WO2021103978A1 - 一种极化码编码方法及装置 - Google Patents

一种极化码编码方法及装置 Download PDF

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Publication number
WO2021103978A1
WO2021103978A1 PCT/CN2020/126836 CN2020126836W WO2021103978A1 WO 2021103978 A1 WO2021103978 A1 WO 2021103978A1 CN 2020126836 W CN2020126836 W CN 2020126836W WO 2021103978 A1 WO2021103978 A1 WO 2021103978A1
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information bits
polarization
bit sequence
bits
matrix
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PCT/CN2020/126836
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English (en)
French (fr)
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李斌
顾佳琦
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华为技术有限公司
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Priority to EP20891850.8A priority Critical patent/EP4050826A4/en
Publication of WO2021103978A1 publication Critical patent/WO2021103978A1/zh
Priority to US17/826,540 priority patent/US11870457B2/en

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    • 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
    • H03M13/1105—Decoding
    • H03M13/1108—Hard decision decoding, e.g. bit flipping, modified or weighted bit flipping
    • 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
    • H03M13/07—Arithmetic 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
    • H03M13/11—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
    • H03M13/1105—Decoding
    • H03M13/1111—Soft-decision decoding, e.g. by means of message passing or belief propagation algorithms
    • 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
    • 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
    • H03M13/611—Specific encoding aspects, e.g. encoding by means of decoding
    • 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
    • H04L1/0041—Arrangements at the transmitter end
    • 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
    • H04L1/0064—Concatenated codes
    • H04L1/0065—Serial concatenated 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
    • H04L1/0067—Rate matching

Definitions

  • the embodiments of the present application relate to the field of encoding and decoding, and in particular, to a polarization code encoding method and device.
  • Communication systems usually use channel coding to improve the reliability of data transmission and ensure the quality of communication.
  • coding methods such as Polar codes and Reed-Muler (RM) codes can be used.
  • Polar code is an encoding method that can obtain Shannon capacity and has low coding and decoding complexity.
  • the RM code was first proposed by David Muller in 1954.
  • the fast decoding algorithm of the RM code is very suitable for optical fiber communication systems.
  • the RM code and the Polar code are combined to generate a coding method, which can be called the RM-Polar code.
  • the embodiments of the present application provide a polarization code encoding method and device to improve encoding performance.
  • a polarization code encoding method is provided, and the execution subject of the method may be an encoding device.
  • the encoding device can be a terminal or a network device.
  • the steps of the method include: obtaining K information bits to be coded, where K is a positive integer; and determining a first bit sequence according to the K information bits to be coded, the length of the first bit sequence is N, and N is A positive integer power of 2, the first bit sequence includes fixed bits and the K information bits to be encoded; a second bit sequence is determined according to the first bit sequence and the upper triangular matrix, and the upper triangular matrix is N A matrix with rows and N columns; performing polarization code coding on the second bit sequence to obtain and output the coded sequence.
  • the upper triangular matrix is an upper triangular Toeplitz matrix.
  • the first bit sequence according to the K information bits to be coded when determining the first bit sequence according to the K information bits to be coded, it can be implemented in the following manner: according to the reliability of the polarization code N polarization channels, and polarization code generation The weight of each row in the N rows of the matrix determines K information bits, wherein the polarization code generation matrix is a matrix with N rows and N columns, and the N rows of the polarization code generation matrix correspond to the one-to-one
  • the N bits of the first bit sequence, the N polarized channels correspond to the N bits of the first bit sequence one by one; the K information bits to be encoded are mapped to the K information bits Bits to obtain the first bit sequence.
  • the minimum Hamming distance is the smallest distance among the mutual distances between all codewords in the codeword set formed by the structure code.
  • the decoding performance can be improved to a certain extent.
  • the K information bits can be determined by way 1 or way 2. achieve.
  • Method 1 Select the polarized channel whose row weight is sorted from large to small in the polarization code generation matrix, and the reliability of the polarized channel is not lower than the second threshold, and the corresponding bits are used as the K pieces of information Bits.
  • the first sorting sequence may be determined according to the order of the reliability of the N polarization channels of the polarization code from high to low, and the N sequence numbers of the first sorting sequence correspond to the N bits of the first bit sequence one by one. Bit; starting from the first sequence number in the first sorting sequence, the bit positions corresponding to the K rows of the polarization code generation matrix whose weight is greater than or equal to the first threshold are selected as the K information bit positions.
  • Method 2 Select the polarized channel whose row weight is sorted from large to small in the polarization code generation matrix, and the reliability of the polarized channel is not lower than the second threshold, and the corresponding bits are used as the K pieces of information Bits.
  • the second sorting sequence may be determined according to the order of the weight of each row in the N rows of the polarization code generation matrix from high to low, and the N serial numbers of the second sorting sequence correspond to the first bit sequence one by one.
  • the second sorting sequence starting from the first sequence number, select the bits corresponding to the K polarization channels with the reliability of the polarization code from high to low, as the Said K information bits.
  • sorting according to reliability is performed from the polarized channels after the rate matching of the N polarized channels.
  • the reordering according to the rows of the generator matrix is performed from the polarized channels after the rate matching of the N polarized channels corresponding to the N rows of the generator matrix.
  • Ways of rate matching can include: punching, shortening, or pre-freezing.
  • the determination of K information bits can be achieved in the following manner: According to the order of the reliability of the polarization channel related to the rate-matching removal of the polarization channel, and the K information bits are determined according to the weight of each row after the N-line removal of the rate-matching related line of the polarization code generation matrix.
  • the rate-matching-related polarization channel includes a punctured, shortened, or pre-frozen polarization channel, and the rate-matching-related line includes a line corresponding to the punctured, shortened, or pre-frozen polarization channel.
  • the reliability of the polarization channel may be considered to determine the K information bits, for example: according to N polarization codes
  • the reliability of the polarized channels is from high to low to determine K information bits, where the N polarized channels correspond to the N bits of the first bit sequence one by one;
  • the information bits to be encoded are mapped to the K information bits to obtain the first bit sequence.
  • determining the K information bits can be achieved in the following way: according to the N polarization channels of the polarization code, the rate-matching related polarization is removed. Determine the K information bits in the order of the reliability of the channel from high to low.
  • the polarization channels related to rate matching include punctured, shortened, or pre-frozen polarization channels.
  • the row weight of the generator matrix may also be considered to determine the K information bits. For example: determine K information bits according to the weight of each of the N rows of the polarization code generation matrix, where the polarization code generation matrix is a matrix with N rows and N columns, and the N of the polarization code generation matrix The rows correspond to the N bits of the first bit sequence one by one; the K information bits to be encoded are mapped to the K information bits to obtain the first bit sequence.
  • the rows related to rate matching include rows corresponding to punctured, shortened, or pre-frozen polarized channels.
  • determining the second bit sequence according to the first bit sequence and the upper triangular matrix includes: multiplying the first bit sequence and the upper triangular matrix to obtain the second bit sequence.
  • performing polarization code encoding on the second bit sequence to obtain an encoded sequence includes: multiplying the second bit sequence by a polarization code generation matrix to obtain the encoded sequence sequence.
  • the information bits include parity bits.
  • the decoding device can decode using a predetermined check relationship to improve decoding performance.
  • a polarization code encoding device which has the function of implementing the method described in the first aspect and any one of the possible designs of the first aspect.
  • the function can be realized by hardware, or by hardware executing corresponding software.
  • the hardware or software includes one or more modules corresponding to the above-mentioned functions.
  • the device may include an acquisition unit, a determination unit, and an encoding unit.
  • the obtaining unit is used to obtain K information bits to be coded, where K is a positive integer; the determining unit is used to determine a first bit sequence according to the K information bits to be coded, and the length of the first bit sequence is N, N are positive integer powers of 2, the first bit sequence includes a fixed bit and the K information bits to be encoded; the coding unit is used to determine the second bit according to the first bit sequence and the upper triangular matrix Sequence, the upper triangular matrix is a matrix with N rows and N columns; and is used to perform polarization code encoding on the second bit sequence to obtain and output the encoded sequence.
  • Polar can theoretically prove that when the code length tends to be infinite (N ⁇ ), the channel capacity can be "reached". But in many practical scenarios, the code length is not unlimited, so performance is limited.
  • the method provided in the embodiment of the present application can help improve the performance of the Polar code under a limited code length.
  • the upper triangular matrix is an upper triangular Toeplitz matrix.
  • the determining unit is configured to determine K information bits according to the reliability ranking of the N polarization channels of the polarization code and the weight of each row in the N rows of the polarization code generation matrix, where ,
  • the polarization code generation matrix is a matrix with N rows and N columns, the N rows of the polarization code generation matrix correspond to the N bits of the first bit sequence one by one, and the N polarization channels have one One corresponds to the N bits of the first bit sequence; the K information bits to be encoded are mapped to the K information bits to obtain the first bit sequence.
  • the minimum Hamming distance of the codeword can be further increased, and the coding performance of the Polar code can be improved, and due to the coding performance Improve, can also improve the decoding performance during decoding.
  • the determining unit is configured to: select the polarized channel whose reliability is sorted in descending order and the row of the polarized code generation matrix whose weight is not lower than the first threshold. , The corresponding bits are used as the K information bits.
  • the first sorting sequence is determined according to the order of the reliability of the N polarization channels of the polarization code from high to low, and the N numbers of the first sorting sequence correspond to the N numbers of the first bit sequence one by one. Bits; starting from the first sequence number in the first sorting sequence, select the bits corresponding to the K rows with a weight greater than or equal to the first threshold in the polarization code generation matrix as the K information bits .
  • the determining unit is used to select a polarized channel whose row weight in the polarization code generation matrix is ranked first in descending order, and the reliability of the polarized channel is ranked not lower than the second threshold.
  • the corresponding bits are used as the K information bits.
  • the second sorting sequence is determined, and the N serial numbers of the second sorting sequence correspond to the first bit one by one.
  • the determining unit is configured to: remove the reliability ranking of the polarization channels related to the rate matching according to the polarization code N polarization channels, and remove the rate matching related according to the N rows of the polarization code generation matrix K information bits are determined by the weight of each row after the row of, the polarization channel related to rate matching includes punctured, shortened or pre-frozen polarization channel, and the row related to rate matching includes punctured, shortened Or the row corresponding to the pre-frozen polarized channel.
  • the determining unit is configured to determine K information bits according to the order of the reliability of the N polarization channels of the polarization code from high to low, where the N polarization channels are one One corresponds to the N bits of the first bit sequence; the K information bits to be encoded are mapped to the K information bits to obtain the first bit sequence.
  • the determining unit when determining the K information bits according to the order of the reliability of the N polarization channels of the polarization code from high to low, the determining unit is used to:
  • the channel removal rate matches the relative reliability of the polarized channel in descending order to determine K information bits.
  • the polarization channels related to rate matching include punctured, shortened, or pre-frozen polarization channels.
  • the determining unit is configured to determine K information bits according to the weight of each of the N rows of the polarization code generation matrix, where the polarization code generation matrix has N rows and N columns.
  • the N rows of the polarization code generation matrix correspond to the N bits of the first bit sequence one by one; the K information bits to be encoded are mapped to the K information bits to obtain The first bit sequence.
  • the determining unit when determining K information bits according to the weight of each row in the N rows of the polarization code generation matrix, is used to: remove rate matching according to the N rows of the polarization code generation matrix The weight of each row after the relevant row determines K information bits.
  • the rows related to rate matching include rows corresponding to punctured, shortened, or pre-frozen polarized channels.
  • the encoding unit is configured to: multiply the first bit sequence by the upper triangular matrix to obtain the second bit sequence.
  • the encoding unit is configured to: multiply the second bit sequence and the polarization code generation matrix to obtain the encoded sequence.
  • the information bits include parity bits.
  • the decoding device can decode using a predetermined check relationship to improve decoding performance.
  • a polarization code encoding device which has the function of implementing the method described in the first aspect and any one of the possible designs of the first aspect.
  • the function can be realized by hardware, or by hardware executing corresponding software.
  • the hardware or software includes one or more modules corresponding to the above-mentioned functions.
  • the polarization code encoding device when part or all of the function is realized by hardware, includes: an input interface circuit for obtaining K information bits to be encoded, and K is a positive integer; logic; The circuit is used to perform the behavior described in the above-mentioned first aspect and any one of the possible designs of the first aspect (except for obtaining K information bits to be encoded and outputting the encoded sequence); the output interface circuit is used To output the encoded sequence.
  • the polarization code encoding device may be a chip or an integrated circuit.
  • the polarization code encoding device when part or all of the function is realized by software, includes: a memory, used to store a program; a processor, used to execute the program stored in the memory When the program is executed, the polarization code encoding device can implement the method described in any one of the above-mentioned first aspect and the first aspect.
  • the foregoing memory may be a physically independent unit, or may be integrated with the processor.
  • the polarization code encoding device when part or all of the functions are implemented by software, includes a processor.
  • the memory for storing the program is located outside the encoding device, and the processor is connected to the memory through a circuit/wire for reading and executing the program stored in the memory.
  • a computer-readable storage medium which stores computer-readable instructions.
  • the computer-readable instructions run on a computer, the computer can execute any possible design as in the first aspect and the first aspect. Any of the methods described.
  • the embodiments of the present application provide a computer program product containing instructions, which when run on a computer, enable the computer to execute the method described in the first aspect and any one of the possible designs of the first aspect.
  • an embodiment of the present application provides a chip system, which includes a processor and may also include a memory, for implementing the method described in the first aspect or any one of the possible designs of the first aspect .
  • the chip system can be composed of chips, or it can include chips and other discrete devices.
  • FIG. 1 is a schematic diagram of the architecture of a communication system in an embodiment of the application
  • FIG. 2 is a schematic diagram of a polarization code encoding method in an embodiment of this application
  • Fig. 3 is a schematic diagram of the RM-Polar code construction method of (256,128) in an embodiment of the application;
  • FIG. 4 is the second schematic diagram of the polarization code encoding method in the embodiment of this application.
  • FIG. 5 is one of schematic diagrams of codeword performance comparison in an embodiment of this application.
  • Figure 6 is the second schematic diagram of codeword performance comparison in an embodiment of this application.
  • FIG. 7 is the third schematic diagram of codeword performance comparison in an embodiment of this application.
  • FIG. 8 is one of the schematic structural diagrams of the polarization code encoding device in the embodiment of the application.
  • FIG. 9 is the second schematic diagram of the structure of the polarization code encoding device in the embodiment of the application.
  • FIG. 10 is the third structural diagram of the polarization code encoding device in the embodiment of the application.
  • the embodiments of the present application provide a polarization code encoding and device.
  • the method and the device are based on the same technical concept. Since the principles of the method and the device to solve the problem are similar, the implementation of the device and the method can be referred to each other, and the repetition will not be repeated.
  • "and/or" describes the association relationship of the associated objects, which means that there can be three relationships, for example, A and/or B, which can mean that there is A alone, and both A and B exist at the same time. There are three cases of B.
  • the character "/" generally indicates that the associated objects before and after are in an "or” relationship. At least one involved in this application refers to one or more; multiple refers to two or more.
  • the decoding method provided by the embodiments of the present application can be applied to a fifth generation (5th generation, 5G) communication system, such as a 5G new radio (NR) system, a device to device (D2D) communication system, or Applied to various communication systems in the future.
  • 5G fifth generation
  • 5G new radio (NR) system such as a 5G new radio (NR) system, a device to device (D2D) communication system, or Applied to various communication systems in the future.
  • NR new radio
  • D2D device to device
  • FIG. 1 shows the architecture of a possible communication system to which the decoding method provided in the embodiment of the present application is applicable.
  • the communication system 100 includes: a network device 101 and one or more terminals 102.
  • the network device 101 may also be connected to the core network.
  • the network device 101 provides services for the terminals 102 within the coverage area.
  • the network device 101 provides wireless access for one or more terminals 102 within the coverage area of the network device 101.
  • the network devices can also communicate with each other.
  • the network device 101 can communicate with the network device 101'.
  • the network device 101 is a node in a radio access network (radio access network, RAN), which may also be referred to as a base station, and may also be referred to as a RAN node (or device).
  • RAN radio access network
  • some examples of network equipment 101 are: next generation nodeB (gNB), next generation evolved nodeB (Ng-eNB), transmission reception point (TRP), evolved type Node B (evolved Node B, eNB), radio network controller (RNC), Node B (Node B, NB), base station controller (BSC), base transceiver station (base transceiver station, BTS), home base station (for example, home evolved NodeB, or home Node B, HNB), baseband unit (BBU), or wireless fidelity (Wifi) access point (AP),
  • the network device 101 may also be a satellite, and the satellite may also be called a high-altitude platform, a high-altitude aircraft, or a satellite base station.
  • the network device 101 may
  • the network equipment may include a centralized unit (CU) and a distributed unit (DU).
  • the network device may also include an active antenna unit (AAU).
  • CU implements some functions of network equipment, and DU implements some functions of network equipment.
  • CU is responsible for processing non-real-time protocols and services, implementing radio resource control (RRC), and packet data convergence protocol, PDCP) layer function.
  • RRC radio resource control
  • PDCP packet data convergence protocol
  • the DU is responsible for processing physical layer protocols and real-time services, and implements the functions of the radio link control (RLC) layer, media access control (MAC) layer, and physical (PHY) layer.
  • RLC radio link control
  • MAC media access control
  • PHY physical
  • the network device may be a device that includes one or more of a CU node, a DU node, and an AAU node.
  • the CU can be divided into network equipment in an access network (radio access network, RAN), and the CU can also be divided into network equipment in a core network (core network, CN), which is not limited in this application.
  • the terminal 102 also called user equipment (UE), mobile station (MS), mobile terminal (MT), etc., is a device that provides voice and/or data connectivity to users .
  • the terminal 102 includes a handheld device with a wireless connection function, a vehicle-mounted device, and the like.
  • the terminal 102 may be: a mobile phone (mobile phone), a tablet computer, a notebook computer, a palmtop computer, a mobile internet device (MID), a wearable device (such as a smart watch, a smart bracelet, a pedometer, etc.) , In-vehicle equipment (for example, cars, bicycles, electric vehicles, airplanes, ships, trains, high-speed rail, etc.), virtual reality (VR) equipment, augmented reality (AR) equipment, industrial control (industrial control) Wireless terminals, smart home equipment (for example, refrigerators, TVs, air conditioners, electric meters, etc.), smart robots, workshop equipment, wireless terminals in self-driving, wireless terminals in remote medical surgery, Wireless terminals in smart grids, wireless terminals in transportation safety, wireless terminals in smart cities, or wireless terminals in smart homes, and flying equipment (for example, Intelligent robots, hot air balloons, drones, airplanes, etc.
  • the terminal 102 may also be other devices with terminal functions.
  • the terminal 102 may also be
  • the implementation subject of the polarization code encoding method may be an encoding device, and the encoding device may be the network device 101 or the terminal 102.
  • the encoding device encodes the information bits to be encoded, obtains an encoded codeword, and sends it to the decoding device.
  • the encoding device can also be called the transmitting end, and the decoding device is the receiving end.
  • the sending end or the encoding device is the network device 101
  • the receiving end or the decoding device is the terminal 102
  • the sending end or the encoding device is the terminal 102
  • the receiving end or the decoding device is the network device 101.
  • Coding method one: the traditional polar code (Polar code) coding method.
  • Polar code is also a kind of linear block code
  • the generator matrix is G N
  • the generator matrix can also be denoted as G
  • the generator matrix can also be called the coding matrix.
  • the encoding process is among them Is a binary row vector with length N, N is the length of Polar code; G N is an N ⁇ N matrix, and It is defined as the Kronecker product of log 2 N matrices F 2.
  • a part of the bits are used to carry information, and the bits that carry information are called information bits.
  • This part of bits used to carry information forms an information bit set.
  • the index set of these bits is denoted as A; the other part of the bits is set as the receiving end and transmitting prearranged end fixed value, a fixed set of bits called set of bits or freezing (frozen bits), which complement the index set a by a represents C.
  • the encoding process of Polar code is equivalent to:
  • G N (A) is a sub-matrix G N obtained by those row index corresponding to the set A
  • G N (AC) is a sub-matrix G N obtained from the set A C those rows corresponding to the index .
  • u A is The set of information bits in, the number is K; for The fixed bit set in, whose number is (NK), is a known bit. These fixed bits are usually set to 0, but as long as the receiving end and the sending end agree in advance, the fixed bits can be set arbitrarily.
  • u A is The set of information bits in
  • u A is a row vector of length K, that is
  • K,
  • K is the size of the information block or K is the number of information bits
  • or K is the information size of the collection of bits
  • G N (a) is a sub-matrix of the matrix G N rows in the set a corresponding to the index obtained
  • G N (a) is a K ⁇ N matrix.
  • the construction process of Polar code is the selection process of set A, which determines the performance of Polar code.
  • the construction process of the Polar code is usually to determine that there are N polarization channels in total according to the length of the mother code N, corresponding to the N rows of the generator matrix, calculate the reliability of the polarization channel, and convert the first K polarizations with higher reliability.
  • channel index as an element of the set a the remaining (NK) polarizations channel corresponding to the index as a fixed-bit index C a set of elements.
  • the set A determines the position of the information bit
  • the set A c determines the position of the fixed bit.
  • an 8 ⁇ 8 generator matrix is shown, where the vector u is represented by (0 , 0, 0, U 4 , 0, U 6 , U 7 , U 8 ).
  • the encoded Bits are represented by vectors (X 1 , X 2 , X 3 , X 4 , X 5 , X 6 , X 7 , X 8 ).
  • the bit corresponding to the high-reliability channel is used for mapping information bits, and the bit corresponding to the low-reliability channel is used for mapping fixed bits.
  • ⁇ u 1 , u 2 , u 3 , u 5 ⁇ are the positions of fixed bits
  • ⁇ u 4 , u 6 , u 7 , u 8 ⁇ are the positions of information bits
  • the length is 4
  • the information vector ⁇ i 1 , i 2 , i 3 , i 4 ⁇ to be encoded is mapped to the position of the information bit, and after encoding, 8-bit encoded bits are generated.
  • the coded sequence is modulated and then passed through the noise channel, and then output.
  • u is a 1 ⁇ 8 row vector
  • the transpose of an 8 ⁇ 1 column vector is used to represent the row vector in the formula expression.
  • Encoding method 2 RM code encoding method.
  • the RM code can use the same generator matrix G structure as the polar code, that is, an N ⁇ N generator matrix structure. But the method of selecting information bits is different.
  • the weight of the row of the G matrix corresponding to each bit is determined, and K bits are selected as the information bits according to the order of the row weight from large to small.
  • the bit with the smallest remaining row weight is regarded as a fixed bit.
  • the fixed bit is usually set to 0. Among them, the number of non-"0" elements in a row of the generator matrix is called the Hamming weight of the row, or the weight of the row, referred to as the row weight for short.
  • the generator matrix G is:
  • the row weights of the first row to the fourth row are 1, 2, 2, and 4, respectively.
  • K 2 information bits are selected.
  • the row with the largest row weight is the fourth row, and the bit corresponding to the fourth row with the largest row weight is an information bit.
  • the second and third rows have the same row weight.
  • the information bit position can also be determined according to the row closest to the row corresponding to the maximum row weight. If the other bit is determined according to the natural order from front to back, select the second line. In this way, the encoding end is easier.
  • the largest row weight here is the fourth row
  • the generator matrix G is:
  • the row weights of the first row to the eighth row are 1, 2, 2, 4, 2, 4, 4, and 8, respectively.
  • Row 8 has the largest weight, followed by rows 4, 6, and 7, followed by rows 2, 3, and 5, and row 1 has the smallest weight.
  • the order is 8, (4, 6, 7), (2, 3, 5), 1.
  • K 6, that is, 6 information bits are selected.
  • the third row in the row reordering has 3 rows. You can select any two of the 2, 3, and 5 rows as the information bits, or you can follow the natural order from front to back.
  • the bits corresponding to the two rows are selected as the information bits, and the information bits can also be determined according to the two rows closest to the row corresponding to the maximum row weight. If you select the bits corresponding to the two rows from the front to the back in the natural order as the information bits, you can choose the second and third rows. In this way, the encoding end is easier.
  • the largest row weight here is the 8th row
  • Coding method 3 RM-Polar code coding method.
  • the construction process of the RM-Polar code is as follows: Get the N ⁇ N generator matrix G, The N rows of the generator matrix G correspond to N bits one by one. The N bits correspond to N polarization channels one by one. According to the sorting of the reliability of the N polarized channels and the row weight in the generator matrix corresponding to each bit, K information bits are determined. According to the order of the reliability of the N polarized channels, and the order of the row weight of the generator matrix, the K information bits are determined. Among them, the reliability of the polarized channels can be sorted according to the Bhattacharyya parameter from small to large, or according to channel capacity from large to small, or according to the normalized reliability or equivalent reliability of the polarized channel.
  • the order of the reliability of the N polarized channels is used as the main reference factor, and the row weight of the generator matrix is used as the auxiliary reference factor to determine the K information. Bits.
  • the polarization code generation matrix whose reliability is sorted in descending order of the highest polarization channel and whose weight is not lower than the first threshold, and the corresponding bits are regarded as K information bits. That is, the bit with the highest reliability ranking of the polarized channel and the row weight not lower than the first threshold can be selected as the information bit.
  • the remaining bits are regarded as fixed bits.
  • the K information bits corresponding to the K polarized channels can be selected according to the order of the reliability of the N polarized channels from large to small, and it is judged whether the row weights of the K rows in the generator matrix corresponding to the K information bits are greater than or It is equal to the first threshold. If yes, determine the K information bits. Otherwise, K information bits are determined according to the following process. If in the K rows of the generator matrix corresponding to the selected K information bits, the row weight of K1 rows is less than the first threshold, then the K1 information corresponding to the K1 rows in the selected K information bits are removed Bit position, you can determine (K-K1) information bits.
  • the K1 information bits corresponding to the polarized channel are judged whether the row weights of K1 rows in the generator matrix corresponding to the K1 information bits are greater than or equal to the first threshold.
  • the K1 information bits are compared with the above-determined (K-K1) information bits are determined as K information bits; otherwise: if in the K1 row of the generator matrix corresponding to the selected K1 information bits, the row weight of K2 rows is less than the first threshold, Then, the K2 information bits corresponding to the K2 row from the selected K1 information bits are removed, and then (K-K2) information bits can be determined.
  • the reliability of the (NK-K1) polarized channels is determined by Select the K2 information bits corresponding to the K2 polarization channels in the order of large to small, and determine whether the row weights of K2 rows in the generator matrix corresponding to the K2 information bits are greater than or equal to the first threshold.
  • the number of information bits and the determined (K-K2) information bits are determined to be K information bits; otherwise, the same operation as described above is performed until K information bits are selected.
  • the polarized channels can be selected in the descending order of reliability of the N polarized channels. Each time a polarized channel is selected, it is judged whether the row weight of the row in the generator matrix corresponding to the polarized channel is greater than or equal to the first. Threshold. If it is, the bit corresponding to the polarized channel is determined as the information bit; otherwise, the bit corresponding to the polarized channel is determined as a fixed bit. And continue to select the next polarized channel, and determine whether the bit corresponding to the polarized channel is a fixed bit or an information bit according to the same method. Until K information bits are determined, the remaining unjudged bits are determined as fixed bits.
  • the RM-Polar code of (256,128) is shown, that is, the code length of the RM-Polar code is 256, and the information bit sequence length is 128.
  • the horizontal axis represents the sequence number of the sorting sequence obtained by sorting from high to low reliability.
  • the sequence number of the sorting sequence corresponds to the sequence number of the polarization channel of the polarization code and also corresponds to the bit position.
  • the vertical axis represents the row weight of each row in the generator matrix.
  • the left side of the solid vertical line in the middle represents the 128 bits with higher reliability of the polarized channel, and the right represents the 128 bits with lower channel reliability.
  • the 128 bits on the left side of the vertical line of the solid line can be selected.
  • the row weight is not lower than the threshold. Assuming that the set threshold is 16, it can be seen from Fig. 3 that there are two bits close to the left side of the solid vertical line and the corresponding row weight is less than 16. Therefore, these two bits will not be selected as the information bits of the RM-polar code, and the two corresponding rows closest to the right of the solid vertical line can be selected as the two information bits. Bits, instead of two bits with a row weight less than 16.
  • the order of the row weight of the generator matrix from large to small is the main reference factor, and the order of the reliability of the N polarized channels is used as the auxiliary reference factor to determine K information Bits.
  • the bits in the generator matrix whose row resize order is higher and the reliability order of the polarized channel is not lower than the second threshold can be selected as information bits, and the remaining bits are fixed bits.
  • the K information bits corresponding to the K rows can be selected according to the order of the row weight of each row in the N rows of the generator matrix from large to small. If (K-K0) information bits have been selected, when selecting the (K-K0+1) to Kth information bits according to the row reordering, there are X rows greater than K0 (X>K0) with the same row weight . Then you can select the first K0 rows of the corresponding polarized channel reliability from high to low in the X rows, and use the bits corresponding to the K0 rows as the (K-K0+1)th to Kth information Bits.
  • the (K-1) information bit has been selected, when the Kth information bit is selected according to the row reordering, there are multiple rows with the same row weight. Then, the row with the highest reliability of the corresponding polarized channel can be reselected among the multiple rows, and the bit corresponding to this row is regarded as the Kth information bit.
  • the (K-2) information bit has been selected, when the K-1 and Kth information bits are selected according to the row reordering, there are multiple rows greater than 2 that have the same row weight. Then, the rows with the highest and the second highest corresponding polarized channel reliability can be reselected from the multiple rows, and the bits corresponding to these two rows are regarded as the K-1th and Kth information bits. And so on.
  • the generator matrix G is:
  • the row weights of the first row to the eighth row are 1, 2, 2, 4, 2, 4, 4, and 8, respectively.
  • Row 8 has the largest weight, followed by rows 4, 6, and 7, followed by rows 2, 3, and 5, and row 1 has the smallest weight.
  • the order is 8, (4, 6, 7), (2, 3, 5), 1.
  • the bits whose rows of the generator matrix are higher and whose polarization channel reliability ranking is not lower than the second threshold are selected as information bits, and the remaining bits are selected as fixed bits.
  • Polar can theoretically prove that the channel capacity can be "reached" when the code length tends to be infinite (N ⁇ ), but in many practical scenarios, the code length is not infinite, so performance is limited.
  • the method provided in the embodiment of the present application can help improve the performance of the Polar code under a limited code length.
  • S402 Determine a first bit sequence according to the K information bits to be encoded.
  • the length of the first bit sequence is N, and N is a positive integer power of 2, and the first bit sequence includes fixed bits and K information bits to be encoded.
  • the K information bits to be encoded can be briefly described as K information bits.
  • N can be the length of the mother code of the polarization code.
  • K is less than or equal to N.
  • the K information bits may be determined first, and the information bits are the positions for placing or mapping the information bits in the N-length sequence.
  • the remaining positions in the N-long sequence excluding the positions for placing the information bits are fixed bits, that is, the positions for placing or mapping fixed bits.
  • the fixed bit is generally 0. Map K information bits to K information bits, or place K information bits into K information bits in an N-long sequence, and set the remaining positions as fixed bits to obtain the first bit sequence.
  • the information bits are ⁇ i 1 , i 2 , i 3 , i 4 ⁇
  • the N-long sequence includes 8 bits, ⁇ u 1 , u 2 , u 3 , u 5 ⁇ are fixed bits Position, ⁇ u 4 , u 6 , u 7 , u 8 ⁇ is the position of the information bit.
  • the N-long sequence is (0, 0, 0, U 4 , 0, U 6 , U 7 , U 8 ).
  • the first bit sequence is (0, 0, 0, i 1 , 0, i 2 , i 3 , i 4 ).
  • the first bit sequence can also be represented by an N-long sequence (0, 0, 0, U 4 , 0, U 6 , U 7 , U 8 ), which characterizes the positions of 4, 6, 7 and 8 as Information bits, place information bits, and other bits place fixed bits.
  • S403 Determine a second bit sequence according to the first bit sequence and the upper triangular matrix.
  • the upper triangular matrix is a matrix with N rows and N columns.
  • the upper triangular matrix can be any upper triangular matrix.
  • the first bit sequence is a vector of size N, including information bits and fixed bits.
  • the first bit sequence can be multiplied by the upper triangular matrix to obtain the second bit sequence.
  • the length of the second bit sequence is N.
  • S404 Perform polarization code encoding on the second bit sequence to obtain and output an encoded sequence.
  • the second bit sequence can be multiplied by the generator matrix to obtain the encoded sequence, and the encoded sequence can be output to complete the encoding process.
  • the length of the second bit sequence is N
  • the size of the generator matrix is N ⁇ N
  • the length of the encoded sequence is N.
  • the following example illustrates the process of determining the second bit sequence according to the first bit sequence and the upper triangular matrix, and obtaining the coded sequence according to the second bit sequence.
  • the first bit sequence can be represented by V
  • the second bit sequence can be represented by U
  • the generator matrix G is:
  • the upper triangular matrix T can be any upper triangular matrix. for example,
  • V is a 1 ⁇ 8 row vector
  • the transpose of an 8 ⁇ 1 column vector is used to represent the row vector in the formula expression.
  • the upper triangular matrix T may also be an upper triangular Toeplitz matrix.
  • the Toeplitz matrix can also be commonly referred to as a convolution operation matrix.
  • the embodiment of the present application adds an upper triangular matrix T between V and G, which can improve the code spectrum and optimize the code.
  • the structure further improves the performance of Polar codes under limited code length.
  • the first bit sequence includes K information bits and (N-K) fixed bits.
  • the embodiment of the present application may provide some possible implementation manners.
  • the N-long sequence represents N bits, including information bits and fixed bits.
  • the information bits in the N bits determine where the information bits are placed in the first bit sequence; the fixed bits in the N bits determine where the fixed bits are placed in the first bit sequence.
  • the N polarization channels of the polarization code correspond to the N bits in a one-to-one correspondence. The higher the reliability of the polarized channel, the more suitable the bit corresponding to the polarized channel is as the information bit.
  • the N rows of the polarization code generation matrix correspond to the N bits in a one-to-one correspondence. The larger the row weight of a row in the polarization code generation matrix is, the more suitable the bit corresponding to the row is to be used as the information bit.
  • Implementation manner 1 K information bits are determined according to the reliability ranking of the N polarization channels of the polarization code and the weight of each row in the N rows of the polarization code generation matrix.
  • the method for determining K information bits in Implementation Mode 1 may refer to the method for determining K information bits in the foregoing coding mode 3.
  • the reliability ranking of the N polarization channels and the weight of each row in the N rows of the polarization code generation matrix need to be combined to determine the K information bits.
  • the order of the reliability of the N polarization channels from increasing to small is the main reference factor, and the order of the row weight of the generator matrix is used as the auxiliary reference factor to determine the K information bits. It is also possible to use the descending order of the row weight of the generator matrix as the main reference factor, and the descending order of the reliability of the N polarized channels as the auxiliary reference factor to determine the K information bits.
  • the positions of the N bits except the K information bits are fixed bits. K information bits are mapped to the selected K information bits, and the remaining positions are 0. Or map K information bits to the selected K information bits, set the remaining positions to 0, and map fixed bits to the fixed bits. Thus, the first bit sequence is determined.
  • Implementation manner 2 According to the order of the reliability of the N polarization channels of the polarization code from high to low, K information bits are determined.
  • the row weight of the polarization code generation matrix is not considered, but the K information bits are determined from the consideration of the reliability of the polarization channel.
  • the N polarization channels of the polarization code correspond to the N bits in a one-to-one correspondence. The higher the reliability of the polarization channel, the more suitable it is to be selected as information bits. According to the order of the reliability of the N polarization channels from high to low, the K polarization channels with the highest reliability ranking can be selected, and the K information bits corresponding to the K polarization channels can be determined.
  • Implementation mode 3 K information bits are determined according to the weight of each of the N rows of the polarization code generation matrix.
  • the method for determining K information bits in the implementation manner 3 can refer to the method for determining K information bits in the encoding manner 2 described above.
  • the reliability ordering of the N polarization channels of the polarization code is not considered, but K information bits are determined from the line re-consideration of the N lines.
  • the N rows of the polarization code generation matrix correspond to the N bits in a one-to-one correspondence. The higher the row weight of a row in the generator matrix, the more suitable it is to be selected as information bits.
  • the K polarization channels can be selected according to the order of the row weight of the N rows of the generator matrix from high to low, and the K information bits corresponding to the K polarization channels can be determined.
  • the method for determining the first bit sequence or the method for determining K information bits may also have other methods, which are not limited.
  • the aforementioned information bits to be encoded may include check bits.
  • the K information bits to be encoded include K1 first information bits and K2 check bits.
  • the encoding device first obtains K1 information bits, performs check coding on K1 information bits, and obtains K2 check bits.
  • the check coding method in the embodiments of the present application may be cyclic redundancy check (cyclic redundancy check, CRC) coding, parity check (PC) coding, or a combination of CRC and PC check Encoding.
  • CRC encoding can be performed on K1 first information bits to obtain K2 CRC check bits.
  • K1 first information bits may be PC-encoded to obtain K2 PC check bits.
  • K1 first information bits may be subjected to CRC encoding and then PC encoding to obtain K2 check bits.
  • the K1 first information bits may be subjected to PC check coding and then CRC coding to obtain K2 check bits.
  • the decoding device can decode using a predetermined check relationship to improve decoding performance.
  • the information bits include CRC check bits.
  • the codeword When the polarization code encoding method provided in the embodiments of the present application is applied to an RM-polar code, the codeword may be referred to as a transformed RM-Polar (T-RM-Polar) code.
  • T-RM-Polar transformed RM-Polar
  • the codeword When the polarization code encoding method provided in the embodiments of the present application is applied to a polar code, the codeword may be referred to as a transformed Polar code (T-Polar) code.
  • simulation graphs for comparing the performance of several codewords through FIGS. 5-7. These simulation graphs are exemplary graphs showing performance gains.
  • the method of the embodiments of the present application is not limited to these examples.
  • Figure 5 shows a simulation diagram of the performance comparison of several codewords. Including the traditional polar code (Polar code) and T-Polar code constructed according to the coding method, and the RM-polar code and T-RM-Polar code constructed according to the coding method.
  • the abscissa is the signal-to-noise ratio (Eb/No), and the ordinate is the frame error rate (FER).
  • the RM-polar code is constructed with comprehensive consideration of the reliability of the polarized channel and the row weight of the generator matrix, which will bring further gains. It can be seen from Figure 5 that, compared to the T-Polar code, the T-RM-Polar code has a performance gain of 0.8dB.
  • the T-RM-Polar code brings a gain of nearly 1dB, which effectively improves the performance of the Polar code under the limited code length.
  • Figure 6 shows the performance comparison of several codewords. It includes the traditional polar code (Polar code) and T-Polar code constructed according to the first coding method, and the RM-polar code and T-RM-Polar code constructed according to the third coding method.
  • N 512
  • K 256
  • the abscissa is the signal-to-noise ratio
  • the ordinate is the frame error rate.
  • the T-RM-Polar code has a performance of 0.2dB Gain.
  • the RM-polar code is constructed with comprehensive consideration of the reliability of the polarized channel and the row weight of the generator matrix, which will bring further gains. It can be seen from Figure 6 that compared to the T-Polar code, the T-RM-Polar code has a performance gain of 0.5 dB.
  • the T-RM-Polar code brings a gain of nearly 0.6dB, which effectively improves the performance of the Polar code under the limited code length.
  • Figure 7 shows the performance comparison of several codewords. Including the RM-polar code constructed according to the coding method three, the codeword T-RM-Polar code constructed according to the upper triangular matrix provided in the embodiment of the application, and the code constructed according to the upper triangular matrix and the information bits include check bits.
  • the word mark is the CRC enhanced transformed RM-Polar code (CRC aided transformed RM-Polar, CA-T-RM-Polar) code.
  • N 512
  • K 256
  • the abscissa is the signal-to-noise ratio
  • the ordinate is the frame error rate.
  • an embodiment of the present application further provides a polarization code encoding device 800, the polarization code encoding device 800 is configured to execute the foregoing polarization code encoding method, and the polarization code encoding device 800 includes:
  • the obtaining unit 801 is configured to obtain K information bits to be encoded, where K is a positive integer;
  • the determining unit 802 is configured to determine a first bit sequence according to the K information bits to be encoded.
  • the length of the first bit sequence is N, and N is a positive integer power of 2, and the first bit sequence includes fixed bits and K waiting bits. Encoded information bits;
  • the encoding unit 803 is configured to determine a second bit sequence according to the first bit sequence and the upper triangular matrix, the upper triangular matrix is a matrix with N rows and N columns; and is used to encode the second bit sequence with a polarization code to obtain and output The encoded sequence.
  • the upper triangular matrix is the upper triangular Toeplitz matrix.
  • the determining unit 802 is configured to: determine K information bits according to the reliability ranking of the N polarization channels of the polarization code and the weight of each row in the N rows of the polarization code generation matrix, where the polarization code
  • the generator matrix is a matrix with N rows and N columns.
  • the N rows of the polarization code generator matrix correspond to the N bits of the first bit sequence, and the N polarization channels correspond to the N bits of the first bit sequence. ; Map the K information bits to be encoded to K information bits to obtain the first bit sequence.
  • the determining unit 802 is configured to: select the row of the polarization code generation matrix whose reliability is sorted from largest to smallest, and the row of the polarization code generation matrix whose weight is not lower than the first threshold, and the corresponding bit Bits are used as K information bits.
  • the determining unit 802 is configured to: select a polarized channel whose row weight is sorted from largest to smallest in the polarization code generation matrix, and the reliability of the polarized channel is ranked not lower than a second threshold, and the corresponding bit Bits are used as K information bits.
  • the determining unit 802 is configured to: remove the reliability rankings of the polarization channels related to the rate matching according to the polarization codes of the N polarization channels, and remove the rate matching related lines according to the N rows of the polarization code generation matrix. The weight of each row determines K information bits.
  • the polarization channel related to rate matching includes a punctured, shortened or pre-frozen polarization channel
  • the line related to rate matching includes a line corresponding to the punctured, shortened or pre-frozen polarization channel.
  • the determining unit 802 is configured to determine K information bits according to the order of the reliability of the N polarization channels of the polarization code from high to low, where the N polarization channels correspond to the first bit one by one. N bits of the sequence; Map the K information bits to be encoded to K information bits to obtain the first bit sequence.
  • the determining unit 802 is configured to determine the K information bits according to the order of the reliability of the polarized channels related to the removal rate matching of the N polarized channels of the polarized codes.
  • the polarization channels related to rate matching include punctured, shortened, or pre-frozen polarization channels.
  • the determining unit 802 is configured to determine K information bits according to the weight of each of the N rows of the polarization code generation matrix, where the polarization code generation matrix is a matrix with N rows and N columns, and the polarization code generation matrix is a matrix with N rows and N columns.
  • the N rows of the generator matrix correspond to the N bits of the first bit sequence one by one; the K information bits to be encoded are mapped to the K information bits to obtain the first bit sequence.
  • the determining unit 802 is configured to determine K information bits according to the weight of each row after the N rows of the polarization code generation matrix are removed from the row related to rate matching.
  • the rows related to rate matching include rows corresponding to punctured, shortened, or pre-frozen polarized channels.
  • the encoding unit 803 is configured to: multiply the first bit sequence by the upper triangular matrix to obtain the second bit sequence.
  • the encoding unit 803 is configured to: multiply the second bit sequence by the polarization code generation matrix to obtain an encoded sequence.
  • the information bits include check bits.
  • an embodiment of the present application also provides a polarization code encoding device 900, and the polarization code encoding device 900 can be used to execute the above-mentioned polarization code encoding method.
  • Part or all of the foregoing polarization code encoding methods can be implemented by hardware or software.
  • the polarization code encoding device 900 includes: an input interface circuit 901 for obtaining K to-be-encoded Information bits; logic circuit 902, used to perform other operations in the polarization code encoding method described above except for obtaining the bits to be encoded and outputting the encoded bits.
  • output The interface circuit 903 is used to output the encoded sequence.
  • the polarization code encoding device 900 may be a chip or an integrated circuit in specific implementation.
  • the polarization code encoding device 900 includes: a memory 1001 for storing a program; a processor 1002 , Is used to execute the program stored in the memory 1001, and when the program is executed, the polarization code encoding apparatus 900 can implement the polarization code encoding method provided in the foregoing embodiment.
  • the foregoing memory 1001 may be a physically independent unit, or the memory 1001 and the processor 1002 may be integrated together.
  • the polarization code encoding apparatus 900 may also only include the processor 1002.
  • the memory 1001 for storing programs is located outside the polarization code encoding device 900, and the processor 1002 is connected to the memory 1001 through a circuit/wire for reading and executing the programs stored in the memory 1001.
  • the processor 1002 may be a central processing unit (CPU), a network processor (NP), or a combination of a CPU and an NP.
  • CPU central processing unit
  • NP network processor
  • the processor 1002 may further include a hardware chip.
  • the aforementioned hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof.
  • ASIC application-specific integrated circuit
  • PLD programmable logic device
  • the above-mentioned PLD may be a complex programmable logic device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL) or any combination thereof.
  • CPLD complex programmable logic device
  • FPGA field-programmable gate array
  • GAL generic array logic
  • the memory 1001 may include a volatile memory (volatile memory), such as a random-access memory (random-access memory, RAM); the memory 1001 may also include a non-volatile memory (non-volatile memory), such as a flash memory (flash memory). memory), a hard disk drive (HDD) or a solid-state drive (SSD); the memory 1001 may also include a combination of the foregoing types of memories.
  • volatile memory such as a random-access memory (random-access memory, RAM
  • non-volatile memory such as a flash memory (flash memory).
  • flash memory flash memory
  • HDD hard disk drive
  • SSD solid-state drive
  • the polarization code encoding device 900 may also be a chip, an integrated circuit, or a chip system.
  • An embodiment of the present application may also provide a chip including a processor, which is used to support the polarization code encoding device 900 to implement the functions involved in the foregoing method embodiments.
  • the chip is connected to a memory or the chip includes a memory, and the memory is used to store the necessary program instructions and data of the polarization code encoding device 900.
  • the embodiment of the present application provides a computer-readable storage medium that stores a computer program, and the computer program includes instructions for executing the foregoing method embodiments.
  • the embodiments of the present application provide a computer program product containing instructions, which when run on a computer, cause the computer to execute the foregoing method embodiments.
  • this application can be provided as methods, systems, or computer program products. Therefore, this application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, this application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.
  • computer-usable storage media including but not limited to disk storage, CD-ROM, optical storage, etc.
  • These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing equipment to work in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including the instruction device.
  • the device implements the functions specified in one process or multiple processes in the flowchart and/or one block or multiple blocks in the block diagram.
  • These computer program instructions can also be loaded on a computer or other programmable data processing equipment, so that a series of operation steps are executed on the computer or other programmable equipment to produce computer-implemented processing, so as to execute on the computer or other programmable equipment.
  • the instructions provide steps for implementing the functions specified in one process or multiple processes in the flowchart and/or one block or multiple blocks in the block diagram.

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Abstract

本申请公开了一种极化码编码方法及装置，可以通过码字构造来提高编码的性能。该方法为：获取K个待编码的信息比特，K为正整数；根据所述K个待编码的信息比特，确定第一比特序列，所述第一比特序列的长度为N，所述第一比特序列包括固定比特和所述K个待编码的信息比特；K个待编码的信息比特还可以包括校验比特。根据第一比特序列和上三角矩阵，确定第二比特序列，所述上三角矩阵为N行N列的矩阵，所述上三角矩阵可以为上三角Toeplitz矩阵，对所述第二比特序列进行极化码编码，得到并输出编码后的序列。

Description

一种极化码编码方法及装置
相关申请的交叉引用
本申请要求在2019年11月30日提交中国专利局、申请号为201911208975.2、申请名称为“一种极化码编码方法及装置”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
本申请实施例涉及编解码领域，尤其涉及一种极化码编码方法及装置。
背景技术
通信系统通常采用信道编码提高数据传输的可靠性，保证通信的质量。例如可以采用极化码(Polar)码、里德-穆勒(Reed-Muler，RM)码等编码方法。其中，Polar码是可以取得香农容量且具有低编译码复杂度的编码方式。RM码由David Muller于1954年首次提出，RM码快速的译码算法非常适合于光纤通信系统。RM码和Polar码的构造方式相结合生成一种编码方法，可以称为RM-Polar码。
如何通过码字构造来提高编码的性能，是业界持续关注的问题。
发明内容
本申请实施例提供一种极化码编码方法及装置，用以提高编码性能。
本申请实施例提供的具体技术方案如下：
第一方面，提供一种极化码编码方法，该方法的执行主体可以是编码设备。编码设备可以是终端，也可以是网络设备。该方法的步骤包括：获取K个待编码的信息比特，K为正整数；根据所述K个待编码的信息比特，确定第一比特序列，所述第一比特序列的长度为N，N为2的正整数次幂，所述第一比特序列包括固定比特和所述K个待编码的信息比特；根据第一比特序列和上三角矩阵，确定第二比特序列，所述上三角矩阵为N行N列的矩阵；对所述第二比特序列进行极化码编码，得到并输出编码后的序列。通过在编码过程中增加上三角矩阵的构造方法，这样能够提升码谱，优化码的构造，Polar能够从理论上证明，当码长趋于无限时能够“达到”信道容量，但是在许多实际的场景中，码长并不是无限的，因此性能受限。本申请实施例提供的方法能够有助于提高有限码长下Polar码的性能。
在一个可能的设计中，所述上三角矩阵为上三角托普利兹(Toeplitz)矩阵。
在一个可能的设计中，在根据所述K个待编码的信息比特，确定第一比特序列时，可以通过以下方式实现：根据极化码N个极化信道的可靠度排序和极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，其中，所述极化码生成矩阵为N行N列的矩阵，所述极化码生成矩阵的N行一一对应于所述第一比特序列的N个比特位，所述N个极化信道一一对应于所述第一比特序列的N个比特位；将所述K个待编码的信息比特映射到所述K个信息比特位，得到所述第一比特序列。在选择Polar码的信息比特位时，综合考虑 极化信道的可靠性以及生成矩阵的行重，能够更进一步增大码字的最小汉明距离，能够改善Polar码的性能。其中，最小汉明距离为构造码形成的码字集合中所有码字间相互的距离中最小的距离。另一方面，由于编码性能提高，所以能够在一定程度上提高译码性能。
在一个可能的设计中，根据极化码N个极化信道的可靠度排序和极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，可以通过方式一或方式二来实现。
方式一：选择极化码生成矩阵中行重由大到小排序靠前的行，且极化信道的可靠度排序不低于第二阈值的极化信道，对应的比特位作为所述K个信息比特位。
可以按照极化码N个极化信道的可靠度由高到低的顺序，确定第一排序序列，所述第一排序序列的N个序号一一对应于所述第一比特序列的N个比特位；在所述第一排序序列中从第一个序号开始，选择所述极化码生成矩阵中重量大于或等于第一阈值的K行对应的比特位，作为所述K个信息比特位。
方式二：选择极化码生成矩阵中行重由大到小排序靠前的行，且极化信道的可靠度排序不低于第二阈值的极化信道，对应的比特位作为所述K个信息比特位。
可以按照所述极化码生成矩阵的N行中每一行的重量由高到低的顺序，确定第二排序序列，所述第二排序序列的N个序号一一对应于所述第一比特序列的N个比特位；在所述第二排序序列中从第一个序号开始，选择极化码N个极化信道的可靠度由高到低的K个极化信道对应的比特位，作为所述K个信息比特位。
在一个可能的设计中，按照可靠度排序，是从N个极化信道速率匹配后的极化信道后进行的。按照生成矩阵的行重排序，是从生成矩阵的N行对应的N个极化信道速率匹配后的极化信道后进行的。速率匹配的方式可以包括：打孔、缩短或者预冻结。
例如，根据极化码N个极化信道的可靠度排序和极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，可以通过以下方式实现：根据极化码N个极化信道去除速率匹配相关的极化信道的可靠度排序，和根据极化码生成矩阵的N行去除速率匹配相关的行之后的每一行的重量，确定K个信息比特位。可选的，所述速率匹配相关的极化信道包括打孔、缩短或预冻结的极化信道，所述速率匹配相关的行包括打孔、缩短或预冻结的极化信道对应的行。
在一个可能的设计中，在根据所述K个待编码的信息比特，确定第一比特序列时，可以考虑极化信道的可靠性来确定K个信息比特位，例如：按照极化码N个极化信道的可靠度由高到低的顺序，确定K个信息比特位，其中，所述N个极化信道一一对应于所述第一比特序列的N个比特位；将所述K个待编码的信息比特映射到所述K个信息比特位，得到所述第一比特序列。
又例如，按照极化码N个极化信道的可靠度由高到低的顺序，确定K个信息比特位，可以通过以下方式实现：按照极化码N个极化信道去除速率匹配相关的极化信道的可靠度由高到低的顺序，确定K个信息比特位。可选的，所述速率匹配相关的极化信道包括打孔、缩短或预冻结的极化信道。
在一个可能的设计中，在根据所述K个待编码的信息比特确定第一比特序列时，还可以考虑生成矩阵的行重来确定K个信息比特位。例如：根据极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，其中，所述极化码生成矩阵为N行N列的矩阵，所述极化码生成矩阵的N行一一对应于所述第一比特序列的N个比特位；将所述K个待编码的信息比特映射到所述K个信息比特位，得到所述第一比特序列。
在一个可能的设计中，根据极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，包括：根据极化码生成矩阵的N行去除速率匹配相关的行之后的每一行的重量，确定K个信息比特位。可选的，所述速率匹配相关的行包括打孔、缩短或预冻结的极化信道对应的行。
在一个可能的设计中，根据第一比特序列和上三角矩阵，确定第二比特序列，包括：将所述第一比特序列与所述上三角矩阵相乘，得到所述第二比特序列。
在一个可能的设计中，对所述第二比特序列进行极化码编码，得到编码后的序列，包括：将所述第二比特序列与极化码生成矩阵相乘，得到所述编码后的序列。
在一个可能的设计中，所述信息比特包括校验比特。当待编码的信息比特中包括校验比特时，译码设备能够使用预先给定的校验关系译码，提高译码性能。
第二方面，提供一种极化码编码装置，该装置具有实现上述第一方面和第一方面的任一种可能的设计中所述的方法的功能。所述功能可以通过硬件实现，也可以通过硬件执行相应的软件实现。所述硬件或软件包括一个或多个与上述功能相对应的模块。一种设计中，该装置可以包括获取单元、确定单元和编码单元。示例性地：
获取单元，用于获取K个待编码的信息比特，K为正整数；确定单元，用于根据所述K个待编码的信息比特，确定第一比特序列，所述第一比特序列的长度为N，N为2的正整数次幂，所述第一比特序列包括固定比特和所述K个待编码的信息比特；编码单元，用于根据第一比特序列和上三角矩阵，确定第二比特序列，所述上三角矩阵为N行N列的矩阵；以及用于对所述第二比特序列进行极化码编码，得到并输出编码后的序列。通过在编码过程中增加上三角矩阵的构造方法，这样能够提升码谱，优化码的构造，Polar能够从理论上证明，当码长趋于无限时(N→∞)能够“达到”信道容量，但是在许多实际的场景中，码长并不是无限的，因此性能受限。本申请实施例提供的方法能够有助于提高有限码长下Polar码的性能。
在一个可能的设计中，所述上三角矩阵为上三角Toeplitz矩阵。
在一个可能的设计中，所述确定单元用于：根据极化码N个极化信道的可靠度排序和极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，其中，所述极化码生成矩阵为N行N列的矩阵，所述极化码生成矩阵的N行一一对应于所述第一比特序列的N个比特位，所述N个极化信道一一对应于所述第一比特序列的N个比特位；将所述K个待编码的信息比特映射到所述K个信息比特位，得到所述第一比特序列。在选择Polar码的信息比特位时，综合考虑极化信道的可靠性以及生成矩阵的行重，能够更进一步增大码字的最小汉明距离，能够改善Polar码的编码性能，并且由于编码性能提高，也能够在译码时提高译码性能。
在一个可能的设计中，所述确定单元用于：选择可靠度按从大到小的排序方式时排序靠前的极化信道、且重量不低于第一阈值的极化码生成矩阵的行，对应的比特位作为所述K个信息比特位。
例如，按照极化码N个极化信道的可靠度由高到低的顺序，确定第一排序序列，所述第一排序序列的N个序号一一对应于所述第一比特序列的N个比特位；在所述第一排序序列中从第一个序号开始，选择所述极化码生成矩阵中重量大于或等于第一阈值的K行对应的比特位，作为所述K个信息比特位。
在一个可能的设计中，所述确定单元用于：选择极化码生成矩阵中行重由大到小排序 靠前的行，且极化信道的可靠度排序不低于第二阈值的极化信道，对应的比特位作为所述K个信息比特位。
例如，按照所述极化码生成矩阵的N行中每一行的重量由高到低的顺序，确定第二排序序列，所述第二排序序列的N个序号一一对应于所述第一比特序列的N个比特位；在所述第二排序序列中从第一个序号开始，选择极化码N个极化信道的可靠度由高到低的K个极化信道对应的比特位，作为所述K个信息比特位。
在一个可能的设计中，所述确定单元用于：根据极化码N个极化信道去除速率匹配相关的极化信道的可靠度排序，和根据极化码生成矩阵的N行去除速率匹配相关的行之后的每一行的重量，确定K个信息比特位，所述速率匹配相关的极化信道包括打孔、缩短或预冻结的极化信道，所述速率匹配相关的行包括打孔、缩短或预冻结的极化信道对应的行。
在一个可能的设计中，所述确定单元用于：按照极化码N个极化信道的可靠度由高到低的顺序，确定K个信息比特位，其中，所述N个极化信道一一对应于所述第一比特序列的N个比特位；将所述K个待编码的信息比特映射到所述K个信息比特位，得到所述第一比特序列。
在一个可能的设计中，在按照极化码N个极化信道的可靠度由高到低的顺序，确定K个信息比特位时，所述确定单元用于：按照极化码N个极化信道去除速率匹配相关的极化信道的可靠度由高到低的顺序，确定K个信息比特位。可选的，所述速率匹配相关的极化信道包括打孔、缩短或预冻结的极化信道。
在一个可能的设计中，所述确定单元用于：根据极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，其中，所述极化码生成矩阵为N行N列的矩阵，所述极化码生成矩阵的N行一一对应于所述第一比特序列的N个比特位；将所述K个待编码的信息比特映射到所述K个信息比特位，得到所述第一比特序列。
在一个可能的设计中，在根据极化码生成矩阵的N行中每一行的重量，确定K个信息比特位时，所述确定单元用于：根据极化码生成矩阵的N行去除速率匹配相关的行之后的每一行的重量，确定K个信息比特位。可选的，所述速率匹配相关的行包括打孔、缩短或预冻结的极化信道对应的行。
在一个可能的设计中，所述编码单元用于：将所述第一比特序列与所述上三角矩阵相乘，得到所述第二比特序列。
在一个可能的设计中，所述编码单元用于：将所述第二比特序列与极化码生成矩阵相乘，得到所述编码后的序列。
在一个可能的设计中，所述信息比特包括校验比特。当待编码的信息比特中包括校验比特时，译码设备能够使用预先给定的校验关系译码，提高译码性能。
第三方面，提供一种极化码编码装置，该装置具有实现上述第一方面和第一方面的任一种可能的设计中所述的方法的功能。所述功能可以通过硬件实现，也可以通过硬件执行相应的软件实现。所述硬件或软件包括一个或多个与上述功能相对应的模块。
在一个可能的设计中，当所述功能的部分或全部通过硬件实现时，所述极化码编码装置包括：输入接口电路，用于获取K个待编码的信息比特，K为正整数；逻辑电路，用于执行上述第一方面和第一方面的任一种可能的设计中所述的(除获取K个待编码的信息比特和输出编码后的序列之外)行为；输出接口电路，用于输出编码后的序列。
可选的，所述极化码编码装置可以是芯片或者集成电路。
在一个可能的设计中，当所述功能的部分或全部通过软件实现时，所述极化码编码装置包括：存储器，用于存储程序；处理器，用于执行所述存储器存储的所述程序，当所述程序被执行时，所述极化码编码装置可以实现如上述第一方面和第一方面的任一种可能的设计中所述的方法。
可选的，上述存储器可以是物理上独立的单元，也可以与处理器集成在一起。
在一个可能的设计中，当所述功能的部分或全部通过软件实现时，所述极化码编码装置包括处理器。用于存储程序的存储器位于所述编码装置之外，处理器通过电路/电线与存储器连接，用于读取并执行所述存储器中存储的程序。
第四方面，提供了一种计算机可读存储介质，存储有计算机可读指令，当所述计算机可读指令在计算机上运行时，使得计算机执行如第一方面和第一方面的任一可能设计中任一种所述的方法。
第五方面，本申请实施例提供了一种包含指令的计算机程序产品，当其在计算机上运行时，使得计算机执行上述第一方面和第一方面的任一可能设计所述的方法。
第六方面，本申请实施例提供了一种芯片系统，该芯片系统包括处理器，还可以包括存储器，用于实现上述第一方面或第一方面中任一种可能的设计中所述的方法。该芯片系统可以由芯片构成，也可以包含芯片和其他分立器件。
附图说明
图1为本申请实施例中通信系统架构示意图；
图2为本申请实施例中极化码编码方法示意图之一；
图3为本申请实施例中(256,128)的RM-Polar码构造方法示意图；
图4为本申请实施例中极化码编码方法示意图之二；
图5为本申请实施例中码字性能对比示意图之一；
图6为本申请实施例中码字性能对比示意图之二；
图7为本申请实施例中码字性能对比示意图之三；
图8为本申请实施例中极化码编码装置结构示意图之一；
图9为本申请实施例中极化码编码装置结构示意图之二；
图10为本申请实施例中极化码编码装置结构示意图之三。
具体实施方式
本申请实施例提供一种极化码编码及装置。其中，方法和装置是基于同一技术构思的，由于方法及装置解决问题的原理相似，因此装置与方法的实施可以相互参见，重复之处不再赘述。本申请实施例的描述中，“和/或”，描述关联对象的关联关系，表示可以存在三种关系，例如，A和/或B，可以表示：单独存在A，同时存在A和B，单独存在B这三种情况。字符“/”一般表示前后关联对象是一种“或”的关系。本申请中所涉及的至少一个是指一个或多个；多个，是指两个或两个以上。另外，需要理解的是，在本申请的描述中，“第一”、“第二”、“第三”等词汇，仅用于区分描述的目的，而不能理解为指示或暗示相对重要性，也不能理解为指示或暗示顺序。
本申请实施例提供的译码方法可以应用于第五代(5th generation，5G)通信系统，例 如5G新空口(new radio，NR)系统，设备到设备(device to device，D2D)通信系统，或应用于未来的各种通信系统。
下面将结合附图，对本申请实施例进行详细描述。
图1示出了本申请实施例提供的译码方法适用的一种可能的通信系统的架构，参阅图1所示，通信系统100中包括：网络设备101和一个或多个终端102。当通信系统100包括核心网时，网络设备101还可以与核心网相连。网络设备101为覆盖范围内的终端102提供服务。例如，参见图1所示，网络设备101为网络设备101覆盖范围内的一个或多个终端102提供无线接入。除此之外，网络设备之间的覆盖范围可以存在重叠的区域，例如网络设备101和网络设备101’。网络设备之间还可以互相通信，例如，网络设备101可以与网络设备101’之间进行通信。
网络设备101为无线接入网(radio access network，RAN)中的节点，又可以称为基站，还可以称为RAN节点(或设备)。目前，一些网络设备101的举例为：下一代基站(next generation nodeB，gNB)、下一代演进的基站(next generation evolved nodeB，Ng-eNB)、传输接收点(transmission reception point，TRP)、演进型节点B(evolved Node B，eNB)、无线网络控制器(radio network controller，RNC)、节点B(Node B，NB)、基站控制器(base station controller，BSC)、基站收发台(base transceiver station,BTS)、家庭基站(例如，home evolved NodeB，或home Node B，HNB)、基带单元(base band unit，BBU)，或无线保真(wireless fidelity，Wifi)接入点(access point，AP)，网络设备101还可以是卫星，卫星还可以称为高空平台、高空飞行器、或卫星基站。网络设备101还可以是其他具有网络设备功能的设备，例如，网络设备101还可以是D2D通信中担任网络设备功能的设备。网络设备101还可以是未来可能的通信系统中的网络设备。
在一些部署中，网络设备可以包括集中式单元(centralized unit，CU)和(distributed unit，DU)。网络设备还可以包括有源天线单元(active antenna unit，AAU)。CU实现网络设备的部分功能，DU实现网络设备的部分功能，比如，CU负责处理非实时协议和服务，实现无线资源控制(radio resource control，RRC)，分组数据汇聚层协议(packet data convergence protocol，PDCP)层的功能。DU负责处理物理层协议和实时服务，实现无线链路控制(radio link control，RLC)层、媒体接入控制(media access control，MAC)层和物理(physical，PHY)层的功能。AAU实现部分物理层处理功能、射频处理及有源天线的相关功能。由于RRC层的信息最终会变成PHY层的信息，或者，由PHY层的信息转变而来，因而，在这种架构下，高层信令，如RRC层信令，也可以认为是由DU发送的，或者，由DU+AAU发送的。可以理解的是，网络设备可以为包括CU节点、DU节点、AAU节点中一项或多项的设备。此外，可以将CU划分为接入网(radio access network，RAN)中的网络设备，也可以将CU划分为核心网(core network，CN)中的网络设备，本申请对此不做限定。
终端102，又称之为用户设备(user equipment，UE)、移动台(mobile station，MS)、移动终端(mobile terminal，MT)等，是一种向用户提供语音和/或数据连通性的设备。例如，终端102包括具有无线连接功能的手持式设备、车载设备等。目前，终端102可以是：手机(mobile phone)、平板电脑、笔记本电脑、掌上电脑、移动互联网设备(mobile internet device，MID)、可穿戴设备(例如智能手表、智能手环、计步器等)，车载设备(例如，汽车、自行车、电动车、飞机、船舶、火车、高铁等)、虚拟现实(virtual reality，VR)设备、增强现实(augmented reality，AR)设备、工业控制(industrial control)中的无线终端、 智能家居设备(例如，冰箱、电视、空调、电表等)、智能机器人、车间设备、无人驾驶(self driving)中的无线终端、远程手术(remote medical surgery)中的无线终端、智能电网(smart grid)中的无线终端、运输安全(transportation safety)中的无线终端、智慧城市(smart city)中的无线终端，或智慧家庭(smart home)中的无线终端、飞行设备(例如，智能机器人、热气球、无人机、飞机)等。终端102还可以是其他具有终端功能的设备，例如，终端102还可以是D2D通信中担任终端功能的终端。
基于图1所示的通信系统架构，以下具体介绍一下本申请实施例提供的极化码编码方法。该极化码编码方法的执行主体可以为编码设备，编码设备可以是网络设备101，也可以是终端102。编码设备对待编码的信息比特进行编码，获得编码码字发送给译码设备。编码设备也可以称为发送端，译码设备为接收端。当发送端或编码设备是网络设备101时，接收端或译码设备为终端102,当发送端或编码设备为终端102时，接收端或译码设备为网络设备101。
首先介绍几种编码方法可能的实现方式。
编码方法一：传统的极化码(Polar码)编码方式。
Polar码也是一种线性块码，生成矩阵为G N，生成矩阵也可以记为G，生成矩阵也可以称为编码矩阵。编码过程为
Figure PCTCN2020126836-appb-000001
其中
Figure PCTCN2020126836-appb-000002
是一个二进制的行矢量，长度为N，N为Polar码码长；G N是一个N×N的矩阵，且
Figure PCTCN2020126836-appb-000003
定义为log 2N个矩阵F 2的克罗内克(Kronecker)乘积。上述矩阵
Figure PCTCN2020126836-appb-000004
Polar码的编码过程中，
Figure PCTCN2020126836-appb-000005
中的一部分比特用来携带信息，携带信息的比特称为信息比特，用来携带信息的这部分比特形成信息比特集合，这些比特的索引的集合记作A；另外的一部分比特设置为接收端和发送端预先约定的固定值，称之为固定比特集合或冻结比特集合(frozen bits)，其索引的集合用A的补集A c表示。Polar码的编码过程相当于：
Figure PCTCN2020126836-appb-000006
这里，G N(A)是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(AC)是G N中由集合A c中的索引对应的那些行得到的子矩阵。u A为
Figure PCTCN2020126836-appb-000007
中的信息比特集合，数量为K；
Figure PCTCN2020126836-appb-000008
为
Figure PCTCN2020126836-appb-000009
中的固定比特集合，其数量为(N-K)，是已知比特。这些固定比特通常被设置为0，但是只要接收端和发送端预先约定，固定比特可以被任意设置。从而，Polar码的编码输出可简化为：
Figure PCTCN2020126836-appb-000010
这里u A为
Figure PCTCN2020126836-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为信息块大小或者K为信息比特的数目，或者K为信息比特集合的大小，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。Polar码的构造过程通常是，根据母码码长N确定共存在N个极化信道，分别对应生成矩阵的N个行，计算极化信道可靠度，将可靠度较高的前K个极化信道的索引作为集合A的元素，剩余(N-K)个极化信道对应的索引作为固定比特的索引集合A c的元素。集合A决定了信息比特的位置，集合A c决定了固定比特的位置。
如图2所示，展示了一个8×8的生成矩阵，其中向量u用(0，0，0，U 4，0，U 6，U 7，U 8)表示，经过生成矩阵，编码后的比特以向量(X 1，X 2，X 3，X 4，X 5，X 6，X 7，X 8)表示。高可靠信道对应的比特位用于映射信息比特，低可靠信道对应的比特位用于映射固定比特。如图2中所示，{u 1,u 2,u 3,u 5}为固定比特的位置，{u 4,u 6,u 7,u 8}为信息比特的位置，将长度为4的待编码的信息向量{i 1,i 2,i 3,i 4}映射在信息比特的位置，经过编码后，生成8位编码后比特。在上述编码后，将编码后的序列经过调制后再经过噪声信道，然后输出。
假设生成矩阵G为：
Figure PCTCN2020126836-appb-000012
则编码后的比特X可以根据X＝uG获得。
Figure PCTCN2020126836-appb-000013
其中，u为1×8的行向量，在公式表示中用8×1的列向量的转置来表示该行向量。
编码方法二：RM码编码方式。
给定参数r和m，其中r≤m。则存在一个r阶的RM码，可以表示为：(r,m)。RM码字长度为N＝2 m,最小码距为d＝2 m-r，信息比特的位数为：
Figure PCTCN2020126836-appb-000014
因此，RM码也可以表示为：(N,K,d)。
RM码可以采用和polar码相同的生成矩阵G的构造，即N×N的生成矩阵
Figure PCTCN2020126836-appb-000015
构造。但是选择信息比特位的方法不同。构造RM码时，确定每个比特位对应的G矩阵的行的重量，按照行重由大到小的顺序选择K个比特位作为信息比特位。剩余行重小的比特位作为固定比特位。固定比特位通常设置为0。其中，生成矩阵一行中非“0”元素的个数称为该行的汉明重量，或者该行的重量，简称为行重。
例如，生成矩阵G为：
Figure PCTCN2020126836-appb-000016
在生成矩阵G中，第1行到第4行的行重分别为1、2、2、4。
假设K＝1，即选择1个信息比特位。可以选择行重最大的第4行对应的比特位作为信息比特位。
假设K＝2，即选择2个信息比特位。可以选择行重从大到小排序的2行对应的比特位作为信息比特位。行重最大的行为第4行，行重最大的第4行对应的比特位为一个信息比特位。第2行和第3行的行重相同，确定另一个比特位时，可以选择第2行和第3行中的任意一行对应的比特位作为信息比特位，也可以按照自然序从前往后选择，也可以按照离最大行重对应的行最近的行来确定信息比特位。若按照自然序从前往后选择的方式确定另 一个比特位，则选择第2行，这种方式下编码端较简易些。若按照离最大行重对应的行最近的行来确定信息比特位，比如这里行重最大的是第4行，那就在第2行和第3行中选择第3行，这种方式下数据更为集中，较为有利于译码。
又例如，生成矩阵G为：
Figure PCTCN2020126836-appb-000017
在生成矩阵G中，第1行到第8行的行重分别为1、2、2、4、2、4、4、8。第8行的行重最大，第4、6、7行的行重次之，第2、3、5行的行重第三，第1行的行重最小。按照行重从大到小排序为8、(4、6、7)、(2、3、5)、1。
假设K＝4，即选择4个信息比特位。可以选择行重从大到小排序，选择第8、4、6、7行对应的比特位作为信息比特位。
假设K＝6，即选择6个信息比特位。可以选择行重从大到小排序，先选择第8、4、6、7行对应的比特位作为4个信息比特位。还需要选择2个信息比特位，行重排序第三的行有3行，可以选择2、3、5行中的任意两行对应的比特位作为信息比特位，也可以按照自然序从前往后选择两行对应的比特位作为信息比特位，也可以按照离最大行重对应的行最近的两行来确定信息比特位。若按照自然序从前往后选择两行对应的比特位作为信息比特位，可以选第2、3行，这种方式下编码端较简易些。若按照离最大行重对应的行最近的两行来确定信息比特位，比如这里行重最大的是第8行，则在第2、3、5行中选择第3、5行，这种方式下数据更为集中，较为有利于译码。
编码方法三：RM-Polar码编码方式。
RM-Polar码的构造流程如下：获取N×N的生成矩阵G，
Figure PCTCN2020126836-appb-000018
生成矩阵G的N行一一对应于N个比特位。N个比特位一一对应于N个极化信道。按照N个极化信道可靠度的排序，以及按照每个比特位对应的生成矩阵中的行重，确定K个信息比特位。按照N个极化信道可靠度由大到小的顺序，且按照生成矩阵的行重由大到小的顺序，确定K个信息比特位。其中，极化信道的可靠度排序可以按照Bhattacharyya参数由小到大排序，或者按照信道容量由大到小排序，或者，按照极化信道的归一化可靠度或等效可靠度排序。
在第一种可能的实施方式中，以N个极化信道可靠度由大到小的顺序为主要参考因素，以生成矩阵的行重由大到小的顺序为辅助参考因素，确定K个信息比特位。
可以选择可靠度按从大到小的排序方式时排序靠前的极化信道、且重量不低于第一阈值的极化码生成矩阵的行，对应的比特位作为K个信息比特位。即可以选择极化信道的可靠度排序靠前且行重不低于第一阈值的比特位作为信息比特位。其余比特位作为固定比特位。
可以按照N个极化信道可靠度由大到小的顺序选择K个极化信道对应的K个信息比特位，判断该K个信息比特位对应的生成矩阵中的K行是否行重均大于或等于第一阈值，若是，则确定该K个信息比特位。否则按照下述过程确定K个信息比特位。若在所选择的K个信息比特位对应的生成矩阵中K行中，有K1行的行重小于第一阈值，则除去所选择的K个信息比特位中该K1行所对应的K1个信息比特位，即可以确定(K-K1)个信息比 特位。并在N个极化信道中除去所选的K个极化信道之外的(N-K)个极化信道中，按照该(N-K)个极化信道的可靠度由大到小的顺序选择K1个极化信道对应的K1个信息比特位，判断该K1个信息比特位对应的生成矩阵中K1行是否行重均大于或等于第一阈值，若是，则将该K1个信息比特位与上述确定的(K-K1)个信息比特位，确定为K个信息比特位；否则：若在所选择的K1个信息比特位对应的生成矩阵中K1行中，有K2行的行重小于第一阈值，则除去所选择的K1个信息比特位中该K2行所对应的K2个信息比特位，即可以确定(K-K2)个信息比特位。并在N个极化信道中除去所选的(K+K1)个极化信道之外的(N-K-K1)个极化信道中，按照该(N-K-K1)个极化信道的可靠度由大到小的顺序选择K2个极化信道对应的K2个信息比特位，判断该K2个信息比特位对应的生成矩阵中K2行是否行重均大于或等于第一阈值，若是，则将该K2个信息比特位与上述确定的(K-K2)个信息比特位，确定为K个信息比特位；否则按照上述同理的操作执行，直到选择出K个信息比特位为止。
可以按照N个极化信道可靠度由大到小的顺序，依次选择极化信道，每选择一个极化信道，判断该极化信道对应的生成矩阵中的行的行重是否大于或等于第一阈值。若是则将该极化信道对应的比特位确定为信息比特位，否则将该极化信道对应的比特位确定为固定比特位。并继续选择下一个极化信道，按照相同的方法判断该极化信道对应的比特位为固定比特位还是信息比特位。直到确定出K个信息比特位，剩余未判断的比特位确定为固定比特位。
如图3所示，示出了(256,128)的RM-Polar码，即RM-Polar码的码长为256，信息比特序列长为128。横轴表示按照可靠性由高到低排序获得的排序序列的序号，排序序列的序号对应极化码的极化信道的序号，也对应比特位置。纵轴表示生成矩阵中每一行的行重。中间的实线竖线左侧代表极化信道可靠性较高的128个比特位，右边代表信道可靠性较低的128个比特位。若按照极化信道可靠性高低来确定K个信息比特位，则选定实线竖线左侧的128个比特位即可。当结合行重来选择信息比特位时，还需要参考行重是否不低于阈值。假设设定的阈值为16，由图3可以看出，靠近实线竖线左侧存在两个比特位对应行重小于16。因此这两个比特位将不会被选为该RM-polar码的信息比特位,可以选择离实线竖线右侧最近的两个对应行重大于或等于16比特位，作为两个信息比特位，以代替行重小于16的两个比特位。
在第二个可能的实施方式中，以生成矩阵的行重由大到小的顺序为主要参考因素，以N个极化信道可靠度由大到小的顺序为辅助参考因素，确定K个信息比特位。
选择极化码生成矩阵中行重由大到小排序靠前的行，且极化信道的可靠度排序不低于第二阈值的极化信道，对应的比特位作为K个信息比特位。即可以选择生成矩阵中行重大小排序靠前且极化信道的可靠度排序不低于第二阈值的比特位，作为信息比特位，其余比特位为固定比特位。
可以按照生成矩阵的N行中各行的行重由大到小的顺序，选择K行对应的K个信息比特位。若已选择(K-K0)个信息比特，在按照行重排序选择第(K-K0+1)到第K个信息比特时，存在大于K0的X个行(X>K0)的行重相同。则可以在该X个行中选择对应的极化信道可靠度从高到低依次排列的前K0行，将这K0行对应的比特位作为第(K-K0+1)个到第K个信息比特位。例如：若已选择(K-1)信息比特，在按照行重排序选择第K个信息比特时，存在多个行的行重相同。则可以在该多个行重选择对应的极化信道可靠度最 高的行，将该行对应的比特位作为第K个信息比特位。类似的，若已选择(K-2)信息比特，在按照行重排序选择第K-1个和第K个信息比特时，存在大于2的多个行的行重相同。则可以在该多个行重选择对应的极化信道可靠度最高和次高的行，将这两行对应的比特位作为第K-1个和第K个信息比特位。依次类推。
生成矩阵G为：
Figure PCTCN2020126836-appb-000019
在生成矩阵G中，第1行到第8行的行重分别为1、2、2、4、2、4、4、8。第8行的行重最大，第4、6、7行的行重次之，第2、3、5行的行重第三，第1行的行重最小。按照行重从大到小排序为8、(4、6、7)、(2、3、5)、1。
假设K＝6，即选择6个信息比特位。可以选择行重从大到小排序，先选择第8、4、6、7行对应的比特位作为4个信息比特位。还需要选择2个信息比特位，可以按照第(2、3、5)行对应的极化信道的可靠度排序，选择可靠度排序最高和次高的两行对应的比特位作为信息比特位。
在另一个可能的实施方式中，选择生成矩阵行重靠前且极化信道可靠度排序不低于第二阈值的比特位作为信息比特位，其余比特位作为固定比特位。
Polar能够从理论上证明，当码长趋于无限时(N→∞)能够“达到”信道容量，但是在许多实际的场景中，码长并不是无限的，因此性能受限。本申请实施例提供的方法能够有助于提高有限码长下Polar码的性能。
如图4所示，本申请实施例提供的一种极化码编码方法具体流程如下所述。
S401、获取K个待编码的信息比特。
K为正整数。例如K＝1、2、3……。
S402、根据K个待编码的信息比特，确定第一比特序列。
其中，第一比特序列的长度为N，N为2的正整数次幂，第一比特序列包括固定比特和K个待编码的信息比特。K个待编码的信息比特可以简述为K个信息比特。
N可以是极化码的母码长度。K小于等于N。在根据K个信息比特确定第一比特序列时，可以先确定K个信息比特位，信息比特位即N长的序列中用于放置或映射信息比特的位置。N长的序列中除去用于放置信息比特的位置的其余位置，为固定比特位，即用于放置或映射固定比特的位置。固定比特一般为0。将K个信息比特映射到K个信息比特位，或者将K个信息比特放置到N长的序列中的K个信息比特位，其余位置设为固定比特，即可获得第一比特序列。N长的序列用于表征N个比特位置。例如N＝8，K＝4。(K＝4)个信息比特为{i 1,i 2,i 3,i 4}，N长的序列包括8个比特位，{u 1,u 2,u 3,u 5}为固定比特的位置，{u 4,u 6,u 7,u 8}为信息比特的位置。则N长的序列为(0，0，0，U 4，0，U 6，U 7，U 8)。第一比特序列为(0，0，0，i 1，0，i 2，i 3，i 4)。或者，第一比特序列也可以用N长的序列(0，0，0，U 4，0，U 6，U 7，U 8)来表示，表征序号为4、6、7和8的位置为信息比特位，放置信息比特，其余比特放置固定比特。
S403、根据第一比特序列和上三角矩阵，确定第二比特序列。
其中，上三角矩阵为N行N列的矩阵。上三角矩阵可以是任意的上三角矩阵。
第一比特序列为大小为N的向量，包括信息比特和固定比特。可选的，可以将第一比特序列与上三角矩阵相乘，获得第二比特序列。第二比特序列的长度为N。
S404、对第二比特序列进行极化码编码，得到并输出编码后的序列。
例如，可以将第二比特序列与生成矩阵相乘，得到编码后的序列，输出编码后的序列，完成编码过程。第二比特序列的长度为N，生成矩阵的大小为N×N，编码后的序列的长度为N。
以下举例说明根据第一比特序列和上三角矩阵确定第二比特序列，并根据第二比特序列得到编码后的序列的过程。第一比特序列可以用V表示，第二比特序列用U表示，上三角矩阵用T表示。若第二比特序列为第一比特序列和上三角矩阵的乘积，则表示为U＝VT。编码后的序列用X表示，若第二比特序列和生成矩阵G相乘得到X，则表示为X＝UG。将U＝VT代入，得到X＝VTG。
参照S402的例子，仍以N＝8，K＝4，第一比特序列V＝(0，0，0，U 4，0，U 6，U 7，U 8)为例。生成矩阵G为：
Figure PCTCN2020126836-appb-000020
上三角矩阵T可以是任意上三角矩阵。举例来说，
Figure PCTCN2020126836-appb-000021
Figure PCTCN2020126836-appb-000022
其中，V为1×8的行向量，在公式表示中用8×1的列向量的转置来表示该行向量。
上三角矩阵T也可以是上三角Toeplitz矩阵。Toeplitz矩阵通常也可以称为卷积操作矩阵。
以下给出一个上三角Toeplitz矩阵的例子。
Figure PCTCN2020126836-appb-000023
上三角Toeplitz矩阵的该举例具有以下特征：第i+1行为第i行向右平移一位，对角线上的元素相同，i＝0、1、2……(N-1)或者，i＝1、2……N。
则编码后的序列
Figure PCTCN2020126836-appb-000024
通过在编码过程中增加上三角矩阵的构造方法，即相比于现有码字的构造方法，本申请实施例在V和G之间，增加上三角矩阵T，这样能够提升码谱，优化码的构造，进一步提高有限码长下Polar码的性能。
本申请实施例中，第一比特序列中包括K个信息比特和(N-K)个固定比特。在确定第一比特序列时，需要确定K个信息比特的位置，并将K个待编码的信息比特映射到K个信息比特位，从而得到该第一比特序列。将K个信息比特映射到K个信息比特位之后，其余位置必然为固定比特位，用于放置固定比特。也可以说，在确定第一比特序列时，需要确定K个信息比特位之外的(N-K)个位置为固定比特位，并将(N-K)个固定比特映射到(N-K)个固定比特位。
如何确定K个信息比特位，以确定第一比特序列，本申请实施例可以提供一些可能的实现方式。
N长的序列表征N个比特位，包括信息比特位和固定比特位。N个比特位中的信息比特位确定了第一比特序列中哪些位置放置信息比特；N个比特位中的固定比特位确定了第一比特序列中哪些位置放置固定比特。极化码N个极化信道与N个比特位一一对应。极化信道的可靠度越高，表征该极化信道对应的比特位越适合作为信息比特位。极化码生成矩阵的N行与N个比特位一一对应。极化码生成矩阵中一行的行重越大，表征该行对应的比特位越适合作为信息比特位。
实现方式1：根据极化码N个极化信道的可靠度排序和极化码生成矩阵的N行中每一行的重量，确定K个信息比特位。
实现方式1确定K个信息比特位的方法可以参照上述编码方式三中确定K个信息比特位的方法。
在实现方式1中，需要结合N个极化信道的可靠度排序和极化码生成矩阵的N行中每一行的重量，这两方面的考量，来确定K个信息比特位。可以以N个极化信道可靠度由大到小的顺序为主要参考因素，以生成矩阵的行重由大到小的顺序为辅助参考因素，确定K个信息比特位。也可以以生成矩阵的行重由大到小的顺序为主要参考因素，以N个极化信道可靠度由大到小的顺序为辅助参考因素，确定K个信息比特位。
N个比特位除K个信息比特位之外的位置为固定比特位。在所选择的K个信息比特位映射K个信息比特，其余位置为0。或者在所选择的K个信息比特位映射K个信息比特，其余位置置为0，在固定比特位映射固定比特。从而确定第一比特序列。
实现方式2：按照极化码N个极化信道的可靠度由高到低的顺序，确定K个信息比特位。
实现方式2中，不考虑极化码生成矩阵的行重，而是从极化信道的可靠度排序考量，来确定K个信息比特位。极化码N个极化信道与N个比特位一一对应，极化信道的可靠度越高，越适合被选择为信息比特位。可以按照N个极化信道的可靠度由高到低的顺序， 选择K个可靠度排序靠前的极化信道，确定该K个极化信道对应的K个信息比特位。
实现方式3：根据极化码生成矩阵的N行中每一行的重量，确定K个信息比特位。
实现方式3确定K个信息比特位的方法可以参照上述编码方式二中确定K个信息比特位的方法。
实现方式3中，不考虑极化码N个极化信道的可靠度的排序，而是从N行的行重考量，来确定K个信息比特位。极化码生成矩阵N行与N个比特位一一对应，生成矩阵中一行的行重越高，越适合被选择为信息比特位。可以按照生成矩阵N行的行重由高到低的顺序，选择K个极化信道，确定该K个极化信道对应的K个信息比特位。
本申请实施例中，确定第一比特序列的方法或者确定K个信息比特位的方法，还可以有其它方法，对此不作限定。
本申请实施例中，上述待编码的信息比特可以包括校验比特。例如，K个待编码的信息比特包括K1个第一信息比特和K2个校验比特。编码设备首先获取K1个信息比特，对K1个信息比特进行校验编码，获得K2个校验比特。本申请实施例中的校验编码方式可以是循环冗余校验(cyclic redundancy check，CRC)编码，也可能是奇偶校验(parity check，PC)编码，也可以是CRC和PC结合的校验编码方式。例如可以对K1个第一信息比特进行CRC编码，获得K2个CRC校验比特。又例如，例如可以对K1个第一信息比特进行PC编码，获得K2个PC校验比特。又例如，例如可以对K1个第一信息比特先进行CRC编码再进行PC编码，获得K2个校验比特。又例如，例如可以对K1个第一信息比特先进行PC校验编码再进行CRC编码，获得K2个校验比特。当待编码的信息比特中包括校验比特时，译码设备能够使用预先给定的校验关系译码，提高译码性能。
举例来说，校验编码采用CRC校验编码，N＝512，K1＝256。CRC生成多项式为：g(x)＝x 8+x 2+x+1＝[1 0 0 0 0 0 1 1 1]。由此可知，K1个第一信息比特通过CRC编码后，将会附加8个CRC校验比特，这8个CRC校验比特即为K1个第一信息比特序列除以对应的CRC生成多项式后得到的余数，表示为：[p 1,p 2,p 3,p 4,p 5,p 6,p 7,p 8]。即K个待编码的信息比特包括256个第一信息比特和8个CRC校验比特，K＝256+8＝264。在确定第一比特序列时，需要在N个比特位中选择256+8＝264个比特位作为信息比特位，信息比特位中包括CRC校验比特位。
当本申请实施例提供的极化码编码方法应用于RM-polar码时，可以将码字称为变化的RM-polar码(transformed RM-Polar，T-RM-Polar)码。当本申请实施例提供的极化码编码方法应用于polar码时，可以将码字称为变化的polar码(transformed Polar，T-Polar)码。
下面通过图5～图7给出几种码字的性能对比仿真图的示例，这几个仿真图为表示性能增益的示例性的图，本申请实施例的方法不局限于这几个举例所采用的译码器和参数。实际应用中，可以通过本申请实施例提供的方法得到性能增益更好的码字。
图5示出了几种码字的性能对比的仿真图。包括按照编码方法一构造的传统的极化码(Polar码)、T-Polar码、按照编码方法一构造的RM-polar码、T-RM-Polar码。N＝256，K＝128。横坐标为信噪比(Eb/No)，纵坐标为误帧率(frame error rate，FER)。采用逐次消除列表算法(successive cancellation list，SCL)且列表大小(list size)＝32的译码器译码。
从图5可以看出，在码长N＝256，码率R＝1/2参数设置下，相比于按照编码方法三构造的RM-polar码，T-RM-Polar码有0.3dB的性能增益。
RM-polar码在构造时综合考虑极化信道可靠性和生成矩阵行重，这样会带来更进一步 的增益。从图5可以看出，相比于T-Polar码，T-RM-Polar码有0.8dB的性能增益。
从图5可以看出，相比于按照编码方法一构造的Polar码，T-RM-Polar码带来了近1dB的增益，有效提高了有限码长下Polar码的性能。
图6示出了几种码字的性能对比。包括按照编码方法一构造的传统的极化码(Polar码)、T-Polar码、按照编码方法三构造的RM-polar码、T-RM-Polar码。N＝512，K＝256，横坐标为信噪比，纵坐标为误帧率。
从图6可以看出，在码长N＝512，码率R＝1/2参数设置下，相比于按照编码方法三构造的RM-polar码，T-RM-Polar码有0.2dB的性能增益。
RM-polar码在构造时综合考虑极化信道可靠性和生成矩阵行重，这样会带来更进一步的增益。从图6可以看出，相比于T-Polar码，T-RM-Polar码有0.5dB的性能增益。
从图6可以看出，相比于按照编码方法一构造的Polar码，T-RM-Polar码带来了近0.6dB的增益，有效提高了有限码长下Polar码的性能。
图7示出了几种码字的性能对比。包括按照编码方法三构造的RM-polar码、按照本申请实施例提供的上三角矩阵构造的码字T-RM-Polar码，按照上三角矩阵并且信息比特中包括校验比特的方式构造的码字记为CRC增强的转换RM-Polar码(CRC aided transformed RM-Polar，CA-T-RM-Polar)码。N＝512，K＝256，横坐标为信噪比，纵坐标为误帧率。
从图7可以看出，在码长N＝512，8bit CRC校验的参数设置下，相比于没有CRC校验的信息比特采用上三角矩阵构造的T-RM-Polar码，CA-T-RM-Polar码有0.4dB的性能增益。相比于按照编码方法三构造的RM-polar码，T-RM-Polar码有0.6dB的性能增益，更加接近了有限码长下的性能极限。
基于上述描述，如图8所示，本申请实施例还提供了一种极化码编码装置800，极化码编码装置800用于执行上述极化码编码方法，极化码编码装置800包括：
获取单元801，用于获取K个待编码的信息比特，K为正整数；
确定单元802，用于根据K个待编码的信息比特，确定第一比特序列，第一比特序列的长度为N，N为2的正整数次幂，第一比特序列包括固定比特和K个待编码的信息比特；
编码单元803，用于根据第一比特序列和上三角矩阵，确定第二比特序列，上三角矩阵为N行N列的矩阵；以及用于对第二比特序列进行极化码编码，得到并输出编码后的序列。
上三角矩阵为上三角Toeplitz矩阵。
可选的，确定单元802用于：根据极化码N个极化信道的可靠度排序和极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，其中，极化码生成矩阵为N行N列的矩阵，极化码生成矩阵的N行一一对应于第一比特序列的N个比特位，N个极化信道一一对应于第一比特序列的N个比特位；将K个待编码的信息比特映射到K个信息比特位，得到第一比特序列。
可选的，确定单元802用于：选择可靠度按从大到小的排序方式时排序靠前的极化信道、且重量不低于第一阈值的极化码生成矩阵的行，对应的比特位作为K个信息比特位。
可选的，确定单元802用于：选择极化码生成矩阵中行重由大到小排序靠前的行，且极化信道的可靠度排序不低于第二阈值的极化信道，对应的比特位作为K个信息比特位。
可选的，确定单元802用于：根据极化码N个极化信道去除速率匹配相关的极化信道的可靠度排序，和根据极化码生成矩阵的N行去除速率匹配相关的行之后的每一行的重量， 确定K个信息比特位。可选的，速率匹配相关的极化信道包括打孔、缩短或预冻结的极化信道，速率匹配相关的行包括打孔、缩短或预冻结的极化信道对应的行。
可选的，确定单元802用于：按照极化码N个极化信道的可靠度由高到低的顺序，确定K个信息比特位，其中，N个极化信道一一对应于第一比特序列的N个比特位；将K个待编码的信息比特映射到K个信息比特位，得到第一比特序列。
可选的，确定单元802用于：按照极化码N个极化信道去除速率匹配相关的极化信道的可靠度由高到低的顺序，确定K个信息比特位。可选的，速率匹配相关的极化信道包括打孔、缩短或预冻结的极化信道。
可选的，确定单元802用于：根据极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，其中，极化码生成矩阵为N行N列的矩阵，极化码生成矩阵的N行一一对应于第一比特序列的N个比特位；将K个待编码的信息比特映射到K个信息比特位，得到第一比特序列。
可选的，确定单元802用于，根据极化码生成矩阵的N行去除速率匹配相关的行之后的每一行的重量，确定K个信息比特位。可选的，速率匹配相关的行包括打孔、缩短或预冻结的极化信道对应的行。
可选的，编码单元803用于：将第一比特序列与上三角矩阵相乘，得到第二比特序列。
可选的，编码单元803用于：将第二比特序列与极化码生成矩阵相乘，得到编码后的序列。
可选的，信息比特包括校验比特。
如图9所示，本申请实施例中还提供一种极化码编码装置900，该极化码编码装置900可以用于执行上述极化码编码方法。上述极化码编码方法中的部分或全部可以通过硬件来实现也可以通过软件来实现，当通过硬件实现时，极化码编码装置900包括：输入接口电路901，用于获取K个待编码的信息比特；逻辑电路902，用于执行上述极化码编码方法中除获取待编码的比特和输出编码后比特的其它操作，具体请见前面方法实施例中的描述，此处不再赘述；输出接口电路903，用于输出编码后的序列。
可选的，极化码编码装置900在具体实现时可以是芯片或者集成电路。
可选的，当上述实施例的极化码编码方法中的部分或全部通过软件来实现时，如图10所示，极化码编码装置900包括：存储器1001，用于存储程序；处理器1002，用于执行存储器1001存储的程序，当程序被执行时，使得极化码编码装置900可以实现上述实施例提供的极化码编码方法。
可选的，上述存储器1001可以是物理上独立的单元，也可以存储器1001与处理器1002集成在一起。
可选的，当上述极化码编码方法中的部分或全部通过软件实现时，极化码编码装置900也可以只包括处理器1002。用于存储程序的存储器1001位于极化码编码装置900之外，处理器1002通过电路/电线与存储器1001连接，用于读取并执行存储器1001中存储的程序。
处理器1002可以是中央处理器(central processing unit，CPU)，网络处理器(network processor，NP)或者CPU和NP的组合。
处理器1002还可以进一步包括硬件芯片。上述硬件芯片可以是专用集成电路(application-specific integrated circuit，ASIC)，可编程逻辑器件(programmable logic device， PLD)或其组合。上述PLD可以是复杂可编程逻辑器件(complex programmable logic device，CPLD)，现场可编程逻辑门阵列(field-programmable gate array，FPGA)，通用阵列逻辑(generic array logic,GAL)或其任意组合。
存储器1001可以包括易失性存储器(volatile memory)，例如随机存取存储器(random-access memory，RAM)；存储器1001也可以包括非易失性存储器(non-volatile memory)，例如快闪存储器(flash memory)，硬盘(hard disk drive，HDD)或固态硬盘(solid-state drive，SSD)；存储器1001还可以包括上述种类的存储器的组合。
极化码编码装置900还可以是芯片、集成电路或者芯片系统。
本申请实施例还可提供一种芯片，包括处理器，用于支持该极化码编码装置900实现上述方法实施例中所涉及的功能。在一种可能的设计中，该芯片与存储器连接或者该芯片包括存储器，该存储器用于保存该极化码编码装置900必要的程序指令和数据。
本申请实施例提供了一种计算机可读存储介质，存储有计算机程序，该计算机程序包括用于执行上述方法实施例的指令。
本申请实施例提供了一种包含指令的计算机程序产品，当其在计算机上运行时，使得计算机执行上述方法实施例。
本领域内的技术人员应明白，本申请的实施例可提供为方法、系统、或计算机程序产品。因此，本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且，本申请可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。
本申请是参照根据本申请实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器，使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。
这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中，使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品，该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。
这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上，使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理，从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。
尽管已描述了本申请的优选实施例，但本领域内的技术人员一旦得知了基本创造性概念，则可对这些实施例作出另外的变更和修改。所以，所附权利要求意欲解释为包括优选实施例以及落入本申请范围的所有变更和修改。
显然，本领域的技术人员可以对本申请实施例进行各种改动和变型而不脱离本申请实施例的精神和范围。这样，倘若本申请实施例的这些修改和变型属于本申请权利要求及其 等同技术的范围之内，则本申请也意图包含这些改动和变型在内。

Claims (27)

  1. 一种极化码编码方法，其特征在于，包括：
    获取K个待编码的信息比特，K为正整数；
    根据所述K个待编码的信息比特，确定第一比特序列，所述第一比特序列的长度为N，N为2的正整数次幂，所述第一比特序列包括固定比特和所述K个待编码的信息比特；
    根据第一比特序列和上三角矩阵，确定第二比特序列，所述上三角矩阵为N行N列的矩阵；
    对所述第二比特序列进行极化码编码，得到并输出编码后的序列。
  2. 如权利要求1所述的方法，其特征在于，所述上三角矩阵为上三角Toeplitz矩阵。
  3. 如权利要求1或2所述的方法，其特征在于，根据所述K个待编码的信息比特，确定第一比特序列，包括：
    根据极化码N个极化信道的可靠度排序和极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，其中，所述极化码生成矩阵为N行N列的矩阵，所述极化码生成矩阵的N行一一对应于所述第一比特序列的N个比特位，所述N个极化信道一一对应于所述第一比特序列的N个比特位；
    将所述K个待编码的信息比特映射到所述K个信息比特位，得到所述第一比特序列。
  4. 如权利要求3所述的方法，其特征在于，根据极化码N个极化信道的可靠度排序和极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，包括：
    选择可靠度按从大到小的排序方式时排序靠前的极化信道、且重量不低于第一阈值的极化码生成矩阵的行，对应的比特位作为所述K个信息比特位。
  5. 如权利要求3所述的方法，其特征在于，根据极化码N个极化信道的可靠度排序和极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，包括：
    选择极化码生成矩阵中行重由大到小排序靠前的行，且极化信道的可靠度排序不低于第二阈值的极化信道，对应的比特位作为所述K个信息比特位。
  6. 如权利要求3～5任一项所述的方法，其特征在于，根据极化码N个极化信道的可靠度排序和极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，包括：
    根据极化码N个极化信道去除速率匹配相关的极化信道的可靠度排序，和根据极化码生成矩阵的N行去除速率匹配相关的行之后的每一行的重量，确定K个信息比特位，所述速率匹配相关的极化信道包括打孔、缩短或预冻结的极化信道，所述速率匹配相关的行包括打孔、缩短或预冻结的极化信道对应的行。
  7. 如权利要求1或2所述的方法，其特征在于，根据所述K个待编码的信息比特，确定第一比特序列，包括：
    按照极化码N个极化信道的可靠度由高到低的顺序，确定K个信息比特位，其中，所述N个极化信道一一对应于所述第一比特序列的N个比特位；
    将所述K个待编码的信息比特映射到所述K个信息比特位，得到所述第一比特序列。
  8. 如权利要求1或2所述的方法，其特征在于，根据所述K个待编码的信息比特，确定第一比特序列，包括：
    根据极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，其中，所述极化码生成矩阵为N行N列的矩阵，所述极化码生成矩阵的N行一一对应于所述第一比特序 列的N个比特位；
    将所述K个待编码的信息比特映射到所述K个信息比特位，得到所述第一比特序列。
  9. 如权利要求1～8任一项所述的方法，其特征在于，根据第一比特序列和上三角矩阵，确定第二比特序列，包括：
    将所述第一比特序列与所述上三角矩阵相乘，得到所述第二比特序列。
  10. 如权利要求1～9任一项所述的方法，其特征在于，对所述第二比特序列进行极化码编码，得到编码后的序列，包括：
    将所述第二比特序列与极化码生成矩阵相乘，得到所述编码后的序列。
  11. 如权利要求1～10任一项所述的方法，其特征在于，所述信息比特包括校验比特。
  12. 一种极化码编码装置，其特征在于，包括：
    获取单元，用于获取K个待编码的信息比特，K为正整数；
    确定单元，用于根据所述K个待编码的信息比特，确定第一比特序列，所述第一比特序列的长度为N，N为2的正整数次幂，所述第一比特序列包括固定比特和所述K个待编码的信息比特；
    编码单元，用于根据第一比特序列和上三角矩阵，确定第二比特序列，所述上三角矩阵为N行N列的矩阵；以及用于对所述第二比特序列进行极化码编码，得到并输出编码后的序列。
  13. 如权利要求12所述的装置，其特征在于，所述上三角矩阵为上三角Toeplitz矩阵。
  14. 如权利要求12或13所述的装置，其特征在于，所述确定单元用于：
    根据极化码N个极化信道的可靠度排序和极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，其中，所述极化码生成矩阵为N行N列的矩阵，所述极化码生成矩阵的N行一一对应于所述第一比特序列的N个比特位，所述N个极化信道一一对应于所述第一比特序列的N个比特位；
    将所述K个待编码的信息比特映射到所述K个信息比特位，得到所述第一比特序列。
  15. 如权利要求14所述的装置，其特征在于，所述确定单元用于：
    选择极化码生成矩阵中行重由大到小排序靠前的行，且极化信道的可靠度排序不低于第二阈值的极化信道，对应的比特位作为所述K个信息比特位。
  16. 如权利要求14所述的装置，其特征在于，所述确定单元用于：
    选择极化码生成矩阵中行重由大到小排序靠前的行，且极化信道的可靠度排序不低于第二阈值的极化信道，对应的比特位作为所述K个信息比特位。
  17. 如权利要求14～16任一项所述的装置，其特征在于，所述确定单元用于：
    根据极化码N个极化信道去除速率匹配相关的极化信道的可靠度排序，和根据极化码生成矩阵的N行去除速率匹配相关的行之后的每一行的重量，确定K个信息比特位，所述速率匹配相关的极化信道包括打孔、缩短或预冻结的极化信道，所述速率匹配相关的行包括打孔、缩短或预冻结的极化信道对应的行。
  18. 如权利要求12或13所述的装置，其特征在于，所述确定单元用于：
    按照极化码N个极化信道的可靠度由高到低的顺序，确定K个信息比特位，其中，所述N个极化信道一一对应于所述第一比特序列的N个比特位；
    将所述K个待编码的信息比特映射到所述K个信息比特位，得到所述第一比特序列。
  19. 如权利要求12或13所述的装置，其特征在于，所述确定单元用于：
    根据极化码生成矩阵的N行中每一行的重量，确定K个信息比特位，其中，所述极化码生成矩阵为N行N列的矩阵，所述极化码生成矩阵的N行一一对应于所述第一比特序列的N个比特位；
    将所述K个待编码的信息比特映射到所述K个信息比特位，得到所述第一比特序列。
  20. 如权利要求12～19任一项所述的装置，其特征在于，所述编码单元用于：
    将所述第一比特序列与所述上三角矩阵相乘，得到所述第二比特序列。
  21. 如权利要求12～20任一项所述的装置，其特征在于，所述编码单元用于：
    将所述第二比特序列与极化码生成矩阵相乘，得到所述编码后的序列。
  22. 如权利要求12～21任一项所述的装置，其特征在于，所述信息比特包括校验比特。
  23. 一种极化码编码装置，其特征在于，包括：
    输入接口电路，用于获取K个待编码的信息比特，K为正整数；
    逻辑电路，用于基于获取的K个待编码的信息比特执行所述权利要求1～11任一项所述的方法，得到编码后的序列；
    输出接口电路，用于输出编码后的序列。
  24. 一种极化码编码装置，其特征在于，包括：
    存储器，用于存储程序；
    处理器，用于执行所述存储器存储的所述程序，当所述程序被执行时，使得所述极化码编码装置执行如权利要求1～11任一项所述的方法。
  25. 如权利要求24所述的装置，其特征在于，所述处理器包括所述存储器。
  26. 如权利要求24或25所述的装置，其特征在于，所述极化码编码装置为芯片或集成电路。
  27. 一种计算机可读存储介质，其特征在于，所述计算机可读存储介质中存储有计算机可读指令，当所述计算机可读指令在极化码编码装置上运行时，使得所述极化码编码装置执行权利要求1～11任一项所述的方法。
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