WO2021208244A1 - 一种列表极化码传播译码方法 - Google Patents

一种列表极化码传播译码方法 Download PDF

Info

Publication number
WO2021208244A1
WO2021208244A1 PCT/CN2020/098758 CN2020098758W WO2021208244A1 WO 2021208244 A1 WO2021208244 A1 WO 2021208244A1 CN 2020098758 W CN2020098758 W CN 2020098758W WO 2021208244 A1 WO2021208244 A1 WO 2021208244A1
Authority
WO
WIPO (PCT)
Prior art keywords
flipped
decoding
estimated
matrix
estimated codeword
Prior art date
Application number
PCT/CN2020/098758
Other languages
English (en)
French (fr)
Inventor
张建勇
Original Assignee
北京交通大学
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 北京交通大学 filed Critical 北京交通大学
Publication of WO2021208244A1 publication Critical patent/WO2021208244A1/zh

Links

Images

Classifications

    • HELECTRICITY
    • H03ELECTRONIC CIRCUITRY
    • H03MCODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00Coding, 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
    • H03M13/03Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05Error 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
    • H03M13/13Linear codes

Definitions

  • the present invention relates to the technical field of decoding algorithms for polarization codes, and in particular to a method for broadcasting and decoding list polarization codes.
  • Polar code is a forward error correction coding method used for signal transmission.
  • the core of the polarization code is through channel polarization processing, and the method is adopted on the coding side to make each sub-channel show different reliability.
  • some channels will tend to be perfect channels with a capacity close to 1 (error-free code). ), another part of the channel tends to be a pure noise channel with a capacity close to 0.
  • Choosing to directly transmit information on a channel with a capacity close to 1 to approach the channel capacity is the only method that can be strictly proven to reach the Shannon limit.
  • the decoding algorithms of polarization codes mainly include SC (Successive Cancellation, serial cancellation) decoding algorithm, maximum likelihood decoding algorithm, linear programming decoding algorithm and belief propagation decoding algorithm.
  • SC decoding algorithm has the lowest complexity, and it has been proved that the polarization code can reach the Shannon limit under the SCL (Successive Cancellation List) decoding algorithm.
  • SCL and SC algorithms have high complexity, high latency and low parallelism.
  • the BP algorithm based on belief propagation has high parallelism, its performance is poor.
  • the prior art BP decoder based on key set bit flipping uses the prior knowledge of unreliable information bits to further reduce the block error rate. By analyzing the bit error rate distribution of the polarization code, the set CS of unreliable bits is identified. In the decoding process, the BFBP-CS algorithm uses cyclic redundancy check to detect block errors. If the traditional BP decoding fails, the received information in CS is set to a preset value, and then BP decoding is used to find the CRC. The code word to be checked.
  • the disadvantage of the above-mentioned prior art BP decoder based on bit flipping of the key set is that the BFBP-CS algorithm has an error leveling phenomenon in the decoder in the high signal-to-noise ratio (SNR) region, and the performance is poor.
  • SNR signal-to-noise ratio
  • the embodiment of the present invention provides a list polarization code propagation decoding method to overcome the problems of the prior art.
  • the present invention adopts the following technical solutions.
  • a list polarization code propagation decoding method including:
  • T m BP-MF-MC(llr, A, ⁇ , ⁇ , S1, S2, F m ) (2)
  • G is the generator matrix
  • the size is (N, N).
  • is 2-norm.
  • the process of decoding the received signal by each BP-MF-MC algorithm includes:
  • the S1 and S2 contain multiple check conditions for the estimated codeword after decoding:
  • the decoder outputs The process ends; otherwise, the set of flipped bits is flipped and decoded using the real number matrix to obtain the flipped estimated codeword set u, and the estimated codeword set u is obtained according to the principle of maximum likelihood. And flip the estimated codeword set u to select the optimal estimated codeword, the decoder outputs the optimal estimated codeword, and the process ends.
  • the set of set check conditions S1 and S2, where S1 and S2 contain multiple check conditions for the estimated codeword after decoding include:
  • the S1 and S2 contain multiple check conditions for the estimated codeword after decoding. S1 and S2 have no intersection.
  • the selection principle of S1 and S2 is that the missed detection rate is the lowest.
  • the log-likelihood ratio of the received signal to be decoded is calculated, and the BP algorithm is used to decode the real number matrix storing the log-likelihood ratio to obtain the estimated codeword include:
  • the received signal to be decoded is a vector of length N
  • llr is the signal to be decoded
  • A is the information bit position of the polarization code
  • a c is the freezing bit position of the polarization code
  • L and R are a real matrix with a size of (N,log2(N)+1), which is the belief propagation algorithm of the polarization code
  • the matrix storing the log-likelihood ratio llr in, L and R are initialized with the following formula:
  • R i,0 represents the element at the position (i,0) in the R matrix
  • Li,0 represents the element at the position (i,0) in the L matrix
  • the matrix L and R are initialized, and the BP algorithm is used to decode L and R to obtain the decoded estimated codeword
  • the set of flipped bits is flipped and decoded by using the real number matrix to obtain the flipped estimated codeword set u, and the estimated codeword set u is obtained according to the principle of maximum likelihood.
  • the decoder outputs the optimal estimated codeword, and the process ends, including:
  • Set ⁇ as a sequence of flipped bits, containing n ⁇ sets of flipped bits, namely ⁇ is a sequence of flipped bits, containing n ⁇ sets of flipped bits, namely
  • the process of flipping and decoding BFBP() includes: Is an element in the set of flipped bits ⁇ n, Is a vector of length ⁇ , which represents the position of the flipped bit, Is a vector of length ⁇ , which represents the value corresponding to the flipped bit, let j l be The l th element in It is the (j l ,1)th element in the matrix R. Each element of the flipped bit set ⁇ n is traversed through the function BFBP().
  • G is the generator matrix, the size is (N, N),
  • Decoder output The process ends.
  • the set of flipped bits is flipped and decoded by using the real number matrix to obtain the flipped estimated codeword set u, and the estimated codeword set u is obtained according to the principle of maximum likelihood. And flip the estimated codeword set u to select the optimal estimated codeword, the decoder outputs the optimal estimated codeword , and the process ends, including:
  • the processing process of the flipping decoding function BFBP() includes: Is an element in the flipped bit set ⁇ n, Is a vector of length ⁇ , which represents the position of the flipped bit, Is a vector of length ⁇ , which represents the value corresponding to the flipped bit, Is the (j l ,1)th element in the R matrix.
  • Each element of the flipped bit set ⁇ n is traversed through the function BFBP(). After initializing L and R, use Assign a value to the first column in R and use the BP decoder for decoding. If the output of the BP decoder is If the check condition S1 is met, the traversal is terminated, and the output
  • n ⁇ estimated codewords After flipping and decoding the set of n ⁇ flipped bits in ⁇ , BFBP(), n ⁇ estimated codewords are obtained All estimated codewords form an estimated codeword set u, According to the principle of maximum likelihood, from the set of n ⁇ +1 estimated codewords Select the best estimated codeword, as shown in the following formula:
  • Decoder output The process ends.
  • the various processing procedures in the decoding method of the embodiments of the present invention can be implemented in parallel.
  • the computational complexity at high signal-to-noise ratios can be less than that of the list.
  • the decoding algorithm is eliminated successively, and the performance is close.
  • the embodiment of the present invention can eliminate the error leveling phenomenon of the (BFBP) decoder.
  • FIG. 1 is a processing flowchart of a list polarization code propagation decoding method provided by an embodiment of the present invention
  • Fig. 2 is a processing flowchart of each BP-MF-MC algorithm provided by an embodiment of the present invention.
  • the BP (Error Back Propagation) algorithm is a currently published decoding algorithm.
  • the embodiment of the present invention proposes a list polarization code propagation decoding method based on the BP algorithm.
  • the factor graph F is a factor graph used by the existing list BP algorithm (BPL), which can be randomly generated.
  • llr the signal to be decoded
  • A is the information bit position of the polarization code
  • a c is the freezing bit position of the polarization code
  • L and R are a real matrix with a size of (N,log2(N)+1), which is the belief propagation algorithm of the polarization code
  • the matrix storing the log-likelihood ratio llr in, L and R are initialized with the following formula:
  • R i,0 represents the element at the position (i,0) in the R matrix
  • Li,0 represents the element at the position (i,0) in the L matrix.
  • BP .,.,.,.
  • CRC Cyclic Redundancy Check
  • S1 and S2 are the pre-check condition set, including the The multiple check conditions can be CRC, LDPC and other check methods. S1 and S2 have no intersection. The selection principle of S1 and S2 is to make the missed detection rate the lowest, S1 can be CRC check, and S2 can be the generator matrix check method.
  • is the sequence of flipped bits, containing n ⁇ sets of flipped bits, namely ⁇ is a sequence of flipped bits, containing n ⁇ sets of flipped bits, namely The set of flipped bits can be a key bit sequence set CS of order n, or can be frozen bits Ac , or all information bits A.
  • can be ⁇ CS1 ⁇ and ⁇ is ⁇ CS3, A ⁇ .
  • the processing flow of the list polarization code propagation decoding algorithm commissioned by the embodiment of the present invention is shown in Fig. 1, and includes the following processing steps: M BP-MF-MC algorithms are simultaneously activated for decoding, and each BP-MF-MC
  • the factor graph used by the algorithm is F m
  • the set of decoding output results of M BP-MF-MC algorithms is T.
  • the decoding result of the BP-MF-MC algorithm corresponding to the m-th factor graph F m is T m , namely
  • T m BP-MF-MC(llr, A, ⁇ , ⁇ , S1, S2, F m ) (2)
  • G is the generator matrix, the size is (N, N).
  • is 2-norm.
  • Generator matrix Where F [1 0; 1 1], Represents log2(N) times kronecker power.
  • FIG. 2 The processing flow of each BP-MF-MC algorithm in the embodiment of the present invention is shown in Fig. 2, and includes the following processing steps:
  • Step S1 first initialize the matrix L and R according to the above formula (1), and then use the traditional BP algorithm to decode L and R to obtain the decoded estimated codeword
  • Step S2 if Meet all the verification conditions in S1 and S2, it can be considered For the correct codeword, the decoder outputs The process ends.
  • Step S2' if All the check conditions in S1 are met, but all check conditions in S2 are not met, and the set of n ⁇ flipped bits in ⁇ is flipped and decoded BFBP().
  • the process of flipping and decoding BFBP() includes: Is an element in the set of flipped bits ⁇ n, Is a vector of length ⁇ , which represents the position of the flipped bit, Is a vector of length ⁇ , which represents the value corresponding to the flipped bit, let j l be The l th element in Is the (j l ,1)th element in the R matrix.
  • G is the generator matrix
  • the size is (N, N).
  • is 2-norm.
  • Decoder output The process ends.
  • Step S2'' if all the check conditions in S1 are not satisfied, the flipping decoding BFBP() is performed on the set of n ⁇ flipped bits in ⁇ .
  • the processing process of the flipping decoding function BFBP() includes: To flip an element in the bit set ⁇ , Is a vector of length ⁇ , which represents the position of the flipped bit, Is a vector of length ⁇ , which represents the value corresponding to the flipped bit, Is the (j l ,1)th element in the R matrix. Use the function BFBP() to traverse each element of the flipped bit set ⁇ . After initializing L and R, use Assign a value to the first column in R, and then use the traditional BP decoder for decoding, if the output of BP decoding If the check condition S1 is met, the traversal is terminated, and the output
  • n ⁇ estimated codewords After flipping and decoding the set of n ⁇ flipped bits in ⁇ , BFBP(), n ⁇ estimated codewords are obtained All estimated codewords form an estimated codeword set u, According to the principle of maximum likelihood, from the set of n ⁇ +1 estimated codewords Select the best estimated codeword, as shown in the following formula:
  • Decoder output The process ends.
  • step S2 step S2' and step S2' can be executed in parallel.
  • Step 1 Start M BP-MF-MC for decoding at the same time, and the set of M decoding output results is T. Assume that the decoding result corresponding to the m-th factor graph F m in F is T m , namely
  • T m BP-MF-MC(llr, A, ⁇ , ⁇ , S1, S2, F m ) (6)
  • Step 2 Use the maximum likelihood method to select the best
  • Step 1 Use formula (1) to initialize L and R
  • Step 4 If Does not meet S2
  • Step 5 For all ⁇ i ⁇
  • Step 7 end for
  • Step 8 else
  • Step 11 for all ⁇ i ⁇
  • Step 13 end for
  • Step 14 end if
  • Step 15 According to formula (4) or formula (5), use the maximum likelihood method to select the best
  • Step 3 Use formula (1) to initialize L and R
  • Step 6 end for
  • Step 11 if Satisfy S
  • Step 15 end for.
  • the various processing procedures in the decoding method of the embodiment of the present invention can be implemented in parallel.
  • the computational complexity at high signal-to-noise ratio can be less than that of the list successive elimination decoding algorithm, and the performance is close.
  • the embodiment of the present invention can eliminate the error leveling phenomenon of the (BFBP) decoder, is a BP decoder with similar performance to the CRC-assisted SCL decoder (CA-SCL), and has high parallelism.
  • the embodiment of the present invention uses a list method to simultaneously start M BP-MF-MC algorithms for decoding, which can further reduce the error leveling phenomenon of the BP-MF-MC algorithm and reduce the minimum complexity of decoding.
  • the present invention can be implemented by means of software plus a necessary general hardware platform.
  • the technical solution of the present invention essentially or the part that contributes to the existing technology can be embodied in the form of a software product, and the computer software product can be stored in a storage medium, such as ROM/RAM, magnetic disk , CD-ROM, etc., including a number of instructions to make a computer device (which may be a personal computer, a server, or a network device, etc.) execute the methods described in the various embodiments or some parts of the embodiments of the present invention.

Landscapes

  • Physics & Mathematics (AREA)
  • Probability & Statistics with Applications (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Error Detection And Correction (AREA)

Abstract

本发明提供了一种列表极化码传播译码方法。包括:同时启动M个基于多翻转比特集合的极化码置信传播译码BP-MF-MC算法对接收信号进行译码,每个BP-MF-MC算法分别使用对应的因子图,M个BP-MF-MC算法的译码输出结果的集合为T,采用最大似然法从T中选出最佳的译码结果。本发明方法中的各种处理流程可以并行实现,在高信噪比时的计算复杂度可以小于列表逐次消除译码算法,性能接近。

Description

一种列表极化码传播译码方法 技术领域
本发明涉及极化码的译码算法技术领域,尤其涉及一种列表极化码传播译码方法。
背景技术
极化码(Polar code)是一种前向错误更正编码方式,用于讯号传输。极化码的核心是通过信道极化处理,在编码侧采用方法使各个子信道呈现出不同的可靠性,当码长持续增加时,部分信道将趋向于容量近于1的完美信道(无误码),另一部分信道趋向于容量接近于0的纯噪声信道,选择在容量接近于1的信道上直接传输信息以逼近信道容量,是目前唯一能够被严格证明可以达到香农极限的方法。
极化码一经提出,立刻受到了众多学者的关注,成为信息领域的研究热点。在信道编码方案中,极化码的编译码复杂度低,并且已经被严格证明能达到香农极限,因此,极化码具有极高的研究意义。在近些年的研究中,极化码的译码算法主要有SC(Successive Cancellation,串行抵消)译码算法、最大似然译码算法、线性规划译码算法及置信传播译码算法。其中,SC译码算法的复杂度最低,且被证明极化码在SCL(Successive Cancellation List,串行抵消列表))译码算法下可以达到香农极限。但SCL及SC算法复杂度高,且延迟大,并行度低。基于置信传播的BP算法虽然并行高,但是性能较差。
现有技术中的基于关键集的比特翻转的BP译码器(BFBP-CS)是利用了不可靠信息位的先验知识,来进一步降低误块率。通过分析极化码的误比特率的 分布,识别出不可靠比特的集合CS。在译码的过程中,BFBP-CS算法使用循环冗余校验来检测块错误,若传统BP译码失败,则将CS中的接收信息设置为预设值,然后采用BP译码寻找通过CRC校验的码字。
上述现有技术中的基于关键集的比特翻转的BP译码器的缺点为:BFBP-CS算法在解码器在高信噪比(SNR)区域具有出误差平层现象,性能较差。
发明内容
本发明的实施例提供了一种列表极化码传播译码方法,以克服现有技术的问题。
为了实现上述目的,本发明采取了如下技术方案。
一种列表极化码传播译码方法,包括:
同时启动M个基于多翻转比特集合的极化码置信传播译码BP-MF-MC算法对接收信号进行译码,每个BP-MF-MC算法所使用的因子图为F m,M个BP-MF-MC算法的译码输出结果的集合为T;
设第m个因子图F m对应的BP-MF-MC算法的译码结果为T m,即
T m=BP-MF-MC(llr,A,Φ,Ψ,S1,S2,F m)    (2)
采用最大似然法从T中选出最佳的
Figure PCTCN2020098758-appb-000001
Figure PCTCN2020098758-appb-000002
其中,G为生成矩阵,大小为(N,N)。||·||为2-范数。
优选地,每个BP-MF-MC算法对接收信号进行译码的过程包括:
设定校验条件集合S1、S2,该S1、S2中包含对译码后的估计码字的多个校验条件:
计算出待译码的接收信号的对数似然比,使用BP算法对存储所述对数似然比的实数矩阵进行译码,得到估计码字
Figure PCTCN2020098758-appb-000003
判断
Figure PCTCN2020098758-appb-000004
是否满足S1及S2中的所有校验条件,如果是,则确定
Figure PCTCN2020098758-appb-000005
为正确码字,译码器输出
Figure PCTCN2020098758-appb-000006
流程结束;否则,利用所述实数矩阵对设定的翻转比特集合进行翻转译码后得到翻转估计码字集合u,按照最大似然原则,从所述估计码字
Figure PCTCN2020098758-appb-000007
和翻转估计码字集合u中选出最优估计码字,译码器输出最优估计码字,流程结束。
优选地,所述的设定校验条件集合S1、S2,该S1、S2中包含对译码后的估计码字的多个校验条件,包括:
预先设定校验条件集合S1、S2,该S1、S2中包含对译码后的估计码字的多个校验条件,S1与S2无交集,S1和S2的选取原则为漏检率最低。
优选地,所述的计算出待译码的接收信号的对数似然比,使用BP算法对存储所述对数似然比的实数矩阵进行译码,得到估计码字
Figure PCTCN2020098758-appb-000008
包括:
Figure PCTCN2020098758-appb-000009
为待译码的接收信号,为一长度为N的一个向量,llr为待译码信号
Figure PCTCN2020098758-appb-000010
的对数似然比,为一长度为N的一个向量,即llr i=p(y i|0)/p(y i|1),其中,llr i为llr中第i个元素,y i
Figure PCTCN2020098758-appb-000011
中第i个元素,p(y i|0)为输入为0时的条件概率,p(y i|1)为输入为1时的条件概率;
A是极化码的信息比特位置,A c是极化码的冻结比特位置,L与R为一实数矩阵,其大小为(N,log2(N)+1),是极化码置信传播算法中存储对数似然比llr的矩阵,L和R采用如下公式初始化:
Figure PCTCN2020098758-appb-000012
其中,R i,0表示R矩阵中位置为(i,0)的元素,L i,0表示L矩阵中位置为(i,0)的元素;
按照上述公式(1)对矩阵L及R进行初始化,使用BP算法对L及R进行译 码,得到译码的估计码字
Figure PCTCN2020098758-appb-000013
优选地,所述的利用所述实数矩阵对设定的翻转比特集合进行翻转译码后得到翻转估计码字集合u,按照最大似然原则,从所述估计码字
Figure PCTCN2020098758-appb-000014
和翻转估计码字集合u中选出最优估计码字,译码器输出最优估计码字,流程结束,包括:
设定Φ为翻转比特序列,含有n φ个翻转比特集合,即
Figure PCTCN2020098758-appb-000015
Ψ为翻转比特序列,含有n ψ个翻转比特集合,即
Figure PCTCN2020098758-appb-000016
如果估计码字
Figure PCTCN2020098758-appb-000017
满足S1中的所有校验条件,但不满足S2中的所有校验条件,对Φ中n φ个翻转比特集合进行翻转译码BFBP(),该翻转译码BFBP()的处理过程包括:设
Figure PCTCN2020098758-appb-000018
为翻转比特集合φ n中的一个元素,
Figure PCTCN2020098758-appb-000019
为长度ω的向量,代表了翻转比特的位置,
Figure PCTCN2020098758-appb-000020
为长度ω的向量,代表了翻转比特对应的值,设j l
Figure PCTCN2020098758-appb-000021
中第l个元素,
Figure PCTCN2020098758-appb-000022
是矩阵R中第(j l,1)个元素,通过函数BFBP()对翻转比特集合φ n的每个元素进行遍历,在对L及R初始化后,使用
Figure PCTCN2020098758-appb-000023
对矩阵R中第1列进行赋值,使用BP译码器对赋值后的矩阵R进行译码,如果BP译码的输出
Figure PCTCN2020098758-appb-000024
满足校验条件S1,则遍历终止,输出
Figure PCTCN2020098758-appb-000025
对Φ中n φ个翻转比特集合进行翻转译码BFBP()后得到n φ个估计码字
Figure PCTCN2020098758-appb-000026
所有估计码字组成估计码字集合u,
Figure PCTCN2020098758-appb-000027
按照最大似然原则,从n φ+1个估计码字集合
Figure PCTCN2020098758-appb-000028
选出最优估计码字,如下式所示:
Figure PCTCN2020098758-appb-000029
其中,G为生成矩阵,大小为(N,N),||·||为2-范数;
译码器输出
Figure PCTCN2020098758-appb-000030
流程结束。
优选地,所述的利用所述实数矩阵对设定的翻转比特集合进行翻转译码后得到翻转估计码字集合u,按照最大似然原则,从所述估计码字
Figure PCTCN2020098758-appb-000031
和翻转估 计码字集合u中选出最优估计码字,译码器输出最优估计码字 流程结束,包括:
如果
Figure PCTCN2020098758-appb-000032
不满足S1中的所有校验条件,对Ψ中n ψ个翻转比特集合进行翻转译码BFBP(),该翻转译码函数BFBP()的处理过程包括:设
Figure PCTCN2020098758-appb-000033
为翻转比特集合ψ n,中的一个元素,
Figure PCTCN2020098758-appb-000034
为长度ω的向量,代表了翻转比特的位置,
Figure PCTCN2020098758-appb-000035
为长度ω的向量,代表了翻转比特对应的值,
Figure PCTCN2020098758-appb-000036
是R矩阵中第(j l,1)个元素,通过函数BFBP()对翻转比特集合ψ n,的每个元素进行遍历,在对L及R初始化后,使用
Figure PCTCN2020098758-appb-000037
对R中第1列进行赋值,使用BP译码器进行译码,如果BP译码的输出
Figure PCTCN2020098758-appb-000038
满足校验条件S1,则遍历终止,输出
Figure PCTCN2020098758-appb-000039
对Ψ中n φ个翻转比特集合进行翻转译码BFBP()后,得到n ψ个估计码字
Figure PCTCN2020098758-appb-000040
所有估计码字组成估计码字集合u,
Figure PCTCN2020098758-appb-000041
按照最大似然原则,从n ψ+1个估计码字集合
Figure PCTCN2020098758-appb-000042
选出最优估计码字,如下式所示:
Figure PCTCN2020098758-appb-000043
译码器输出
Figure PCTCN2020098758-appb-000044
流程结束。
由上述本发明的实施例提供的技术方案可以看出,本发明实施例的译码方法中的各种处理流程可以并行实现,通过本发明,在高信噪比时的计算复杂度可以小于列表逐次消除译码算法,性能接近。本发明实施例可以消除(BFBP)解码器的误码平层现象。
本发明附加的方面和优点将在下面的描述中部分给出,这些将从下面的描述中变得明显,或通过本发明的实践了解到。
附图说明
为了更清楚地说明本发明实施例的技术方案,下面将对实施例描述中所需要使用的附图作简单地介绍,显而易见地,下面描述中的附图仅仅是本发 明的一些实施例,对于本领域普通技术人员来讲,在不付出创造性劳动的前提下,还可以根据这些附图获得其他的附图。
图1为本发明实施例提供的一种列表极化码传播译码方法的处理流程图;
图2为本发明实施例提供的一种每个BP-MF-MC算法的处理流程图。
具体实施方式
下面详细描述本发明的实施方式,所述实施方式的示例在附图中示出,其中自始至终相同或类似的标号表示相同或类似的元件或具有相同或类似功能的元件。下面通过参考附图描述的实施方式是示例性的,仅用于解释本发明,而不能解释为对本发明的限制。
本技术领域技术人员可以理解,除非特意声明,这里使用的单数形式“一”、“一个”、“所述”和“该”也可包括复数形式。应该进一步理解的是,本发明的说明书中使用的措辞“包括”是指存在所述特征、整数、步骤、操作、元件和/或组件,但是并不排除存在或添加一个或多个其他特征、整数、步骤、操作、元件、组件和/或它们的组。应该理解,当我们称元件被“连接”或“耦接”到另一元件时,它可以直接连接或耦接到其他元件,或者也可以存在中间元件。此外,这里使用的“连接”或“耦接”可以包括无线连接或耦接。这里使用的措辞“和/或”包括一个或更多个相关联的列出项的任一单元和全部组合。
本技术领域技术人员可以理解,除非另外定义,这里使用的所有术语(包括技术术语和科学术语)具有与本发明所属领域中的普通技术人员的一般理解相同的意义。还应该理解的是,诸如通用字典中定义的那些术语应该被理解为具有与现有技术的上下文中的意义一致的意义,并且除非像这里一样定义,不会用理想化或过于正式的含义来解释。
为便于对本发明实施例的理解,下面将结合附图以几个具体实施例为例 做进一步的解释说明,且各个实施例并不构成对本发明实施例的限定。
BP(Error Back Propagation,误差反向传播)算法是目前一种已经公开的译码算法,本发明实施例基于BP算法提出了一种列表极化码传播译码方法。该方法含有M个BP-MF-MC(基于多翻转比特集合的极化码置信传播译码)算法,使用了F={F 1,...,F M}M个因子图。因子图F是已有的列表BP算法(BPL)使用的因子图,可以随机产生。
在该算法中,假定,
Figure PCTCN2020098758-appb-000045
为待译码的接收信号,为一长度为N的一个向量。llr为待译码信号
Figure PCTCN2020098758-appb-000046
的对数似然比,由
Figure PCTCN2020098758-appb-000047
计算出,为一长度为N的一个向量。即llr i=p(y i|0)/p(y i|1),其中,llr i为llr中第i个元素,y i
Figure PCTCN2020098758-appb-000048
中第i个元素,p(y i|0)为输入为0时的条件概率,p(y i|1)为输入为1时的条件概率。
A是极化码的信息比特位置,A c是极化码的冻结比特位置,L与R为一实数矩阵,其大小为(N,log2(N)+1),是极化码置信传播算法中存储对数似然比llr的矩阵,L和R采用如下公式初始化:
Figure PCTCN2020098758-appb-000049
其中,R i,0表示R矩阵中位置为(i,0)的元素,L i,0表示L矩阵中位置为(i,0)的元素。
Figure PCTCN2020098758-appb-000050
为本发明实施例的译码器的输出比特,长度为N。BP(.,.,.,.)为使用CRC(Cyclic Redundancy Check,循环冗余校验)校验作为停止条件的传统BP算法,其输出为
Figure PCTCN2020098758-appb-000051
长度为N,BFBP()参见算法2。S1,S2为预先校验条件集合,包含对
Figure PCTCN2020098758-appb-000052
的多个校验条件,可以为CRC,LDPC等校验方法。S1与S2无交集。S1和S2的选取原则是让漏检率最低,S1可以为CRC校验,S2可以为生成矩阵校验法。
Φ为翻转比特序列,含有n φ个翻转比特集合,即
Figure PCTCN2020098758-appb-000053
Ψ为翻转比 特序列,含有n ψ个翻转比特集合,即
Figure PCTCN2020098758-appb-000054
翻转比特集合可以为n阶关键比特序列集合CS,也可以是冻结比特A c,或全部信息比特A。例如,Φ可为{CS1},Ψ为{CS3,A}。
本发明实施例提成的列表极化码传播译码算法的处理流程如图1所示,包括如下的处理步骤:同时启动M个BP-MF-MC算法进行译码,每个BP-MF-MC算法所使用的因子图为F m,M个BP-MF-MC算法的译码输出结果的集合为T。假设第m个因子图F m对应的BP-MF-MC算法的译码结果为T m,即
T m=BP-MF-MC(llr,A,Φ,Ψ,S1,S2,F m)    (2)
最后,采用最大似然法从T中选出最佳的译码结果
Figure PCTCN2020098758-appb-000055
Figure PCTCN2020098758-appb-000056
其中,G为生成矩阵,大小为(N,N)。||·||为2-范数。生成矩阵
Figure PCTCN2020098758-appb-000057
Figure PCTCN2020098758-appb-000058
其中F=[1 0;1 1],
Figure PCTCN2020098758-appb-000059
表示log2(N)次kronecker幂。
本发明实施例中的每个BP-MF-MC算法的处理流程如图2所示,包括如下的处理步骤:
步骤S1、首先按照上述公式(1)对矩阵L及R进行初始化,然后使用传统的BP算法对L及R进行译码,得到译码的估计码字
Figure PCTCN2020098758-appb-000060
步骤S2、如果
Figure PCTCN2020098758-appb-000061
满足S1及S2中的所有校验条件,则可以认为
Figure PCTCN2020098758-appb-000062
为正确码字,译码器输出
Figure PCTCN2020098758-appb-000063
流程结束。
步骤S2‘、如果
Figure PCTCN2020098758-appb-000064
满足S1中的所有校验条件,但不满足S2中的所有校验条件,对Φ中n φ个翻转比特集合进行翻转译码BFBP(),该翻转译码BFBP()的处理过程包括:设
Figure PCTCN2020098758-appb-000065
为翻转比特集合φ n中的一个元素,
Figure PCTCN2020098758-appb-000066
为长度ω的向量,代表了翻转比特的位置,
Figure PCTCN2020098758-appb-000067
为长度ω的向量,代表了翻转比特对应的 值,设j l
Figure PCTCN2020098758-appb-000068
中第l个元素,
Figure PCTCN2020098758-appb-000069
是R矩阵中第(j l,1)个元素。通过函数BFBP()对翻转比特集合φ n的每个元素进行遍历,在对L及R初始化后,使用
Figure PCTCN2020098758-appb-000070
对矩阵R中第1列进行赋值,使用传统的BP译码器对赋值后的矩阵R进行译码,如果BP译码的输出
Figure PCTCN2020098758-appb-000071
满足校验条件S1,则遍历终止,输出
Figure PCTCN2020098758-appb-000072
对Φ中n φ个翻转比特集合进行翻转译码BFBP()后得到n φ个估计码字
Figure PCTCN2020098758-appb-000073
所有估计码字组成估计码字集合u,
Figure PCTCN2020098758-appb-000074
按照最大似然原则,从n φ+1个估计码字集合
Figure PCTCN2020098758-appb-000075
选出最优估计码字,如下式所示:
Figure PCTCN2020098758-appb-000076
其中,G为生成矩阵,大小为(N,N)。||·||为2-范数。
译码器输出
Figure PCTCN2020098758-appb-000077
流程结束。
步骤S2’‘、如果
Figure PCTCN2020098758-appb-000078
不满足S1中的所有校验条件,对Ψ中n ψ个翻转比特集合进行翻转译码BFBP(),该翻转译码函数BFBP()的处理过程包括:设
Figure PCTCN2020098758-appb-000079
为翻转比特集合Ψ中的一个元素,
Figure PCTCN2020098758-appb-000080
为长度ω的向量,代表了翻转比特的位置,
Figure PCTCN2020098758-appb-000081
为长度ω的向量,代表了翻转比特对应的值,
Figure PCTCN2020098758-appb-000082
是R矩阵中第(j l,1)个元素。通过函数BFBP()对翻转比特集合Ψ的每个元素进行遍历,在对L及R初始化后,使用
Figure PCTCN2020098758-appb-000083
对R中第1列进行赋值,然后使用传统的BP译码器进行译码,如果BP译码的输出
Figure PCTCN2020098758-appb-000084
满足校验条件S1,则遍历终止,输出
Figure PCTCN2020098758-appb-000085
对Ψ中n φ个翻转比特集合进行翻转译码BFBP()后,得到n ψ个估计码字
Figure PCTCN2020098758-appb-000086
所有估计码字组成估计码字集合u,
Figure PCTCN2020098758-appb-000087
按照最大似然原则,从n ψ+1个估计码字集合
Figure PCTCN2020098758-appb-000088
选出最优估计码字,如下式所示:
Figure PCTCN2020098758-appb-000089
译码器输出
Figure PCTCN2020098758-appb-000090
流程结束。
上述步骤S2、步骤S2‘和步骤S2’‘可并列执行。
算法1 BPL-MF-MC()的代码流程如下:
输入:llr,A,Φ,Ψ,S1,S2,F
输出:
Figure PCTCN2020098758-appb-000091
步骤1:同时启动M个BP-MF-MC进行译码,M个译码输出结果的集合为T。假设F中第m个因子图F m对应的译码结果为T m,即
T m=BP-MF-MC(llr,A,Φ,Ψ,S1,S2,F m)    (6)
步骤2:采用最大似然法从选出最好的
Figure PCTCN2020098758-appb-000092
Figure PCTCN2020098758-appb-000093
算法2 BP-MF-MC()的代码流程如下:
输入:llr,A,Φ,Ψ,S1,S2,FG
输出:
Figure PCTCN2020098758-appb-000094
步骤1:使用公式(1)初始化L及R
步骤2:
Figure PCTCN2020098758-appb-000095
步骤3:If
Figure PCTCN2020098758-appb-000096
满足S1
步骤4:If
Figure PCTCN2020098758-appb-000097
不满足S2
步骤5:For all Φ i∈Φ
步骤6:Ui=BFBP(llr,A,Φi,S1,FG)
步骤7:end for
步骤8:else
步骤9:return
Figure PCTCN2020098758-appb-000098
步骤10:else
步骤11:for all Ψ i∈Ψ
步骤12:Ui=BFBP(llr,A,Ψi,S1,FG)
步骤13:end for
步骤14:end if
步骤15:据式(4)或式(5)采用最大似然法从选出最好的
Figure PCTCN2020098758-appb-000099
算法3函数BFBP()的的代码流程如下:
输入:llr,A,Ω,S,FG
输出:
Figure PCTCN2020098758-appb-000100
步骤1:i=1
步骤2:for all
Figure PCTCN2020098758-appb-000101
do
步骤3:使用公式(1)初始化L及R
步骤4:for l=1 to ω do
步骤5:
Figure PCTCN2020098758-appb-000102
步骤6:end for
步骤7:
Figure PCTCN2020098758-appb-000103
步骤8:if i==1
步骤9:
Figure PCTCN2020098758-appb-000104
步骤10:end
步骤11:if
Figure PCTCN2020098758-appb-000105
满足S
步骤12:return
Figure PCTCN2020098758-appb-000106
步骤13:end
步骤14:i++
步骤15:end for。
综上所述,本发明实施例的译码方法中的各种处理流程可以并行实现,通过本发明,在高信噪比时的计算复杂度可以小于列表逐次消除译码算法, 性能接近。本发明实施例可以消除(BFBP)解码器的误码平层现象,是一种与CRC辅助的SCL解码器(CA-SCL)性能相近的BP解码器,且并行度高。
本发明实施例采用列表的方法同时启动M个BP-MF-MC算法进行译码,可以进一步降低BP-MF-MC算法误码平层现象,降低译码的最小复杂度。
本领域普通技术人员可以理解:附图只是一个实施例的示意图,附图中的模块或流程并不一定是实施本发明所必须的。
通过以上的实施方式的描述可知,本领域的技术人员可以清楚地了解到本发明可借助软件加必需的通用硬件平台的方式来实现。基于这样的理解,本发明的技术方案本质上或者说对现有技术做出贡献的部分可以以软件产品的形式体现出来,该计算机软件产品可以存储在存储介质中,如ROM/RAM、磁碟、光盘等,包括若干指令用以使得一台计算机设备(可以是个人计算机,服务器,或者网络设备等)执行本发明各个实施例或者实施例的某些部分所述的方法。
本说明书中的各个实施例均采用递进的方式描述,各个实施例之间相同相似的部分互相参见即可,每个实施例重点说明的都是与其他实施例的不同之处。尤其,对于装置或系统实施例而言,由于其基本相似于方法实施例,所以描述得比较简单,相关之处参见方法实施例的部分说明即可。以上所描述的装置及系统实施例仅仅是示意性的,其中所述作为分离部件说明的单元可以是或者也可以不是物理上分开的,作为单元显示的部件可以是或者也可以不是物理单元,即可以位于一个地方,或者也可以分布到多个网络单元上。可以根据实际的需要选择其中的部分或者全部模块来实现本实施例方案的目的。本领域普通技术人员在不付出创造性劳动的情况下,即可以理解并实施。
以上所述,仅为本发明较佳的具体实施方式,但本发明的保护范围并不局限于此,任何熟悉本技术领域的技术人员在本发明揭露的技术范围内,可 轻易想到的变化或替换,都应涵盖在本发明的保护范围之内。因此,本发明的保护范围应该以权利要求的保护范围为准。

Claims (6)

  1. 一种列表极化码传播译码方法,其特征在于,包括:
    同时启动M个基于多翻转比特集合的极化码置信传播译码BP-MF-MC算法对接收信号进行译码,每个BP-MF-MC算法所使用的因子图为F m,M个BP-MF-MC算法的译码输出结果的集合为T;
    设第m个因子图F m对应的BP-MF-MC算法的译码结果为T m,即
    T m=BP-MF-MC(llr,A,Φ,Ψ,S1,S2,F m)  (2)
    采用最大似然法从T中选出最佳的
    Figure PCTCN2020098758-appb-100001
    Figure PCTCN2020098758-appb-100002
    其中,G为生成矩阵,大小为(N,N),||·||为2-范数。
  2. 根据权利要求1所述的方法,其特征在于,每个BP-MF-MC算法对接收信号进行译码的过程包括:
    设定校验条件集合S1、S2,该S1、S2中包含对译码后的估计码字的多个校验条件:
    计算出待译码的接收信号的对数似然比,使用BP算法对存储所述对数似然比的实数矩阵进行译码,得到估计码字
    Figure PCTCN2020098758-appb-100003
    判断
    Figure PCTCN2020098758-appb-100004
    是否满足S1及S2中的所有校验条件,如果是,则确定
    Figure PCTCN2020098758-appb-100005
    为正确码字,译码器输出
    Figure PCTCN2020098758-appb-100006
    流程结束;否则,利用所述实数矩阵对设定的翻转比特集合进行翻转译码后得到翻转估计码字集合u,按照最大似然原则,从所述估计码字
    Figure PCTCN2020098758-appb-100007
    和翻转估计码字集合u中选出最优估计码字,译码器输出最优估计码字,流程结束。
  3. 根据权利要求2所述的方法,其特征在于,所述的设定校验条件集合S1、S2,该S1、S2中包含对译码后的估计码字的多个校验条件,包括:
    预先设定校验条件集合S1、S2,该S1、S2中包含对译码后的估计码字的多个校验条件,S1与S2无交集,S1和S2的选取原则为漏检率最低。
  4. 根据权利要求2所述的方法,其特征在于,所述的计算出待译码的接收信号的对数似然比,使用BP算法对存储所述对数似然比的实数矩阵进行译码,得到估计码字
    Figure PCTCN2020098758-appb-100008
    包括:
    Figure PCTCN2020098758-appb-100009
    为待译码的接收信号,为一长度为N的一个向量,llr为待译码信号
    Figure PCTCN2020098758-appb-100010
    的对数似然比,为一长度为N的一个向量,即llr i=p(y i|0)/p(y i|1),其中,llr i为llr中第i个元素,y i
    Figure PCTCN2020098758-appb-100011
    中第i个元素,p(y i|0)为输入为0时的条件概率,p(y i|1)为输入为1时的条件概率;
    A是极化码的信息比特位置,A c是极化码的冻结比特位置,L与R为一实数矩阵,其大小为(N,log2(N)+1),是极化码置信传播算法中存储对数似然比llr的矩阵,L和R采用如下公式初始化:
    Figure PCTCN2020098758-appb-100012
    其中,R i,0表示R矩阵中位置为(i,0)的元素,L i,0表示L矩阵中位置为(i,0)的元素;
    按照上述公式(1)对矩阵L及R进行初始化,使用BP算法对L及R进行译码,得到译码的估计码字
    Figure PCTCN2020098758-appb-100013
  5. 根据权利要求4所述的方法,其特征在于,所述的利用所述实数矩阵对设定的翻转比特集合进行翻转译码后得到翻转估计码字集合u,按照最大似然原则,从所述估计码字
    Figure PCTCN2020098758-appb-100014
    和翻转估计码字集合u中选出最优估计码字,译码器输出最优估计码字,流程结束,包括:
    设定Φ为翻转比特序列,含有n φ个翻转比特集合,即
    Figure PCTCN2020098758-appb-100015
    Ψ为翻 转比特序列,含有n ψ个翻转比特集合,即
    Figure PCTCN2020098758-appb-100016
    如果估计码字
    Figure PCTCN2020098758-appb-100017
    满足S1中的所有校验条件,但不满足S2中的所有校验条件,对Φ中n φ个翻转比特集合进行翻转译码BFBP(),该翻转译码BFBP()的处理过程包括:设
    Figure PCTCN2020098758-appb-100018
    为翻转比特集合φ n中的一个元素,
    Figure PCTCN2020098758-appb-100019
    为长度ω的向量,代表了翻转比特的位置,
    Figure PCTCN2020098758-appb-100020
    为长度ω的向量,代表了翻转比特对应的值,设j l
    Figure PCTCN2020098758-appb-100021
    中第l个元素,
    Figure PCTCN2020098758-appb-100022
    是矩阵R中第(j l,1)个元素,通过函数BFBP()对翻转比特集合φ n的每个元素进行遍历,在对L及R初始化后,使用
    Figure PCTCN2020098758-appb-100023
    对矩阵R中第1列进行赋值,使用BP译码器对赋值后的矩阵R进行译码,如果BP译码的输出
    Figure PCTCN2020098758-appb-100024
    满足校验条件S1,则遍历终止,输出
    Figure PCTCN2020098758-appb-100025
    对Φ中n φ个翻转比特集合进行翻转译码BFBP()后得到n φ个估计码字
    Figure PCTCN2020098758-appb-100026
    所有估计码字组成估计码字集合u,
    Figure PCTCN2020098758-appb-100027
    按照最大似然原则,从n φ+1个估计码字集合
    Figure PCTCN2020098758-appb-100028
    选出最优估计码字,如下式所示:
    Figure PCTCN2020098758-appb-100029
    其中,G为生成矩阵,大小为(N,N),||·||为2-范数;
    译码器输出
    Figure PCTCN2020098758-appb-100030
    流程结束。
  6. 根据权利要求4所述的方法,其特征在于,所述的利用所述实数矩阵对设定的翻转比特集合进行翻转译码后得到翻转估计码字集合u,按照最大似然原则,从所述估计码字
    Figure PCTCN2020098758-appb-100031
    和翻转估计码字集合u中选出最优估计码字,译码器输出最优估计码字,流程结束,包括:
    如果
    Figure PCTCN2020098758-appb-100032
    不满足S1中的所有校验条件,对Ψ中n ψ个翻转比特集合进行翻转译码BFBP(),该翻转译码函数BFBP()的处理过程包括:设
    Figure PCTCN2020098758-appb-100033
    为翻转比特集合ψ n,中的一个元素,
    Figure PCTCN2020098758-appb-100034
    为长度ω的向量,代表了翻转比特的位置,
    Figure PCTCN2020098758-appb-100035
    为长度ω的向量,代表了翻转比特对应的值,
    Figure PCTCN2020098758-appb-100036
    是R矩阵中第(j l,1)个元素,通过函数BFBP()对翻转比特集合ψ n,的每个元素进行遍历,在对L及R初始化后,使用
    Figure PCTCN2020098758-appb-100037
    对R中第1列进行赋值,使用BP译码器进行译码,如果BP译码的输出
    Figure PCTCN2020098758-appb-100038
    满足校验条件S1,则遍历终止,输出
    Figure PCTCN2020098758-appb-100039
    对Ψ中n φ个翻转比特集合进行翻转译码BFBP()后,得到n ψ个估计码字
    Figure PCTCN2020098758-appb-100040
    所有估计码字组成估计码字集合u,
    Figure PCTCN2020098758-appb-100041
    按照最大似然原则,从n ψ+1个估计码字集合
    Figure PCTCN2020098758-appb-100042
    选出最优估计码字,如下式所示:
    Figure PCTCN2020098758-appb-100043
    译码器输出
    Figure PCTCN2020098758-appb-100044
    流程结束。
PCT/CN2020/098758 2020-04-17 2020-06-29 一种列表极化码传播译码方法 WO2021208244A1 (zh)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CN202010305395.1 2020-04-17
CN202010305395.1A CN111446973B (zh) 2020-04-17 2020-04-17 基于多翻转比特集合的极化码置信传播译码方法

Publications (1)

Publication Number Publication Date
WO2021208244A1 true WO2021208244A1 (zh) 2021-10-21

Family

ID=71654176

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2020/098758 WO2021208244A1 (zh) 2020-04-17 2020-06-29 一种列表极化码传播译码方法

Country Status (2)

Country Link
CN (1) CN111446973B (zh)
WO (1) WO2021208244A1 (zh)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116505958A (zh) * 2023-05-08 2023-07-28 江西财经大学 一种噪声辅助bpl级联osd的极化码译码方法、系统、设备及介质

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111490796B (zh) * 2020-04-24 2022-05-20 北京交通大学 基于动态翻转比特的置信传播译码方法

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2018118289A1 (en) * 2016-12-20 2018-06-28 Intel Corporation Multi-path decoding of a polar code using in parallel permuted graphs of the polar code
CN110233628A (zh) * 2019-05-22 2019-09-13 东南大学 极化码的自适应置信传播列表译码方法
CN110278002A (zh) * 2019-06-19 2019-09-24 东南大学 基于比特翻转的极化码置信传播列表译码方法
CN110492974A (zh) * 2019-08-19 2019-11-22 北京邮电大学 一种并行的极化码译码方法及装置
CN111541517A (zh) * 2020-04-17 2020-08-14 北京交通大学 一种列表极化码传播译码方法

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US9960790B2 (en) * 2013-11-29 2018-05-01 Kabushiki Kaisha Toshiba Belief propagation decoding for short algebraic codes with permutations within the code space
CN106130690A (zh) * 2016-06-21 2016-11-16 东南大学 结合极化码的mimo系统联合检测译码方法
CN108847848B (zh) * 2018-06-13 2021-10-01 电子科技大学 一种基于信息后处理的极化码的bp译码算法
CN109412611B (zh) * 2018-09-12 2022-06-10 珠海妙存科技有限公司 一种降低ldpc误码平层的方法

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2018118289A1 (en) * 2016-12-20 2018-06-28 Intel Corporation Multi-path decoding of a polar code using in parallel permuted graphs of the polar code
CN110233628A (zh) * 2019-05-22 2019-09-13 东南大学 极化码的自适应置信传播列表译码方法
CN110278002A (zh) * 2019-06-19 2019-09-24 东南大学 基于比特翻转的极化码置信传播列表译码方法
CN110492974A (zh) * 2019-08-19 2019-11-22 北京邮电大学 一种并行的极化码译码方法及装置
CN111541517A (zh) * 2020-04-17 2020-08-14 北京交通大学 一种列表极化码传播译码方法

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
ZHANG JIANYONG; WANG MUGUANG: "Belief Propagation Decoder With Multiple Bit-Flipping Sets and Stopping Criteria for Polar Codes", IEEE ACCESS, vol. 8, 20 April 2020 (2020-04-20), USA , pages 83710 - 83717, XP011787778, DOI: 10.1109/ACCESS.2020.2988878 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116505958A (zh) * 2023-05-08 2023-07-28 江西财经大学 一种噪声辅助bpl级联osd的极化码译码方法、系统、设备及介质

Also Published As

Publication number Publication date
CN111446973A (zh) 2020-07-24
CN111446973B (zh) 2022-03-25

Similar Documents

Publication Publication Date Title
WO2021208243A1 (zh) 基于多翻转比特集合的极化码置信传播译码方法
WO2021000531A1 (zh) 一种基于llr的分段翻转极化码译码方法和智能终端
CN107026656B (zh) 一种基于扰动的CRC辅助中短码长Polar码有效译码方法
WO2017107761A1 (zh) 一种极化码与重复码或多比特偶校验码级联的纠错编码方法
CN109660264B (zh) 高性能极化码译码算法
US10312947B2 (en) Concatenated and sliding-window polar coding
JP6451955B2 (ja) 多段ソフト入力デコードのためのシステムおよび方法
CN106452460B (zh) 一种极化码与重复码级联的纠错编码方法
WO2014059780A1 (zh) 一种编译码的方法、装置及系统
WO2017054164A1 (zh) 极化码的编译码方法及其装置
CN101621299B (zh) 一种突发纠错的方法、设备和装置
WO2020108586A1 (zh) 一种极化码译码方法及装置、多级译码器、存储介质
KR101625273B1 (ko) 더 짧은 블록 길이를 이용하여 더 긴 선형 블록 코드워드를 생성 및 디코딩하기 위한 장치, 시스템 및 방법
US20200007170A1 (en) System and method for early termination of decoding in a multi user equipment environment
WO2021208244A1 (zh) 一种列表极化码传播译码方法
TW201018095A (en) Overcoming LDPC trapping sets by decoder reset
CN106888026A (zh) 基于lsc‑crc译码的分段极化码编译码方法及系统
CN111490796B (zh) 基于动态翻转比特的置信传播译码方法
WO2019096184A1 (zh) 阶梯码的解码方法、装置及存储介质
WO2018127140A1 (zh) 数据编码及译码的方法和装置
CN110233698A (zh) 极化码的编码及译码方法、发送设备、接收设备、介质
CN102780496A (zh) Rs码译码方法及装置
WO2016015288A1 (zh) 译码方法和译码器
CN112803954B (zh) 一种基于CRC分段处理的改进BP List译码算法
CN116614142A (zh) 一种基于bpl译码和osd译码的联合译码方法

Legal Events

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

Ref document number: 20931342

Country of ref document: EP

Kind code of ref document: A1

NENP Non-entry into the national phase

Ref country code: DE

32PN Ep: public notification in the ep bulletin as address of the adressee cannot be established

Free format text: NOTING OF LOSS OF RIGHTS PURSUANT TO RULE 112(1) EPC (EPO FORM 1205A DATED 17/03/2023)

122 Ep: pct application non-entry in european phase

Ref document number: 20931342

Country of ref document: EP

Kind code of ref document: A1