CN116318551A - Intermediate channel selection and decoding method of LDPC-Polar cascade system - Google Patents

Intermediate channel selection and decoding method of LDPC-Polar cascade system Download PDF

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CN116318551A
CN116318551A CN202310275481.6A CN202310275481A CN116318551A CN 116318551 A CN116318551 A CN 116318551A CN 202310275481 A CN202310275481 A CN 202310275481A CN 116318551 A CN116318551 A CN 116318551A
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node
ldpc
polar
decoding
code
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张盛峰
李纯
黄胜
张寄林
王乐
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0061—Error detection codes
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    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
    • H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
    • H03M13/1148—Structural properties of the code parity-check or generator matrix
    • H03M13/116—Quasi-cyclic LDPC [QC-LDPC] codes, i.e. the parity-check matrix being composed of permutation or circulant sub-matrices
    • 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
    • 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
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Abstract

The invention relates to a channel coding technology, in particular to an intermediate channel selection and decoding method of an LDPC-Polar cascade system; the method utilizes a Rate-1 node to extract a selection set of an intermediate channel, and sorts the selection set according to She Ziji size and Gaussian construction error probability; distributing the sorted selection set and the LDPC variable nodes; based on a joint factor graph in the decoding process, simplifying the right transmission process of the prior information of the nodes such as Rate-1, rate-0 and the like according to BP decoding information updating rules; the invention improves the error code performance of the LDPC-Polar cascade system and reduces the calculation complexity of the whole system according to the special nodes.

Description

Intermediate channel selection and decoding method of LDPC-Polar cascade system
Technical Field
The invention relates to a channel coding technology, in particular to a polarization code, and particularly relates to an intermediate channel selection and decoding method of an LDPC-Polar cascade system.
Background
The polar code was proposed by Arikan as the first channel coding scheme to reach shannon's limit theoretically under binary input discrete memoryless symmetric channels (Binary Input Discrete Memoryless Symmetric Channel, BI-DMSC). Two well-known decoding algorithms are the serial cancellation (Successive Cancellation, SC) and belief propagation (Belief Propagation, BP) decoding algorithms. However, the SC decoding algorithm is a serial decoding algorithm, the decoding delay is high, and the SC decoding algorithm error performance under a limited code length is not ideal. Besides the SC decoding algorithm, the BP decoding algorithm is an iterative parallel decoding algorithm, and the parallel characteristic makes the algorithm suitable for a low-delay and high-throughput system, and simultaneously has the characteristic of relatively high complexity.
The Polar code can improve error correction performance by concatenating other codewords, such as a concatenation of Polar codes and (Reed-solomon) RS codes, a concatenation of LDPC codes and Polar codes. In the invention, the cascade system takes LDPC codes as external codes and Polar codes as internal codes, the external code LDPC codes improve the decoding performance by protecting the middle channel of the internal code Polar codes, and the right information calculation is simplified by a special node matrix in the decoding process.
However, the intermediate channel selection method proposed by the article (Abbas S M, fan Y Z, chen J, et al, connected LDPC-Polar Codes Decoding Through Belief Propagation [ C ]. ISCAS, 2017.) uses the pasteurization parameters as part of the selection method, but the pasteurization parameters can only be accurately calculated when the channel is deleted in binary (Binary Erasure Channel, BEC), so that the selection of the intermediate channel is not suitable when the channel is not BEC, resulting in poor decoding performance of the concatenated system. The bit mapping method (Yu Q P, shi Z P, deng L, et al, an improved belief propagation decoding of concatenated polar codes with bit mapping [ J ]. IEEE Communications Letters,2018,22 (6): 1160-1163.) does not take into account the ordering of intermediate channel reliabilities in the correspondence of the intermediate channels to the variable nodes of the LDPC code, but is divided into reliable and unreliable, resulting in poor error performance of the concatenated system.
Disclosure of Invention
In order to solve the above problems, the present invention provides a method for selecting and decoding an intermediate channel of an LDPC-Polar cascade system, comprising the steps of:
constructing a polarization code with a code length of N by a Gaussian approximation construction method, wherein the polarization code comprises K information bits and N-K freeze bits; acquiring all Rate-1 nodes of the polarization code, and respectively adopting a first information bit and a first two information bits of all Rate-1 nodes to form a set CS and a set CS 2 ；
Based on set CS and set CS 2 Obtaining a new set CS by adopting an improved intermediate channel selection method 2 And (2) a step of performing; according to the new set CS 2 Extracting a plurality of Polar intermediate channels and arranging the Polar intermediate channels in descending order according to the reliability to obtain a Polar intermediate channel selection sequence;
constructing a code length of N by a Mackey construction method P A regular LDPC code of (2), which includes K P Information bits and N P A plurality of LDPC variable nodes; based on the Polar intermediate channel selection sequence, distributing a Polar intermediate channel to each LDPC variable node through an intermediate channel distribution method; wherein K is P <K,N P <N；
The transmitting end divides K information bits to be transmitted into two parts, and selects K P LDPC coding is carried out on the information bits, and transmission is carried out through corresponding Polar intermediate channels; the rest of K-K P The information bits are directly transmitted through a high-reliability channel of the polarization code;
the receiving end adopts a low-complexity decoding method to carry out the joint decoding of the polarization code and the LDPC code.
Further, a new set CS is obtained by adopting an improved intermediate channel selection method 2 Comprising the following steps:
the first information bit of all Rate-1 nodes is used to form a set cs= { c 1 ,c 2 ,...,c n }, wherein c i The ith element in the table set CS, n representing the total number of elements of the set CS; employing the first two information bits of all Rate-1 nodes to form a set
Figure BDA0004136090120000021
Wherein->
Figure BDA0004136090120000022
Table set CS 2 In (a) and (b)The ith element, m represents the total number of elements of the set, and m>n；
First round screening: determining whether an element exists in the set CS
Figure BDA0004136090120000031
If present, the element ∈>
Figure BDA0004136090120000035
If not, element->
Figure BDA0004136090120000032
Performing a second round of screening;
second round screening: setting leaf set threshold, if element
Figure BDA0004136090120000033
Not less than the leaf set threshold, then the element is retained
Figure BDA0004136090120000036
Otherwise delete element->
Figure BDA0004136090120000034
Third round screening: acquiring the minimum polarization weight of the set CS, and combining the minimum polarization weight with the updated set CS after the second round of screening 2 Comparing the polarization weights of each element in the plurality of elements; if the polarization weight of the element is not less than the minimum polarization weight of the set CS, deleting the element;
the third round of updated set CS after screening 2 Each element in the list is arranged in ascending order according to the leaf set size to obtain a new set CS 2 And (2) a step of performing; extracting a new set CS 2 Front N in P And arranging the elements in descending order according to the Gaussian construction error probability of the elements to finally obtain the Polar intermediate channel selection sequence.
Further, for K information bits to be transmitted, K is selected from P LDPC encoding of information bits to produce a code length of N P Selecting a match from the polarized channels of the polarized codesN is matched with P The LDPC code is transmitted by a plurality of Polar intermediate channels, and the rest K-K P The individual information bits pass directly through the rest of the K-K of the polarization code P Transmitting the polarized channels; and then, coding K information bits and N-K frozen bits of the incoming polarized channel through a polarized code to form N transmission code words, and transmitting the N transmission code words through an AWGN channel after BPSK modulation.
Further, the receiving end adopts a low complexity decoding method to perform joint decoding of the polarization code and the LDPC code, and the method comprises the following steps:
the receiving end obtains modulated polarization code information and performs a first round of decoding, including:
s1, carrying out information transfer from the rightmost side to the left of the LDPC-Polar joint factor graph according to the calculation rule of the BP decoding operation unit;
s2, when information is transmitted to the leftmost side of the LDPC-Polar joint factor graph, searching an LPDC code correspondingly connected with a Polar intermediate channel, and receiving soft information transmitted by a polarization code by a variable node of the LPDC code and performing primary BP decoding;
s3, after the LDPC code finishes BP decoding once, soft information updated by the LDPC code is transmitted to the leftmost side of the LDPC-Polar joint factor graph, and then information transmission is carried out from the leftmost side of the LDPC-Polar joint factor graph to the right by combining with a special node updating rule;
after the first round of decoding is completed, continuing to perform multiple rounds of decoding according to the similar process of the first round of decoding until the maximum iteration number is reached, and then performing hard decision on soft information to output a decoding result.
Further, a special matrix is constructed through the special nodes, and a special node updating rule is constructed through the special matrix; the special matrix is an explanation of the situation that the PE node is scheduled by the child node corresponding to the special node, and the special node refers to a Rate-1 node, a Rate-0 node and a Rep node which are obtained when the polarization code is constructed.
Further, the special node update rule comprises an update rule of a Rate-1 node, an update rule of a Rate-0 node and an update rule of a Rep node;
when the special matrix shows that the current PE unit calculates a Rate-1 node, an update rule of the Rate-1 node is adopted as follows:
R c ＝g(R a ,L d +R b )＝s×sign(∞)×sign(L d +∞)×min(∞,∞)＝∞
R d ＝g(R a ,L c )+R b ＝∞
when the special matrix shows that the current PE unit calculates a Rate-0 node, an update rule of the Rate-0 node is adopted as follows:
R c ＝g(R a ,L d +R b )＝s×sign(0)sign(L d +0)min(0,0)＝0
R d ＝g(R a ,L c )+R b ＝s×sign(0)×sign(L c )×min(|L c |,0)+0＝0
when the special matrix shows that the current PE unit calculates a Rep node, an updating rule of the Rep node is adopted as follows:
R c ＝g(R a ,L d +R b )＝s×sign(∞)sign(L d +∞)min(∞,∞)＝∞
R d ＝g(R a ,L c )+R b ＝∞
wherein R is c Representing right-hand information on node c in the current PE unit, R a Representing right-hand information on node d in current PE unit, L d Representing left-hand information on node d in the current PE unit, R b Representing right-hand information on node b in the current PE unit, L c Representing left-hand information on node c in the current PE unit, sign represents a sign function, s represents a value of 0.9375, g (x, y) =ln [ 1+xy/(x+y)]，R d And representing right-hand information on the d node in the current PE unit.
The invention has the beneficial effects that:
the intermediate channel selection and decoding method based on the LDPC-Polar cascade system provided by the invention performs simulation analysis and simulation parameter setting with the traditional cascade system method: the polarized code is used as an inner code, the polarized code length N=1024, K=560 and the LDPC code is used as an outer code, and a (3, 6) regular LDPC code with the code length of 96 and the information bit of 48 is constructed. Simulation results show that when the polarization codeWhen the code length is 1024, the bler=10 -3 The proposed intermediate channel selection plus allocation method has a gain of about 0.12dB compared to the bit mapped method. And the cascade system has lower decoding delay relative to the CA-SCL decoding algorithm. Furthermore, n=1024 polarization codes need to be calculated into nlog2 (N) =10240 calculation units in one iteration process, but the calculation of 1381 PE calculation units is reduced by the simplified algorithm provided by the invention, namely, the calculation complexity of 13.5% of the polarization codes is reduced.
Drawings
FIG. 1 is a flowchart of an intermediate channel selection and decoding method of an LDPC-Polar cascade system according to the present invention;
FIG. 2 is a diagram of low complexity decoding joint factors for LDPC-Polar concatenated codes in accordance with an embodiment of the present invention;
FIG. 3 is a diagram of an allocation method of intermediate channels and LDPC variable nodes according to an embodiment of the present invention;
FIG. 4 is a diagram of a particular node type of the present invention;
FIG. 5 is a diagram of a correlation simplified calculation BP decoding unit according to the present invention;
fig. 6 is a diagram of simulation results according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention provides a method for selecting and decoding an intermediate channel of an LDPC-Polar cascade system, which is shown in figure 1 and comprises the following steps:
step one: constructing code length N by Mackey construction method P =96, information bit K P Regular LDPC code of=48.
Step two: constructing a polarization code with a code length of n=1024 by a gaussian approximation construction method, which includes k=560 information bits andn-k=464 freeze bits; and then carrying out channel polarization on the channels transmitted by the polarization codes, wherein when the number of the combined channels tends to infinity, one part of the channels tends to be noise-free channels, and the other part of the channels tend to be all-noise channels. The transmission rate of the noiseless channel would reach the channel capacity I (W), while the transmission rate of the full-noise channel would tend to be 0. By utilizing the characteristic, the polarized channels are ordered from small to large according to the reliability, and the set v= { v is obtained 0 ,...,v 1023 }, where v i Representing the ith polarized channel in set v. The set v is divided into two parts, namely 560 polarized channels are selected for transmitting information bits of information bits, and the remaining 464 polarized channels are used for transmitting freeze bits of freeze bits.
Step three: acquiring all Rate-1 nodes of the polarization code, and respectively adopting a first information bit and a first two information bits of all Rate-1 nodes to form a set CS and a set CS 2 。
Specifically, the Rate-1 node is a node of which leaf nodes are all information bits; simultaneously acquiring a Rate-0 node and a Rep node of the polarization code, wherein the Rate-0 node is a node of which leaf nodes are frozen bits; the Rep node is the node whose rightmost leaf node is the information bit, and the rest leaf nodes are all freezing bits. As shown in fig. 4, black circles represent information bits, white circles represent freeze bits, and gray circles represent both information bits and freeze bits.
Step four: based on set CS and set CS 2 Obtaining a new set CS by adopting an improved intermediate channel selection method 2 And (2) a step of performing; according to the new set CS 2 Extracting a plurality of Polar intermediate channels and arranging the Polar intermediate channels according to the descending order of reliability to obtain a Polar intermediate channel selection sequence.
Specifically, a new set CS is obtained by adopting an improved intermediate channel selection method 2 Comprising the following steps:
the first information bit of all Rate-1 nodes is used to form a set cs= { c 1 ,c 2 ,...,c n }, wherein c i The ith element in the table set CS, n representing the total number of elements of the set CS; employing the first two information bits of all Rate-1 nodes to form a set
Figure BDA0004136090120000061
Wherein->
Figure BDA0004136090120000062
Table set CS 2 The ith element in (a), m represents the total number of elements in the set, and m>n. In this embodiment, n=122, and the channel index of the Polar intermediate channel corresponding to the set CS is {128,190, …,961}; m=194, set CS 2 The channel index of the corresponding Polar intermediate channel is {128,190, …,962}.
First round screening: for the set CS 2 Elements of (a)
Figure BDA0004136090120000071
Judgment element->
Figure BDA0004136090120000072
Whether it belongs to set CS, if so, the element +.>
Figure BDA0004136090120000074
If not, element->
Figure BDA0004136090120000073
A second round of screening was performed.
Second round screening: setting leaf set threshold, if element
Figure BDA0004136090120000075
Not less than the leaf set threshold, then the element is retained
Figure BDA0004136090120000077
Otherwise delete element->
Figure BDA0004136090120000076
The leaf subset threshold in this embodiment is the smallest She Ziji size in the set CS, i.e. 8.
Third round screening: acquiring the minimum polarization weight of the set CS, and combining the minimum polarization weight with the updated set CS after the second round of screening 2 Poles of each element in (a)Comparing the chemical weights; if the polarization weight of the element is not less than the minimum polarization weight of the set CS, the element is deleted. In this embodiment, the third round of post-filter updated set CS 2 A total of 112 elements are included, which correspond to channel indexes 128,190, …, 961.
CS updated after third round of screening 2 Each element in the set is arranged in ascending order according to the size of the leaf set to obtain a new set CS 2 And (2) a step of performing; extracting a new set CS 2 Front N in P And the elements are arranged in descending order according to the Gaussian construction error probability of the elements, and finally the Polar intermediate channel selection sequence is obtained.
Step five: based on the Polar intermediate channel selection sequence, each LDPC variable node is allocated a Polar intermediate channel by an intermediate channel allocation method.
Specifically, as shown in fig. 3, the allocation procedure of the Polar intermediate channel includes:
the LPDC variable node is controlled according to 1 to N LDPC Sequentially numbering and selecting elements in the Polar intermediate channel selection sequence from left to right according to 1-N LDPC And are numbered sequentially. Example N LDPC ＝96。
The LDPC variable node numbered 1 is assigned the Polar intermediate channel corresponding to the element numbered 1, which is the least reliable. In this embodiment, the channel index of the Polar intermediate channel corresponding to the element with the reference number 1 is 961, and the LDPC variable node with the reference number 1 is connected to the 9 th LDPC check node and the 11 th LDPC check node.
Acquiring all LDPC variable nodes connected with the same LDPC check node as the LDPC variable node with the reference number of 1 and assigning the same with the reference number of { N } LDPC ，N LDPC -1，...，N LDPC -k1+1} represents the number of LDPC variable nodes connecting the same LDPC check node as the LDPC variable node numbered 1. Specifically, in this embodiment, the LDPC variable node labeled {20,37,55,63,94} of the 9 th LDPC check node is commonly connected with the LDPC variable node labeled 1, and is assigned with the Polar corresponding to the element labeled {96,95,94,93,92}, among the PolarInter-channel, and the corresponding channel index of these Polar intermediate channels is {365,370,371,373,377}; the LDPC variable node of 11 th LDPC check node is connected with the LDPC variable node of 1 and has the reference number {2,4,50,52,83}, the LDPC variable node is allocated with the Polar intermediate channels corresponding to the elements of the reference number {91,90,89,88,87}, and the channel index corresponding to the Polar intermediate channels is {406,407,410,411,413}.
After all LDPC variable nodes connected with the same LDPC check node with the LDPC variable node with the number of 1 are distributed; searching the next unmatched LDPC variable node with the minimum label, distributing the LDPC variable node with the minimum label to the Polar intermediate channel corresponding to the element with the label of 2, and searching and matching according to the process until all LDPC variable nodes are matched. In this embodiment, after the correlation lookup matching of the LDPC variable node with the reference number 1 is completed, the minimum reference number 3 of the unmatched LDPC variable node is left, so that the LDPC variable node with the reference number 3 is allocated a Polar intermediate channel corresponding to the element with the reference number 2, and the channel index of the Polar intermediate channel is 929.
Step six: the transmitting end divides K information bits to be transmitted into two parts, firstly selects K P LDPC encoding of information bits to produce a code length of N P And selecting a matching N from the polarized channels of the polarized codes by the above operation P Transmitting the Polar intermediate channels; the rest of K-K P The individual information bits pass directly through the rest of the K-K of the polarization code P A high reliability channel is transmitted. This embodiment requires transmission of k=560 information bits, K being selected P Code length N obtained by LDPC encoding of 48 information bits P =96, and transmitting the LDPC code through the Polar intermediate channel matched with the LDPC variable node, while the rest K-K P The 512 information bits are transmitted directly over 512 polarized channels except for the allocated Polar intermediate channel; the 560 information bits of the incoming polarized channel and the N-k=464 frozen bits are then encoded by the polarization code to form n=1024 transmission codewords.
Step seven: the 1024 transmission codewords are BPSK modulated, 0 and 1 codewords are converted into 1 and-1, and transmitted through AWGN channel.
Step eight: the receiving end adopts a low-complexity decoding method to carry out the joint decoding of the polarization code and the LDPC code.
Specifically, as shown in fig. 2, the low complexity decoding method includes:
the receiving end obtains modulated polarization code information and performs a first round of decoding, including:
s1, carrying out information transfer from the rightmost side to the left of the LDPC-Polar joint factor graph according to the calculation rule of a PE unit of the BP decoder shown in FIG. 5;
s2, when information is transmitted to the leftmost side of the LDPC-Polar joint factor graph, searching an LPDC code correspondingly connected with a Polar intermediate channel, and receiving soft information transmitted by a polarization code by a variable node of the LPDC code and performing primary BP decoding;
s3, after the LDPC code finishes BP decoding once, soft information after the LDPC code iteration update is transmitted to the leftmost side of the LDPC-Polar joint factor graph, and then information transmission is carried out from the leftmost side of the LDPC-Polar joint factor graph to the right by combining with a special node update rule;
after the first round of decoding is completed, continuing to perform multiple rounds of decoding according to the similar process of the first round of decoding until the maximum iteration number is reached, and then performing hard decision on soft information to output a decoding result. Specifically, the prior right transmission information corresponding to all the child nodes of the Rate-0 node is infinite, so that in the subsequent calculation process, the value transmitted by all the child nodes of the Rate-0 node in the corresponding BP decoding unit is infinite. The Rep node has a special sub-node containing information bits, and after the special sub-node is eliminated, the priori right transmission information of the rest sub-nodes of the Rep node is infinite, so that the calculated value of the part of sub-nodes of the Rep node in the subsequent calculation process is infinite. For the Rate-1 node, excluding partial Rate-1 nodes connected with the LDPC code word, the prior right information of the child nodes of the rest Rate-1 nodes is 0, so that the value calculated in the subsequent transmission process is 0. The special node is used for determining the distribution condition of the sub-nodes and scheduling and simplifying the decoding process, and the aim of simplifying the calculation process can be achieved by directly setting the value to 0 or infinity based on the analysis design special node updating rule, and the latter half-round iteration process is continuously completed.
Specifically, a special matrix is constructed through special nodes, and the special matrix is a description of the situation that the special nodes correspond to child nodes for scheduling PE nodes. BP decoding is based on Nlog2 (N)/2 PE nodes to complete a round of scheduling using [ N/2, log2 (N)]Corresponding to the scheduling process of BP decoding. If the child node length of the special node is Nsepecial, the corresponding special matrix size is [ N ] special /2,log 2 (N special )]I.e. the dimensions of the rows and columns are N respectively special 2 and log 2 (N special ) When the special matrix shows that the current PE unit is of a special node type, namely an R0 node, a Rep node or a Rep node, the operation is simplified according to the following updating rule.
Specifically, the Rate-1 node update rule is as follows:
R c ＝g(R a ,L d +R b )＝s×sign(∞)×sign(L d +∞)×min(∞,∞)＝∞
R d ＝g(R a ,L c )+R b ＝∞
the Rate-0 node update rule is as follows:
R c ＝g(R a ,L d +R b )＝s×sign(0)sign(L d +0)min(0,0)＝0
R d ＝g(R a ,L c )+R b ＝s×sign(0)×sign(L c )×min(|L c |,0)+0＝0
the Rep node update rule is as follows:
R c ＝g(R a ,L d +R b )＝s×sign(∞)sign(L d +∞)min(∞,∞)＝∞
R d ＝g(R a ,L c )+R b ＝∞
the LDPC-Polar cascade system of the present invention adopts BP decoder for decoding, the BP decoder is built by a plurality of PE units, as shown in FIG. 5, which is the calculation process of one PE unit, R c Representing right-hand information on node c in PE unit, R a Representing right-hand information on node d in PE unit, L d Representation ofLeft-hand information on node d in PE unit, R b Representing right-hand information on node b in PE unit, L c Representing left-hand information on node c in the PE unit, sign represents a sign function, s represents a value of 0.9375, g (x, y) =ln [ 1+xy/(x+y)]，R d Representing the right-hand information on node d in the PE unit.
The intermediate channel selection and decoding method based on the LDPC-Polar cascade system provided by the invention performs simulation analysis and simulation parameter setting with the traditional cascade system method: the polarized code is used as an inner code, the polarized code length N=1024, K=560 and the LDPC code is used as an outer code, and a (3, 6) regular LDPC code with the code length of 96 and the information bit of 48 is constructed. Simulation results fig. 6 shows that when the code length of the polarization code is 1024, at bler=10 -3 The proposed intermediate channel selection plus allocation method has a gain of about 0.12dB compared to the bit mapped method. And the cascade system has lower decoding delay relative to the CA-SCL decoding algorithm.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (6)

1. An intermediate channel selecting and decoding method of an LDPC-Polar cascade system, comprising the steps of:
constructing a polarization code with a code length of N by a Gaussian approximation construction method, wherein the polarization code comprises K information bits and N-K freeze bits; acquiring all Rate-1 nodes of the polarization code, and respectively adopting a first information bit and a first two information bits of all Rate-1 nodes to form a set CS and a set CS 2 ；
Based on set CS and set CS 2 Obtaining a new set CS by adopting an improved intermediate channel selection method 2 And (2) a step of performing; according to the new set CS 2 Extracting a plurality of Polar intermediate channels and arranging the Polar intermediate channels in descending order according to the reliability to obtain a Polar intermediate channel selection sequence;
constructing code length by Mackey construction methodN P A regular LDPC code of (2), which includes K P Information bits and N P A plurality of LDPC variable nodes; based on the Polar intermediate channel selection sequence, distributing a Polar intermediate channel to each LDPC variable node through an intermediate channel distribution method; wherein K is P <K,N P <N；
The transmitting end divides K information bits to be transmitted into two parts, and selects K P LDPC coding is carried out on the information bits, and transmission is carried out through corresponding Polar intermediate channels; the rest of K-K P The information bits are directly transmitted through a high-reliability channel of the polarization code;
the receiving end adopts a low-complexity decoding method to carry out the joint decoding of the polarization code and the LDPC code.
2. The method for selecting and decoding an intermediate channel of an LDPC-Polar cascade system according to claim 1 wherein a new set CS is obtained by using an improved intermediate channel selection method 2 Comprising the following steps:
the first information bit of all Rate-1 nodes is used to form a set cs= { c 1 ,c 2 ,...,c n }, wherein c i The ith element in the table set CS, n representing the total number of elements of the set CS; employing the first two information bits of all Rate-1 nodes to form a set
Figure FDA0004136090110000011
Wherein->
Figure FDA0004136090110000012
Table set CS 2 The ith element in (a), m represents the total number of elements in the set, and m>n；
First round screening: determining whether an element exists in the set CS
Figure FDA0004136090110000013
If present, the element ∈>
Figure FDA0004136090110000014
If not presentElement->
Figure FDA0004136090110000015
Performing a second round of screening;
second round screening: setting leaf set threshold, if element
Figure FDA0004136090110000021
The leaf set of (2) is not less than the leaf set threshold, the element +.>
Figure FDA0004136090110000022
Otherwise delete element->
Figure FDA0004136090110000023
Third round screening: acquiring the minimum polarization weight of the set CS, and combining the minimum polarization weight with the updated set CS after the second round of screening 2 Comparing the polarization weights of each element in the plurality of elements; if the polarization weight of the element is not less than the minimum polarization weight of the set CS, deleting the element;
the third round of updated set CS after screening 2 Each element in the list is arranged in ascending order according to the leaf set size to obtain a new set CS 2 And (2) a step of performing; extracting a new set CS 2 Front N in P And the elements are arranged in descending order according to the Gaussian construction error probability of the elements, and finally the Polar intermediate channel selection sequence is obtained.
3. The method for selecting and decoding an intermediate channel of an LDPC-Polar cascade system according to claim 1 wherein for K information bits to be transmitted, K is first selected from P LDPC encoding of information bits to produce a code length of N P Selecting matching N from the polarized channels of the polarized codes P The LDPC code is transmitted by a plurality of Polar intermediate channels, and the rest K-K P The individual information bits pass directly through the rest of the K-K of the polarization code P Transmitting the polarized channels; then the K information bits and N-K frozen bits of the incoming polarized channel are encoded by a polarization codeThe N transmission code words are transmitted through an AWGN channel after BPSK modulation.
4. The method for selecting and decoding an intermediate channel of an LDPC-Polar cascade system according to claim 1, wherein the receiving end performs joint decoding of the Polar code and the LDPC code by using a low complexity decoding method, comprising:
the receiving end obtains modulated polarization code information and performs a first round of decoding, including:
s1, carrying out information transfer from the rightmost side to the left of the LDPC-Polar joint factor graph according to the calculation rule of the BP decoding operation unit;
s2, when information is transmitted to the leftmost side of the LDPC-Polar joint factor graph, searching an LPDC code correspondingly connected with a Polar intermediate channel, and receiving soft information transmitted by a polarization code by a variable node of the LPDC code and performing primary BP decoding;
s3, after the LDPC code finishes BP decoding once, soft information generated by the LDPC code is transmitted to the leftmost side of the LDPC-Polar joint factor graph, and then information transmission is carried out from the leftmost side of the LDPC-Polar joint factor graph to the right by combining with a special node updating rule;
after the first round of decoding is completed, continuing to perform multiple rounds of decoding according to the similar process of the first round of decoding until the maximum iteration number is reached, and then performing hard decision on soft information to output a decoding result.
5. The method for selecting and decoding an intermediate channel of an LDPC-Polar cascade system according to claim 4 wherein a special matrix is constructed by the special nodes and a special node update rule is constructed by the special matrix; the special matrix is an explanation of the condition that the special node corresponds to the child node to schedule the PE node, and the special node refers to a Rate-1 node, a Rate-0 node and a Rep node which are obtained when the polarization code is constructed.
6. The method for selecting and decoding an intermediate channel in an LDPC-Polar cascade system according to claim 5 wherein the special node update rule comprises an update rule of a Rate-1 node, an update rule of a Rate-0 node and an update rule of a Rep node;
when the special matrix shows that the current PE unit calculates a Rate-1 node, an update rule of the Rate-1 node is adopted as follows:
R c ＝g(R a ,L d +R b )＝s×sign(∞)×sign(L d +∞)×min(∞,∞)＝∞
R d ＝g(R a ,L c )+R b ＝∞
when the special matrix shows that the current PE unit calculates a Rate-0 node, an update rule of the Rate-0 node is adopted as follows:
R c ＝g(R a ,L d +R b )＝s×sign(0)sign(L d +0)min(0,0)＝0
R d ＝g(R a ,L c )+R b ＝s×sign(0)×sign(L c )×min(|L c |,0)+0＝0
when the special matrix shows that the current PE unit calculates a Rep node, an updating rule of the Rep node is adopted as follows:
R c ＝g(R a ,L d +R b )＝s×sign(∞)sign(L d +∞)min(∞,∞)＝∞
R d ＝g(R a ,L c )+R b ＝∞
wherein R is c Representing right-hand information on node c in the current PE unit, R a Representing right-hand information on node d in current PE unit, L d Representing left-hand information on node d in the current PE unit, R b Representing right-hand information on node b in the current PE unit, L c Representing left-hand information on node c in the current PE unit, sign represents a sign function, s represents a value of 0.9375, g (x, y) =ln [ 1+xy/(x+y)]，R d And representing right-hand information on the d node in the current PE unit.
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Publication number Priority date Publication date Assignee Title
CN117176185A (en) * 2023-10-18 2023-12-05 苏州元脑智能科技有限公司 Data encoding and decoding method and device based on polarization code and storage medium

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117176185A (en) * 2023-10-18 2023-12-05 苏州元脑智能科技有限公司 Data encoding and decoding method and device based on polarization code and storage medium
CN117176185B (en) * 2023-10-18 2024-02-09 苏州元脑智能科技有限公司 Data encoding and decoding method and device based on polarization code and storage medium

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