CN114978196B - Multi-core polarization code rapid serial offset list decoding method - Google Patents

Multi-core polarization code rapid serial offset list decoding method Download PDF

Info

Publication number
CN114978196B
CN114978196B CN202210469859.1A CN202210469859A CN114978196B CN 114978196 B CN114978196 B CN 114978196B CN 202210469859 A CN202210469859 A CN 202210469859A CN 114978196 B CN114978196 B CN 114978196B
Authority
CN
China
Prior art keywords
path
node
sequence
code
likelihood value
Prior art date
Legal status (The legal status 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 status listed.)
Active
Application number
CN202210469859.1A
Other languages
Chinese (zh)
Other versions
CN114978196A (en
Inventor
赵延龙
尹振东
吴芝路
范浩天
李大森
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Harbin Institute of Technology
Original Assignee
Harbin Institute of Technology
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 Harbin Institute of Technology filed Critical Harbin Institute of Technology
Priority to CN202210469859.1A priority Critical patent/CN114978196B/en
Publication of CN114978196A publication Critical patent/CN114978196A/en
Application granted granted Critical
Publication of CN114978196B publication Critical patent/CN114978196B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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

Abstract

A multi-core polar code rapid serial offset list decoding method relates to the technical field of polar code decoding and is used for solving the problem of high delay of an existing multi-core polar code serial offset list decoding algorithm. The technical points of the invention comprise: for the reaction of F 2 Nuclear momentArray sum F 3 The multi-core polarization code composed of the core matrix is decoded by using a serial offset list decoding algorithm, and in the depth-first traversal process of the complete multi-branch tree structure, the core matrix is F 2 Or F 3 The node of (2) provides different formulas for recursively calculating the likelihood value and the codeword sequence of each path; additional update procedures are provided for nodes for special outer code rates-1 and Rate-0, including calculation of codeword sequences and updated calculation of path metrics. The invention enriches the code length application range of the polarization code and reduces the corresponding decoding delay.

Description

Multi-core polarization code rapid serial offset list decoding method
Technical Field
The invention relates to the technical field of polar code decoding, in particular to a multi-core polar code rapid serial cancellation list decoding method.
Background
The polarization code is a coding scheme in the field of channel coding, and is a strict construction code aiming at binary symmetric channels. Compared with other channel coding schemes, the polarization code is proved by Arikan to reach the channel capacity of binary symmetric channel [1] . The kernel of the polar code design originally proposed by Arikan is a 2 × 2 matrix, the code length of the corresponding coding matrix is limited to be a power of 2, and the current 5G standard polar code coding link uses a puncturing and shortening equal rate matching mode to support information transmission with any code length and code rate. However, in this mode, part of the bits of the code word of the polar code are directly wasted. The proposal of the multi-core polarization code can alleviate the problem, and the size of the core matrix is not 2 [2] Are proposed one after the other, which simultaneously have polarization properties. Therefore, the multi-core polarization code breaks the limit of the code length and provides more flexible and richer code length.
Serial offset decoding method [1] Is a classical decoding method of polarization codesFirstly, the current decoding mode related to the multi-core polarization code depends on the original serial offset list decoding method [3] The error correction performance of this method improves with the increase of the list, but, due to its decoding mechanism, its decoding delay also increases correspondingly greatly. Thus, the fast serial cancellation list decoding algorithm [4] The polarization code is also the key point for practical application, the traditional research focuses on 2 x 2 Arikan polarization core, the fast serial offset list decoding of the multi-core polarization code is still in the blank stage, and the research becomes a more complex problem due to the expansion of the types of the polarization core. The existing multi-core polar code does not introduce the fast serial offset list decoding method which can be realized, so that the practicability of the multi-core polar code is challenged.
Disclosure of Invention
In view of the above problems, the present invention provides a method for decoding a multi-core polar code fast serial cancellation list, so as to alleviate the problem of high delay of the existing multi-core polar code serial cancellation list decoding algorithm.
A multi-core polar code fast serial offset list decoding method is disclosed, the multi-core polar code is one or more F 2 Kernel matrix and one or more F 3 Kronecker product of kernel matrix; in the process of decoding the multi-core polarization code, a complete multi-branch tree structure obeying the decoding of a serial offset list is adopted, depth-first traversal is carried out from a root node of the complete multi-branch tree, and in the traversal process, the input likelihood value sequence of the current node v is
Figure BDA0003626064660000011
1) If the core matrix corresponding to the current node v is F 2 Then, the child node corresponding to the current node v is divided into a left child node and a right child node, where the input likelihood value sequence of the left child node is expressed as:
Figure BDA0003626064660000021
in the formula, N v Representing the length of the input likelihood value sequence of the current node v;
Figure BDA0003626064660000022
the sequence of input likelihood values for the right child node is represented as:
Figure BDA0003626064660000023
Figure BDA0003626064660000024
the output codeword sequence representing the left child node and the output codeword sequence representing the right child node are represented as
Figure BDA0003626064660000025
β F2l And beta F2r Respectively obtained by the lower nodes through recursive operation; then the corresponding kernel matrix F 2 Is represented as a sequence of output codewords of the current node v
Figure BDA0003626064660000026
The calculation formula is as follows:
Figure BDA0003626064660000027
Figure BDA0003626064660000028
in the formula, i is more than or equal to 1 and less than or equal to N v /2；
Figure BDA0003626064660000029
Represents a modulo-2 addition;
2) If the core matrix corresponding to the current node v is F 3 Then, the child node corresponding to the current node v is divided into a left child node, a child node, and a right child node, where the input likelihood value sequence of the left child node is expressed as:
Figure BDA00036260646600000210
the sequence of input likelihood values for a neutron node is represented as:
Figure BDA00036260646600000211
the sequence of input likelihood values for the right child node is represented as:
Figure BDA00036260646600000212
Figure BDA00036260646600000213
an output codeword sequence representing the left child node;
Figure BDA00036260646600000214
a sequence of output codewords representing the child nodes; the output codeword sequence of the right child node is represented as
Figure BDA00036260646600000215
β F3l ，β F3m And beta F3r Respectively obtained by the lower nodes through recursive operation; then the corresponding kernel matrix F 3 The calculation formula of the output codeword sequence of the current node v is:
Figure BDA00036260646600000216
Figure BDA00036260646600000217
Figure BDA00036260646600000218
in the formula, i is more than or equal to 1 and less than or equal to N v /3。
Further, F 2 Kernel matrix and F 3 The kernel matrices are:
Figure BDA0003626064660000031
Figure BDA0003626064660000032
further, when the current node is a leaf node in the traversal process, if the leaf node contains information bits, outputting a codeword as a hard decision function of the input likelihood value sequence; if the leaf node does not contain information bits, the output codeword is 0.
Further, when the current node is a leaf node in the traversal process, updating the corresponding path metric, and obtaining an output codeword sequence corresponding to each path; the method specifically comprises the following steps:
when the ith path traverses to the ith leaf node, the corresponding path metric calculation formula is as follows:
pm l,i ＝pm l,i-1
wherein pm l,i-1 Representing the path metric corresponding to the ith path from the traversal to the (i-1) th leaf node;
the corresponding output codeword sequence is:
Figure BDA0003626064660000033
representing a sequence of input likelihood values for an ith leaf node; h (.) represents a hard decision function that makes a decision on the sequence of input likelihood values;
when traversing to the ith leaf node, due to path splitting selection, the generated new path metric calculation formula corresponding to the (l + num) th path is as follows:
Figure BDA0003626064660000034
the corresponding output codeword sequence is:
Figure BDA0003626064660000035
further, when the current node is a special outer code in the traversal process, if the special outer code is a Rate-1 outer code, the output code word is a hard decision function of the input likelihood value sequence; if the special outer code is a Rate-0 outer code, the output code word is 0.
Furthermore, in the traversal process, for the current node as a Rate-1 outer code, updating the corresponding path metric, and obtaining an output code word sequence corresponding to each path; the method specifically comprises the following steps:
sorting the likelihood value absolute values of the input likelihood value sequence corresponding to the L paths traversing to the current Rate-1 outer code in an ascending order to obtain the top min (N) corresponding to each path v L-1) position coordinates of the absolute value of the small likelihood value, using a l,i Expressed as 1. Ltoreq. L.ltoreq.L, 1. Ltoreq. I.ltoreq.min (N) v ,L-1)；
And (3) initialization updating:
Figure BDA0003626064660000041
in the formula (I), the compound is shown in the specification,
Figure BDA0003626064660000042
indicating the a-th of the code word after the 1 st path splitting result is judged for the l-th path l,1 Selecting the path metric corresponding to the input likelihood value hard decision result; pm l,in Representing the path metric corresponding to the first path before traversing to the current Rate-1 outer code;
its corresponding codeword sequence is represented as:
Figure BDA0003626064660000043
in the formula (I), the compound is shown in the specification,
Figure BDA0003626064660000044
a represents the input likelihood sequence of the l path l,1 A bit;
Figure BDA0003626064660000045
in the formula (I), the compound is shown in the specification,
Figure BDA0003626064660000046
showing that the newly generated (l + num) th path is at the a-th path of the code word after the 1 st path splitting result is judged l,1 The bit does not select the path metric corresponding to the input likelihood value hard decision result;
the codeword sequence corresponding to the l + num path is represented as:
Figure BDA0003626064660000047
after the initialization update, i.e. the 1 st path split is judged, the path metric update process during the other path splits is as follows:
Figure BDA0003626064660000048
in the formula (I), the compound is shown in the specification,
Figure BDA0003626064660000049
representing the path measurement of the ith path after judging the (i-1) th path splitting result;
its corresponding codeword sequence is represented as:
Figure BDA00036260646600000410
in the formula (I), the compound is shown in the specification,
Figure BDA00036260646600000411
a representing the input likelihood sequence of the l path l,i A bit;
Figure BDA00036260646600000412
in the formula (I), the compound is shown in the specification,
Figure BDA00036260646600000413
showing that the newly generated (l + num) th path is at the a-th position of the code word after the ith path is judged to be the path splitting result of the ith time l,i The bit does not select the path metric corresponding to the input likelihood value hard decision result;
the codeword sequence corresponding to the l + num path is represented as:
Figure BDA00036260646600000414
further, if L-1 < N v Then, the path metric corresponding to the l-th path after the current Rate-1 outer code is traversed
Figure BDA00036260646600000415
Representing the path measurement of the L-1 th path after judging the L-1 th path splitting result; remaining N v The (L-1) code words all obey the hard decision result of the input likelihood value sequence and do not carry out path splitting; if N is present v < L-1, then
Figure BDA0003626064660000051
The beneficial technical effects of the invention are as follows:
the invention popularizes the fast serial offset list decoding method to the decoding acceleration scheme of the multi-core polarization code and designs the F-oriented code 2 And F 3 The mixed multi-core polarization code decoding method realizes F 2 And F 3 The fast serial offset list decoding algorithm of the multi-core polarized code formed by the cores enriches the code length application range of the polarized code, increases the decoding throughput and reduces the corresponding decoding delay.
Drawings
The present invention may be better understood by reference to the following description taken in conjunction with the accompanying drawings, which are incorporated in and form a part of this specification, and which are used to further illustrate preferred embodiments of the present invention and to explain the principles and advantages of the present invention.
Fig. 1 is a flowchart of a method for decoding a fast serial cancellation list of multi-core polar codes according to an embodiment of the present invention.
FIG. 2 is a comparison graph of decoding throughput of different decoders by the method of the present invention and a conventional multi-core polar code series cancellation list decoding algorithm.
FIG. 3 is a comparison graph of the error correction performance of the method of the present invention and the decoding algorithm of the multi-core polar code serial offset list.
Detailed Description
In order that those skilled in the art will better understand the disclosure, exemplary embodiments or examples of the disclosure are described below with reference to the accompanying drawings. It is to be understood that the disclosed embodiments or examples are only some, but not all embodiments or examples of the invention. All other embodiments or examples obtained by a person of ordinary skill in the art based on the embodiments or examples of the present invention without any creative effort shall fall within the protection scope of the present invention.
Aiming at the multi-core polar code, the invention provides a multi-core polar code rapid serial offset list decoding method in order to reduce the time delay and the calculation complexity of the serial offset list decoding method. The invention aims to popularize the polar code rapid serial offset list algorithm into the serial offset list decoding of the multi-core polar code so as to reduce the corresponding decoding delay and enhance the practicability of the decoding.
For the (N, K) multi-core polarization code, the generating matrix is expressed by the mathematical expression:
Figure BDA0003626064660000052
where K denotes the length of the information sequence to be transmitted, N = N (1) · N (2) · N (D), denotes the code length, i.e. the information sequence actually transmittedColumn length, F n(i) Representing a polarized nucleus of size n (i),
Figure BDA0003626064660000053
and representing a Kronecker product, wherein n (i) belongs to {2,3}, i is more than or equal to 1 and less than or equal to D, and D represents the total number of polarization cores adopted by the multi-core polarization code.
The coding and decoding process of polar codes can be generally described as: using u = (u) 1 ,u 2 ,…,u N ) The code sequence to be coded is represented by 0,1, K bit information sequences are dispersedly stored in a sequence u, corresponding position coordinates are stored in a set A, the size of A is K, the design of A is related to signal-to-noise ratio and code length code rate, the invention uses a Gaussian approximation method [5] And obtaining a corresponding coding scheme. With c = (c) 1 ,c 2 ,…,c N ) Denotes the encoded sequence, c = uBG N ，c i Also composed of 0,1 ≦ i ≦ N, B represents a bit transition matrix specific to the polar code. The invention selects the most basic binary phase shift keying to map the 0,1 digital signal into the modulated sequence x, x = (x) of 1-1 1 ,x 2 ,…,x N )， x i ＝1-2c i And i is more than or equal to 1 and less than or equal to N. The modulated sequence is sent to the transmission channel, the set channel is contaminated by additive white gaussian noise, and the sequence y is received, where y = (y) 1 ,y 2 ,…,y N ). It is assumed that the variance of the additive white Gaussian noise is obtained as sigma through channel estimation 2 Then the received sequence corresponds to a log-likelihood value of
Figure BDA0003626064660000061
And i is more than or equal to 1 and less than or equal to N.
The existing serial cancellation list decoding algorithm of multi-core polar codes can be generally described as follows: and in the depth-first traversal process of the multi-branch tree, carrying out flow updating on the likelihood value sequence alpha and the corresponding code word sequence beta. Since the code word sequence length of the node v is equal to the input likelihood value sequence length, N is used V Representing the input likelihood value sequence length or the input likelihood value sequence length of the node v.By definition, when the current node is the root node, nv = N, i.e. the code length; when the current node is a leaf node, D = D, and Nv =1; when the current node v is a non-leaf node, N v ＝n(1)·n(2)·...·n(D-d)，0≤d＜D。
The serial offset list decoding algorithm considers two possibilities of a certain code word at the same time, maintains a list with the maximum size of L, introduces a path concept for describing a certain decoding result, and the list with the size of num is used for representing num decoding results, wherein num is more than or equal to 1 and less than or equal to L. For any path, it corresponds to a sequence of likelihood values α and a corresponding sequence of code words β associated with the coding tree structure. The serial offset list decoding code word sequence beta considers two possibilities of corresponding information bits, path splitting is generated at the moment, the corresponding subsequent likelihood value sequence alpha and the code word sequence beta are different, code words of the two paths are different at the current information bit, and path measurement is used for measuring the reliability of a certain path. Only when the leaf node containing the information bit is traversed, the number of the paths is doubled, and when the current num is 2L, the smallest L paths are selected and reserved through a sorting algorithm for storage. And modifying the path number corresponding to each reserved path to keep num = L, wherein the path number comprises the likelihood value sequence alpha corresponding to each path, the corresponding code word sequence beta and the path metric value.
As shown in fig. 1, the present invention provides a fast serial cancellation list decoding method for multi-core polar codes, which includes the following steps:
step one, a complete multi-branch tree structure obeying the serial offset list decoding in the process of decoding the multi-core polarization code, depth-first traversal is carried out from a root node of the complete multi-branch tree, and in the traversal process, the input likelihood value sequence of a current node v is
Figure BDA0003626064660000071
1) If the core matrix corresponding to the current node v is F 2 Then, the child node corresponding to the current node v is divided into a left child node and a right child node, where the input likelihood value sequence of the left child node is expressed as:
Figure BDA0003626064660000072
in the formula, N v Representing the length of the input likelihood value sequence of the current node v;
Figure BDA0003626064660000073
the input likelihood value sequence for the right child node is represented as:
Figure BDA0003626064660000074
Figure BDA0003626064660000075
the output codeword sequence representing the left child node and the output codeword sequence representing the right child node are represented as
Figure BDA0003626064660000076
β F2l And beta F2r Respectively obtained by the lower nodes through recursive operation; then the corresponding kernel matrix F 2 Is represented as a sequence of output codewords of the current node v
Figure BDA0003626064660000077
The calculation formula is as follows:
Figure BDA0003626064660000078
Figure BDA0003626064660000079
in the formula, i is more than or equal to 1 and less than or equal to N v /2；
Figure BDA00036260646600000710
Represents a modulo-2 addition;
2) If the core matrix corresponding to the current node v is F 3 And dividing the child node corresponding to the current node v into a left child node, a child node and a right child node, wherein the input likelihood value sequence of the left child node is expressed as:
Figure BDA00036260646600000711
the sequence of input likelihood values for a neutron node is represented as:
Figure BDA00036260646600000712
the sequence of input likelihood values for the right child node is represented as:
Figure BDA00036260646600000713
Figure BDA00036260646600000714
an output codeword sequence representing a left child node;
Figure BDA00036260646600000715
a sequence of output codewords representing the child nodes; the output codeword sequence of the right child node is represented as
Figure BDA00036260646600000716
β F3l ，β F3m And beta F3r Respectively obtained by the subordinate nodes through recursive operation; then the corresponding kernel matrix F 3 The calculation formula of the output codeword sequence of the current node v is:
Figure BDA0003626064660000081
Figure BDA0003626064660000082
Figure BDA0003626064660000083
in the formula, i is more than or equal to 1 and less than or equal to N v /3。
According to the embodiment of the invention, the serial offset decoding process of the multi-core polarization code follows a multi-branch tree decoding structure, the algorithm is subjected to depth-first traversal by the root node of the multi-branch tree, and the nodes traversing each multi-branch tree need to be subjected to corresponding likelihood value alpha calculation and corresponding code word beta updating. In the depth-first traversal process, the serial offset list algorithm maintains a path updating process with the size of L, which is equivalent to the process of synchronously traversing L paths, and after the traversal is finished, L output code words are obtained, and the code word with the highest reliability in the output code words is selected as an estimation sequence of the coded sequence. The multi-core polarization code corresponding multi-decoding tree is restricted by the following conditions:
topology of multi-branch tree is composed of
Figure BDA0003626064660000084
A full multi-way tree is defined, i.e. all leaf nodes have the same depth, its depth is D, the total number of leaf nodes is N, N = N (1) · N (2) ·. For a chemical reaction formed by F 3 Or F 2 And F 3 In the mixed multi-core polarization code, leaf nodes have no child nodes, and the rest nodes except the leaf nodes have 2 or 3 child nodes. And D is set as the depth of the current node, if the current node is not a leaf node, D is more than or equal to 0 and less than D, and the number of corresponding child nodes is n (D-D). Polarized nucleus
Figure BDA0003626064660000085
Polarized nucleus
Figure BDA0003626064660000086
When traversing to the node v with the depth d, if the corresponding kernel matrix F n(D-d) ＝F 2 The input likelihood value sequence length Nv is a multiple of 2, and N v N (1) · n (2) · n (D-D). The number of the child nodes corresponding to the current node v is two, and the child nodes are distinguished by a left child node and a right child node. Input likelihood value sequence corresponding to left child node
Figure BDA0003626064660000087
The corresponding calculation formula is:
Figure BDA0003626064660000088
and i is more than or equal to 1 and less than or equal to N v /2
Figure BDA0003626064660000089
sgn (x) is a sign discriminant function, sgn (x) =1, when x is>At 0; sgn (x) = -1, when x<0 (0). According to the nature of depth-first traversal, the output code word sequence related to the left sub-node of the current node v
Figure BDA00036260646600000810
After traversing the left child node of the current node v, the input likelihood value sequence corresponding to the right child node is obtained if the left child node is known
Figure BDA00036260646600000811
The corresponding calculation formula is:
Figure BDA0003626064660000091
and i is more than or equal to 1 and less than or equal to N v /2
At the same time, the output code word sequence corresponding to the right subnode can also be assumed
Figure BDA0003626064660000092
The calculation formula corresponding to the output codeword sequence corresponding to the current node is as follows:
Figure BDA0003626064660000093
and
Figure BDA0003626064660000094
wherein i is more than or equal to 1 and less than or equal to N v /2
Wherein
Figure BDA0003626064660000095
Representing modulo-2 addition.
When traversing to the node v with the depth d, if the corresponding kernel matrix F n(D-d) ＝F 3 The input likelihood value sequence length Nv is a multiple of 3, and N v N (1) · n (2) · n (D-D). The current node corresponds to three sub-nodes which are distinguished by a left sub-node, a middle sub-node and a right sub-node. Wherein, the input likelihood value sequence corresponding to the left child node
Figure BDA0003626064660000096
The corresponding calculation formula is:
Figure BDA0003626064660000097
and i is more than or equal to 1 and less than or equal to N v /3
Wherein i is more than or equal to 1 and less than or equal to n/3. Similarly, suppose that the output codeword sequences β corresponding to the left, middle and right three sub-nodes F3l ，β F3m And beta F3r Obtained by a recursive algorithm, the sequence of likelihood values being input by sub-nodes
Figure BDA0003626064660000098
The calculation formula of (2) is as follows:
Figure BDA0003626064660000099
and i is more than or equal to 1 and less than or equal to N v /3，
Wherein i is more than or equal to 1 and less than or equal to n/3. Right child node input likelihood value sequence
Figure BDA00036260646600000910
The corresponding calculation formula is:
Figure BDA00036260646600000911
and i is more than or equal to 1 and less than or equal to N v /3，
Wherein i is more than or equal to 1 and less than or equal to n/3. After the three sub-nodes obtain the corresponding output code word sequence through the recursive algorithm, the calculation formula of the output code word sequence of the current node is
Figure BDA00036260646600000912
And
Figure BDA00036260646600000913
wherein i is more than or equal to 1 and less than or equal to N v /3
The above is a method for calculating the corresponding output codeword sequence according to the input likelihood value sequence of some non-leaf node v, which is a recursive operation method, and the operation flow is from G N And starting the defined multi-branch tree root node, and performing depth-first traversal. Namely: if the current traversal point is neither a leaf node nor a special outer code which can be rapidly operated, the likelihood value and the code word of each path are calculated recursively according to all the formulas.
Step two: when traversing to a leaf node or a special foreign code capable of fast operation, an additional update flow is enabled: for the special outer code, the corresponding output code word can be directly obtained through the input likelihood value, and further traversal of the child node is omitted, so that the effects of reducing the calculation complexity and reducing the decoding delay are achieved; for a leaf node, if the current node is the ith leaf node, the polarization coding set a needs to be considered, and if the position coordinate corresponding to the current leaf node exists in the set a, that is, the leaf node includes the corresponding information bit, the output codeword corresponding to the leaf node is:
Figure BDA0003626064660000101
wherein h (x) is a hard decision function, h (x) =0, if x > 0; otherwise h (x) =1; if the position coordinate corresponding to the current leaf node does not exist in the set A, that is, the leaf node does not contain information bits, the output code word corresponding to the leaf node
Figure BDA0003626064660000102
According to the embodiment of the present invention, when traversing to a certain non-leaf node, all child nodes with the non-leaf node as an ancestor and the non-leaf node form a sub-tree, and if the distribution of the information bit positions included in all leaf nodes of the sub-tree meets a certain condition, the root node of the current sub-tree, i.e. the current traversal node, can be called a certain outer code. If the current node is a special outer code, the type of the outer code needs to be considered. If all leaf nodes of the subtree corresponding to the current node contain information bits, the external code is called Rate-1; if all leaf nodes of the subtree corresponding to the current node do not contain information bits, the outer code is called Rate-0.
For the reaction of F 2 And F 3 The formed multi-core polarization code serially counteracts the Rate-1 outer code in the decoding process, and the corresponding output code word sequence is
Figure BDA0003626064660000103
The specific calculation is as follows:
Figure BDA0003626064660000104
and i is more than or equal to 1 and less than or equal to N v
For the multi-core polarization code serial offset decoding process of the random-0 outer code composed of any polarization core, the corresponding output code word sequence is
Figure BDA0003626064660000105
The specific values are as follows:
Figure BDA0003626064660000106
and i is more than or equal to 1 and less than or equal to N v
Step three: when the leaf node or the special outer code is traversed, the corresponding path metric is also required to be updated so as to reflect the reliability corresponding to each path and obtain the output codeword sequence corresponding to each path. The details are as follows.
Path metric update for leaf nodes: definition of pm l,0 For initialization values of path metrics, pm is defined l,i Corresponding path metric value when the path l traverses to the ith leaf node, and initial value pm of the path metric 1,0 =0; when the ith path traverses to the ith leaf node, the corresponding path metric calculation formula is as follows:
pm l,i ＝pm l,i-1
pm l,i-1 representing the path metric corresponding to the ith path from the traversal to the (i-1) th leaf node; corresponding output codeword
Figure BDA0003626064660000107
Figure BDA0003626064660000108
An input likelihood value representing the leaf node;
when the (l + num) th path traverses to the ith leaf node, the corresponding path metric calculation formula is as follows:
Figure BDA0003626064660000109
corresponding output codeword
Figure BDA00036260646600001010
Path metric update for special outer code Rate-1: before depth-first traversal to Rate-1 outer code is defined, the path metric corresponding to the ith path is pm l,in After traversing the current outer code, the path metric corresponding to the l-th path is pm l,out . When the algorithm traverses to the Rate-1 outer code, F 2 And F 3 The corresponding paths of the multi-core polarization code subtrees can be generated by a traditional polarization code rapid serial cancellation list decoding algorithm, and the corresponding path metric updating mode is proved to be equivalent to the traditional polarization code rapid serial cancellation list decoding algorithm.
The method specifically comprises the following steps: when the Rate-1 outer code is decoded, for each path, the decoding is carried outThe absolute values of the input likelihood values need to be sorted, and the smaller first min (N) is sorted v L-1) positions are subjected to path splitting, namely two conditions of outputting outer code sequences of corresponding positions are considered, and outer code output values of other positions are equal to hard decision results of input likelihood value sequences of corresponding positions. To a length of N v The Rate-1 outer code decoder performs decoding algorithm with the list size of L, and only min (N) is needed v And L-1) splitting paths, wherein each splitting generates a new path twice as much as the total number of the current paths, and if the total number of the new paths is 2L, path selection is required, and L paths with the highest reliability, namely the minimum corresponding path metric value, are reserved.
Let a l,i And sorting the absolute values of the input likelihood values corresponding to the ith path to obtain position coordinates corresponding to the ith small value. The new path metric and output codeword calculation process at this time is:
a. initialization:
Figure BDA0003626064660000111
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003626064660000112
shows that the a-th path of the code word after judging the splitting result of the 1 st path in the decoding of the Rate-1 outer code l,1 Selecting the path metric corresponding to the input likelihood value hard decision result; pm l,in Representing the path metric corresponding to the first path before traversing to the current Rate-1 outer code;
Figure BDA0003626064660000113
a represents the input likelihood sequence of the l path l,1 A bit;
Figure BDA0003626064660000114
showing that the newly generated (l + num) th path is in the a-th path of the code word after the 1 st path splitting result is judged during the Rate-1 outer code decoding of the l-th path l,1 The bit does not select the path metric corresponding to the input likelihood value hard decision result;
Figure BDA0003626064660000115
representing a code word sequence corresponding to the l + num path;
b. after the Rate-1 outer code decoding judges the 1 st path splitting, the path metric updating process when the rest paths split is as follows. If the codeword selection of the corresponding bit complies with the hard decision result of the corresponding input likelihood value when the current path l path is split, the corresponding path metric and output codeword are updated as follows:
Figure BDA0003626064660000116
wherein i is more than 1 and less than or equal to min (N) v ,L-1)；
Figure BDA0003626064660000117
Shows that after the ith path splitting result is judged when the ith path is decoded in the external code of Rate-1, the ith path splitting result is carried out on the a th code word l,i Selecting the path metric corresponding to the input likelihood value hard decision result;
Figure BDA0003626064660000118
a represents the input likelihood sequence of the l path l,i A bit;
Figure BDA0003626064660000121
showing that the newly generated l + num path is the a th path of the first code word after the ith path splitting result is judged during the Rate-1 outer code decoding of the l path l,i The corresponding path metric when the bit does not select the corresponding input likelihood value hard decision result;
Figure BDA0003626064660000122
representing the path measurement of the ith path after judging the (i-1) th path splitting result;
Figure BDA0003626064660000123
indicating the codeword sequence corresponding to the l + num path.
Further, if L-1 < N v Then, then
Figure BDA0003626064660000124
Remaining N v - (L-1) code words are subject to the hard decision result of the input likelihood value, and path splitting is not carried out; namely:
Figure BDA0003626064660000125
if N is present v < L-1, then
Figure BDA0003626064660000126
Path metric update for special outer code Rate-0: no matter what polarization core the sub-tree of the multi-core polarization code is composed of, the path metric of the corresponding path is not changed, namely pm l,out ＝pm l,in And L is more than or equal to 1 and less than or equal to num and less than or equal to L. The path measurement mode adopted in the invention ensures that the greater the path measurement value pm is, the lower the reliability of the path is.
The technical effect of the invention is further verified through experiments.
Fig. 2 is a comparison of decoding throughputs of different decoders, where throughput is defined as the number of information bits correctly decoded by a decoder per unit time, and when the error correction performance of a decoding algorithm is the same, the higher the throughput is, the faster the decoding speed is. The dotted line with a plus sign in fig. 2 is the decoding throughput corresponding to the method of the present invention, and the dash-dot line with a multiply sign is the decoding throughput corresponding to the conventional multi-core polar code serial offset list decoding algorithm. The existing multi-core polar code serial offset list decoding algorithm needs to deeply traverse to leaf nodes for the calculation of input likelihood values and output code words, so that the path measurement corresponding to each path is only performed in the process of traversing the leaf nodes, which is also the reason that the fast decoding method of the multi-core polar code can save the decoding time. As can be seen from FIG. 2, the method of the present invention significantly improves the decoding speed of the multi-core polar code fast serial offset list decoding method.
Fig. 3 shows the corresponding error correction performance of the method of the present invention and the conventional multi-core polar code serial cancellation list decoding algorithm under the same channel environment and list size, where the vertical axis represents the block error rate, and the block error rate represents the probability of error of the currently transmitted sequence, i.e., the ratio of the total number of code words with decoding errors to the total number of transmitted code words. The dotted line with plus sign in fig. 3 is the block error rate performance curve when the 0-bit signal-to-noise ratio is 0-2.25 dB, and the dot-dash line with multiplier sign corresponds to the existing multi-core polar code serial offset list decoding algorithm. As can be seen from fig. 3, the method of the present invention does not lose the error correction performance with respect to the original decoding method.
While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this description, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as disclosed herein. The present invention has been disclosed in an illustrative rather than a restrictive sense, and the scope of the present invention is defined by the appended claims.
The documents cited in the present invention are as follows:
[1]Arikan,Erdal."Channel polarization:A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels."IEEE Transactions on information Theory 55.7(2009):3051-3073.
[2]Presman,Noam,et al."Binary polarization kernels from code decompositions."IEEE Transactions on Information Theory 61.5(2015):2227-2239.
[3]Tal,Ido,and Alexander Vardy."List decoding of polar codes."IEEE Transactions on Information Theory 61.5 (2015):2213-2226.
[4]Hashemi,Seyyed Ali,Carlo Condo,and Warren J.Gross."A fast polar code list decoder architecture based on sphere decoding."IEEE Transactions on Circuits and Systems I:Regular Papers 63.12(2016):2368-2380.
[5]Trifonov,Peter."Efficient design and decoding of polar codes."IEEE Transactions on Communications 60.11 (2012):3221-3227。

Claims (6)

1. multi-purpose deviceThe decoding method of the rapid serial offset list of the nuclear polarization code is characterized in that: multiple core polar codes are one or more F 2 Kernel matrix and one or more F 3 Kronecker product of nuclear matrix, where F 2 Kernel matrix and F 3 The kernel matrices are:
Figure FDA0003910862010000011
Figure FDA0003910862010000012
in the process of decoding the multi-core polarization code, a complete multi-branch tree structure obeying the decoding of a serial offset list is adopted, depth-first traversal is carried out from a root node of the complete multi-branch tree, and in the traversal process, the input likelihood value sequence of the current node v is
Figure FDA0003910862010000013
1) If the core matrix corresponding to the current node v is F 2 Then, the child node corresponding to the current node v is divided into a left child node and a right child node, where the input likelihood value sequence of the left child node is expressed as:
Figure FDA0003910862010000014
in the formula, N v Representing the length of the input likelihood value sequence of the current node v, wherein the length of the input likelihood value sequence is equal to the code length when the current node v is a root node, the length of the input likelihood value sequence is equal to 1 when the current node v is a leaf node, and the length N of the input likelihood value sequence is equal to the length N of the input likelihood value sequence when the current node v is a non-leaf node v N (1) · n (2) · n (D-D), 0 ≦ D < D, n (D-D) representing the size of the polarization kernel, D being the depth of the current node v, D representing the total number of polarization kernels adopted by the multi-core polarization code;
Figure FDA0003910862010000015
the input likelihood value sequence for the right child node is represented as:
Figure FDA0003910862010000016
Figure FDA0003910862010000017
the output codeword sequence representing the left child node and the output codeword sequence representing the right child node are represented as
Figure FDA0003910862010000018
β F2l And beta F2r Respectively obtained by the lower nodes through recursive operation; then the corresponding kernel matrix F 2 Is represented as a sequence of output codewords of the current node v
Figure FDA00039108620100000112
The calculation formula is as follows:
Figure FDA0003910862010000019
Figure FDA00039108620100000110
in the formula, i is more than or equal to 1 and less than or equal to N v /2；
Figure FDA00039108620100000111
Represents a modulo-2 addition;
2) If the core matrix corresponding to the current node v is F 3 Then, the child node corresponding to the current node v is divided into a left child node, a child node, and a right child node, where the input likelihood value sequence of the left child node is expressed as:
Figure FDA0003910862010000021
the sequence of input likelihood values for a neutron node is represented as:
Figure FDA0003910862010000022
the input likelihood value sequence for the right child node is represented as:
Figure FDA0003910862010000023
Figure FDA0003910862010000024
an output codeword sequence representing a left child node;
Figure FDA0003910862010000025
a sequence of output codewords representing the child nodes; the output codeword sequence of the right child node is represented as
Figure FDA0003910862010000026
β F3l ，β F3m And beta F3r Respectively obtained by the lower nodes through recursive operation; then the corresponding kernel matrix F 3 The calculation formula of the output codeword sequence of the current node v is:
Figure FDA0003910862010000027
Figure FDA0003910862010000028
Figure FDA0003910862010000029
in the formula, i is more than or equal to 1 and less than or equal to N v /3。
2. The method according to claim 1, wherein when a current node is a leaf node in a traversal process, if the leaf node contains information bits, the output codeword is a hard decision function of the input likelihood value sequence; if the leaf node does not contain information bits, the output codeword is 0.
3. The method according to claim 2, wherein in the traversal process, when the current node is a leaf node, the corresponding path metric is updated, and an output codeword sequence corresponding to each path is obtained; the method comprises the following specific steps:
when the ith path traverses to the ith leaf node, the corresponding path metric calculation formula is as follows:
pm l,i ＝pm l,i-1
wherein pm l,i-1 Representing the path metric corresponding to the ith path from the traversal to the (i-1) th leaf node;
the corresponding output codeword sequence is:
Figure FDA00039108620100000210
Figure FDA00039108620100000211
representing a sequence of input likelihood values for an ith leaf node; h (.) represents a hard decision function that makes a decision on the sequence of input likelihood values;
when traversing to the ith leaf node, due to path splitting selection, the generated new path metric calculation formula corresponding to the (l + num) th path is as follows:
Figure FDA0003910862010000031
the corresponding output codeword sequence is:
Figure FDA0003910862010000032
4. the fast serial cancellation list decoding method for multi-core polar codes according to any one of claims 1 to 3, wherein when a current node is a special outer code in a traversal process, if the special outer code is a Rate-1 outer code, an output codeword is a hard decision function of an input likelihood value sequence; if the special outer code is a Rate-0 outer code, the output code word is 0.
5. The method according to claim 4, wherein in the traversal process, for the current node being a Rate-1 outer code, the corresponding path metric is updated, and an output codeword sequence corresponding to each path is obtained; the method specifically comprises the following steps:
sorting likelihood value absolute values of input likelihood value sequences corresponding to L paths traversing to the current Rate-1 outer code in an ascending order to obtain top min (N) corresponding to each path v L-1) position coordinates of the absolute value of the small likelihood value, using a l,i Expressed as 1. Ltoreq. L.ltoreq.L, 1. Ltoreq. I.ltoreq.min (N) v ,L-1)；
Initialization and updating:
Figure FDA0003910862010000033
in the formula (I), the compound is shown in the specification,
Figure FDA0003910862010000034
indicating the a-th of the code word after the 1 st path splitting result is judged for the l-th path l,1 Selecting the path metric corresponding to the input likelihood value hard decision result; pm l,in Representing the path metric corresponding to the first path before traversing to the current Rate-1 outer code;
its corresponding codeword sequence is represented as:
Figure FDA0003910862010000035
in the formula (I), the compound is shown in the specification,
Figure FDA0003910862010000036
a representing the input likelihood sequence of the l path l,1 A bit;
Figure FDA0003910862010000037
in the formula (I), the compound is shown in the specification,
Figure FDA0003910862010000038
showing that the newly generated (l + num) th path is at the a-th path of the code word after the 1 st path splitting result is judged l,1 The bit does not select the path metric corresponding to the input likelihood value hard decision result;
the codeword sequence corresponding to the l + num path is represented as:
Figure FDA0003910862010000039
after the initialization update, i.e. the 1 st path split is judged, the path metric update process during the other path splits is as follows:
Figure FDA0003910862010000041
in the formula (I), the compound is shown in the specification,
Figure FDA0003910862010000042
representing the path measurement of the ith path after judging the (i-1) th path splitting result;
its corresponding codeword sequence is represented as:
Figure FDA0003910862010000043
in the formula (I), the compound is shown in the specification,
Figure FDA0003910862010000044
a represents the input likelihood sequence of the l path l,i A bit;
Figure FDA0003910862010000045
in the formula (I), the compound is shown in the specification,
Figure FDA0003910862010000046
showing that the newly generated (l + num) th path is at the a-th position of the code word after the ith path is judged to be the path splitting result of the ith time l,i The bit does not select the path metric corresponding to the input likelihood value hard decision result;
the codeword sequence corresponding to the l + num path is represented as:
Figure FDA0003910862010000047
6. the method as claimed in claim 5, wherein if L-1 < N, the method further comprises v Then, the path metric corresponding to the l-th path after the current Rate-1 outer code is traversed
Figure FDA0003910862010000048
Figure FDA00039108620100000410
Representing the path measurement of the L-1 th path after judging the L-1 th path splitting result; remaining N v -(L-1) All the code words obey the hard decision result of the input likelihood value sequence, and the path splitting is not carried out any more; if N is present v < L-1, then
Figure FDA0003910862010000049
CN202210469859.1A 2022-04-30 2022-04-30 Multi-core polarization code rapid serial offset list decoding method Active CN114978196B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210469859.1A CN114978196B (en) 2022-04-30 2022-04-30 Multi-core polarization code rapid serial offset list decoding method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210469859.1A CN114978196B (en) 2022-04-30 2022-04-30 Multi-core polarization code rapid serial offset list decoding method

Publications (2)

Publication Number Publication Date
CN114978196A CN114978196A (en) 2022-08-30
CN114978196B true CN114978196B (en) 2023-02-03

Family

ID=82978620

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210469859.1A Active CN114978196B (en) 2022-04-30 2022-04-30 Multi-core polarization code rapid serial offset list decoding method

Country Status (1)

Country Link
CN (1) CN114978196B (en)

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107248866B (en) * 2017-05-31 2020-10-27 东南大学 Method for reducing decoding time delay of polarization code
WO2019020182A1 (en) * 2017-07-26 2019-01-31 Huawei Technologies Co., Ltd. Construction of a polar code based on a distance criterion and a reliability criterion, in particular of a multi-kernel polar code

Also Published As

Publication number Publication date
CN114978196A (en) 2022-08-30

Similar Documents

Publication Publication Date Title
US6857097B2 (en) Evaluating and optimizing error-correcting codes using a renormalization group transformation
JP5506878B2 (en) Parity check matrix generation method for low density parity check code
Dai et al. Does Gaussian approximation work well for the long-length polar code construction?
Seidl et al. Improving successive cancellation decoding of polar codes by usage of inner block codes
CN110868226B (en) Coding and decoding method of polarization code based on mixed polarization kernel
CN107896137B (en) Sequencing method suitable for splitting decoding path of polar code
CN1961517B (en) Encoding, decoding method and device, device for storing encoding data
CN108833052B (en) Channel polarization decoding path metric value sorting method
CN108650029B (en) Error correction coding and decoding method suitable for quantum secure direct communication
CN114978196B (en) Multi-core polarization code rapid serial offset list decoding method
CN116614142A (en) Combined decoding method based on BPL decoding and OSD decoding
CN116760425A (en) CRC auxiliary OSD decoding method of LDPC code
CN116015538A (en) Non-orthogonal multiple access communication method based on Polar codes
CN113014271B (en) Polarization code BP decoding method for reducing turnover set
CN114257342A (en) Coding and decoding method for two-user multiple access system based on non-binary polarization code
WO2022012258A1 (en) Modulation and encoding method and apparatus, demodulation and decoding method and apparatus, device, and communication system
CN109525252A (en) List decoding method is serially offset based on the polarization code for simplifying three rank key set
CN113055029A (en) System polarization code encoding and decoding integrated device capable of multiplexing resources and encoding and decoding method
Gelincik et al. Achieving PAC code performance with SCL decoding without extra computational complexity
CN109639394B (en) Edge-dividing type relay decoding method for multi-edge type low-density parity check code
CN106921396B (en) mixed decoding method for LDPC code
CN111541457A (en) Low-time-delay low-complexity decoding method for polar code serial offset list
Xia et al. A two-staged adaptive successive cancellation list decoding for polar codes
CN111835363A (en) LDPC code decoding method based on alternative direction multiplier method
CN115348010B (en) Method and system suitable for eliminating residual error codes of continuous variable quantum key distribution

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant