定的；其中，所述校验方程表格至少包括校验比特、信息比特以及参与校验方程的信息比特。
  22. 一种信息的传输装置，其特征在于，包括：
    接收模块，用于接收发送设备发送的编码后的序列；所述编码后的序列是根据预设的参数对待编码的序列进行编码后得到的，所述待编码的序列长度为K，所述K为大于0的整数；
    处理模块，用于根据所述预设的参数对所述编码后的序列进行译码，得到译码后的序列；所述参数包括校验比特的数量、所述校验比特的位置以及校验方程。
  23. 根据权利要求22所述的装置，其特征在于：
    所述校验比特的数量是预先配置的；
    或者，
    所述校验比特的数量是根据译码器的列表长度确定的；
    或者，
    所述校验比特的数量是根据码长和码率确定的；
    或者，
    所述校验比特的数量是根据预先配置的比特数、译码器的列表长度、码长和码率确定的；
    或者，
    所述校验比特的数量为J，所述J≥log 2(T/FAR)；所述T为允许使用校验比特进行校验的最大次数，所述FAR为使用校验比特进行单次检验的最大虚警概率；
    或者，
    所述校验比特的数量为J(T)，所述
    J(T)＝J(1)+ΔJ＝J(1)+log 2T，
    所述J(1)为单次校验是需要使用的校验比特的数量，所述J(T)为T次校验需要使用的校验比特的数量，所述T为允许使用校验比特进行校验的最大次数。
  24. 根据权利要求22或23所述的装置，其特征在于，所述待编码序列中比特的位置序号为大于等于0且小于K的任意整数；所述校验比特的位置为：
    在待编码序列中按照比特的位置序号从大到小的顺序，从位置序号为N X的比特开始选择的连续F P个比特的位置；或者在待编码序列中按照比特的位置序号从小到大的顺序，从位置序号为N X的比特开始选择的连续F P个比特的位置；其中，0≤N X≤K，0<Fp<K。
  25. 根据权利要求22或23所述的装置，其特征在于，所述校验比特的位置为：
    从一个新的生成矩阵中选择出的比特位置；所述新的生成矩阵是通过对校验生成矩阵进行行列转换，将其中只依赖部分信息比特的校验比特置换至序号更小的子信道得到的。
  26. 根据权利要求22或23所述的装置，其特征在于，所述校验比特的位置对应待编码序列中任意一个比特的位置；
    或者，
    所述校验比特的位置对应待编码序列多个比特的位置，所述多个比特中至少有两个比特的位置是非连续的；
    或者，
    所述校验比特的位置是根据位置参数确定的，所述位置参数至少包括信息阈值Z I和校验阈值Z P；所述信息阈值Z I用于表示所有信息子信道中可靠度最低子信道对应的可靠度；所述校验阈值Z P用于表示所有校验子信道中，可靠度大于信息阈值Z I且行重最大的子信道集合中可靠度最低的子信道对应的可靠度。
  27. 根据权利要求22至26任一项所述的装置，其特征在于，所述校验方程是根据多项式确定的；其中，所述多项式采用以下任一种形式表示：二进制，八进制，十进制，十六进制，位置向量。
  28. 根据权利要求22至26任一项所述的装置，其特征在于，所述校验方程是根据校验方程表格确定的；其中，所述校验方程表格至少包括校验比特、信息比特以及参与校验方程的信息比特。
  29. 一种译码方法，其特征在于，所述方法包括：
    接收设备从发送设备接收待译码的比特序列；所述待译码的比特序列中至少包括信息比特和至少一个校验比特；所述接收设备采用串行抵消列表SCL译码算法按顺序对所述待译码的比特进行译码，输出度量值最优的l条候选路径；所述1≤l≤L，所述L为SCL的宽度，所述L为大于或等于1的整数；
    从度量值最优的候选路径开始，用所述至少一个校验比特对其中的T条候选路径进行校验，将校验通过的第一个候选路径中的比特序列作为译码输出；所述T为整数，所述1≤T≤l。
  30. 根据权利要求29所述的方法，其特征在于，所述接收设备采用串行抵消列表SCL译码算法按顺序对所述待译码的比特进行译码包括：
    对于所述信息比特，则将该信息比特对应的路径扩展为0和1的两个路径，并分别计算两条 路径的度量值；
    如果扩展后的路径数小于或等于L，则保留所有路径；
    如扩展后路径数大于L，则保留度量值最优的L条路径。
  31. 根据权利要求29或30所述的方法，其特征在于，所述接收设备采用串行抵消列表SCL译码算法按顺序对所述待译码的比特进行译码包括：
    所述校验比特有多个，当所述接收设备译到最后一个校验比特之前，则将该最后一个校验比特之前的校验比特对应的路径扩展为0和1的两个路径，并分别计算两条路径的度量值；
    如果扩展后的路径数小于或等于L，则保留所有路径；
    如扩展后路径数大于L，则保留度量值最小的L条路径；
    所述从度量值最优的候选路径开始，对其中的T条候选路径进行校验包括：
    当所述接收设备译到最后一个校验比特时，所述接收设备从保留的l条路径中度量值最优的候选路径开始，使用所述最后一个校验比特对其中的T条候选路径进行校验。
  32. 根据权利要求29至31任一项所述的方法，其特征在于，所述校验比特的数量为J，所述J≥log 2(T/FAR)；所述T为允许使用校验比特进行校验的最大次数，所述FAR为使用校验比特进行单次检验的最大虚警概率。
  33. 根据权利要求29至31任一项所述的方法，其特征在于，所述校验比特的数量为J(T)，所述
    J(T)＝J(1)+ΔJ＝J(1)+log 2T，
    所述J(1)为单次校验是需要使用的校验比特的数量，所述J(T)为T次校验需要使用的校验比特的数量，所述T为允许使用校验比特进行校验的最大次数。
  34. 根据权利要求29至32任一项所述的方法，其特征在于，所述待译码的比特序列中还包括校验冻结比特，所述校验冻结比特的数量P为如下多个值中的一个：
    P＝1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16。
  35. 一种译码装置，其特征在于，包括：
    接收模块，用于从发送设备接收待译码的比特序列；所述待译码的比特序列中至少包括信息比特和至少一个校验比特；
    处理模块，用于采用串行抵消列表SCL译码算法按顺序对所述待译码的比特进行译码，输出度量值最优的l条候选路径；所述1≤l≤L，所述L为SCL的宽度，所述L为大于或等于1的整数；
    所述处理模块还用于从度量值最优的候选路径开始，用所述至少一个校验比特对其中的T条候选路径进行校验，将校验通过的第一个候选路径中的比特序列作为译码输出；所述T为整数，所述1≤T≤l。
  36. 根据权利要求35所述的装置，其特征在于，所述处理模块具体用于：
    对于所述信息比特，则将该信息比特对应的路径扩展为0和1的两个路径，并分别计算两条路径的度量值；
    如果扩展后的路径数小于或等于L，则保留所有路径；
    如扩展后路径数大于L，则保留度量值最优的L条路径。
  37. 根据权利要求35或36所述的装置，其特征在于，所述处理模块具体用于：
    所述校验比特有多个，当所述接收设备译到最后一个校验比特之前，则将该最后一个校验比特之前的校验比特对应的路径扩展为0和1的两个路径，并分别计算两条路径的度量值；
    如果扩展后的路径数小于或等于L，则保留所有路径；
    如扩展后路径数大于L，则保留度量值最小的L条路径；
    所述从度量值最优的候选路径开始，对其中的T条候选路径进行校验包括：
    当所述接收设备译到最后一个校验比特时，所述接收设备从保留的l条路径中度量值最优的候选路径开始，使用所述最后一个校验比特对其中的T条候选路径进行校验。
  38. 根据权利要求35至37任一项所述的装置，其特征在于，所述校验比特的数量为J，所述J≥log 2(T/FAR)；所述T为允许使用校验比特进行校验的最大次数，所述FAR为使用校验比特进行单次检验的最大虚警概率。
  39. 根据权利要求35至37任一项所述的装置，其特征在于，所述校验比特的数量为J(T)，所述
    J(T)＝J(1)+ΔJ＝J(1)+log 2T，
    所述J(1)为单次校验是需要使用的校验比特的数量，所述J(T)为T次校验需要使用的校验比特的数量，所述T为允许使用校验比特进行校验的最大次数。
  40. 根据权利要求35至39任一项所述的装置，其特征在于，所述待译码的比特序列中还包括校验冻结比特，所述校验冻结比特的数量P为如下多个值中的一个：
    P＝1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16。
  41. 一种可读存储介质，其特征在于，所述可读存储介质中存储有指令，当发送设备的至少一个处理器执行所述指令时，所述发送设备执行权利要求1至7任一项所述的信息的传输方法。
  42. 一种可读存储介质，其特征在于，所述可读存储介质中存储有指令，当接收设备的至少一个处理器执行所述指令时，所述接收设备执行权利要求8至14任一项所述的信息的传输方法。
  43. 一种可读存储介质，其特征在于，所述可读存储介质中存储有指令，当接收设备的至少一个处理器执行所述指令时，所述接收设备执行权利要求29至34任一项所述的译码方法。
PCT/CN2018/073229 2017-02-03 2018-01-18 一种信息的传输方法、译码方法和装置 WO2018141212A1 (zh)

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