CN114221664A - Low-complexity polar code simplified soft elimination list decoder and decoding method - Google Patents

Low-complexity polar code simplified soft elimination list decoder and decoding method Download PDF

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CN114221664A
CN114221664A CN202111546123.1A CN202111546123A CN114221664A CN 114221664 A CN114221664 A CN 114221664A CN 202111546123 A CN202111546123 A CN 202111546123A CN 114221664 A CN114221664 A CN 114221664A
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information
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郭锐
刘重阳
应娜
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Hangzhou Dianzi University
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    • 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
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Abstract

The invention discloses a low-complexity decoding device and a decoding method for a simplified soft elimination list of a polar code. The invention comprises the following steps: a parameter configuration module for providing the required information for the following module before the decoding starts; a permutation arrangement selection module for providing a required set of permutation arrangements for subsequent modules; the preprocessing module is used for carrying out corresponding replacement on the channel receiving information according to the replacement arrangement set; a plurality of simplified soft elimination decoding modules with the same factor graph form are used for decoding in parallel, and each simplified soft elimination decoding module comprises an initialization sub-module, an iterative decoding sub-module and a decoding bit judgment sub-module; and the decision device module is used for selecting the decoding sequence corresponding to the minimum path metric value and extracting the initial information sequence from the decoding sequence. The invention solves the technical problem that the soft elimination list decoder in the prior art has high computational complexity, and reduces the computational complexity of the soft elimination list decoder.

Description

Low-complexity polar code simplified soft elimination list decoder and decoding method
Technical Field
The invention belongs to the technical field of channel coding, and relates to a low-complexity decoding device and a decoding method for a simplified soft elimination list of a polarization code.
Background
Polar codes are a class of linear error correcting codes that are mathematically proven to achieve channel capacity when their code length is close to infinity. The polar code coding scheme has been adopted as a coding method for a control channel of a fifth generation communication system in the discussion of the 87 th meeting in the RANI, and has wide application in very large scale machine communication (mtc), ultra-reliable low-latency (URRLC) communication and enhanced mobile broadband communication (eMBB).
The polar code decoders currently in the mainstream can be classified into two categories according to their decoding outputs, namely hard output decoders and soft output decoders. The polar code hard output decoder is used for directly judging the information transmission bit according to the received signal, and the polar code soft output decoder is used for calculating the soft information value of the transmitted information according to the received signal and then carrying out hard judgment on the soft information value. Therefore, the soft output decoder has better flexibility and adaptability. Currently, a polar code hard output decoder mainly includes a Successive Cancellation (SC) decoder, a Successive Cancellation List (SCL) decoder, and a CRC-assisted successive cancellation list (CA-SCL) decoder, and a polar code soft output decoder mainly includes a Belief Propagation (BP) decoder, a Soft Cancellation (SCAN) decoder, and a soft cancellation list (SCANL) decoder. In terms of decoding performance, the performance of the SC decoder is the worst, the BP decoder and the SCAN decoder have similar performance and are superior to the SC decoder, and the performance of the SCANL decoder is greatly improved compared with the former three, but is not as good as that of the SCL decoder and the CA-SCL decoder.
In some 5G scene applications, the decoder is required to output soft information, so that the purpose of outputting soft information can be achieved only by using soft output decoders such as a BP decoder, a SCAN decoder, a scall decoder and the like in this case. Although the performance of the SCANL decoder is good, the calculation complexity is high, and the SCANL decoder is difficult to realize in practical application. Therefore, how to design a decoder which can maintain the high decoding performance of the SCANL decoder and reduce the computational complexity of the SCANL decoder is a technical problem to be solved at present.
Disclosure of Invention
An object of the present invention is to solve the problem of high computational complexity of the soft erasure list decoder in the prior art, and to provide a low-complexity polarization code simplified soft erasure list decoder for reducing the computational complexity of the soft erasure list decoder.
The decoder of the present invention includes: the device comprises a parameter configuration module, a permutation and arrangement selection module, a preprocessing module, a plurality of simplified soft elimination decoding modules and a decision device module; the simplified soft cancellation decoding module includes: initializing a sub-module, iterating a decoding sub-module and decoding a bit judgment sub-module;
the parameter configuration module is used for providing required information for the subsequent module before decoding begins;
the permutation and arrangement selection module is used for providing a required permutation and arrangement set for a subsequent module;
the preprocessing module is used for carrying out corresponding replacement on the channel receiving information according to the replacement arrangement set;
the simplified soft elimination decoding modules have the same factor graph form, and the simplified soft elimination decoding modules decode in parallel, wherein: the initialization sub-module carries out initial parameter setting on the decoding factor graph; the iterative decoding submodule is used for soft information updating and transmitting operation, decoding nodes are deleted, and nodes in a factor graph are classified by taking initial parameters set on nodes corresponding to freezing positions in the initialization submodule as standards; the decoding bit decision submodule is used for acquiring decoding sequence information;
the decision device module is used for selecting the decoding sequence corresponding to the minimum path metric value and taking out the initial information sequence from the decoding sequence.
Another object of the present invention is to provide a decoding method of the decoder. The method comprises the following specific steps:
step (1) inputs given polarization code parameter information (N, K, F) and received channel log likelihood ratio information LLRs into a parameter configuration module, wherein LLRs is { LLR }0,LLR1,…,LLRN-1Determining index information pos as (0,1, …, N-1) according to the channel log-likelihood ratio information LLRs, wherein N represents a polar code length, K represents an initial information sequence length, F represents a frozen bit index set, and the length is N-K;
and performing parameter configuration according to the polarization code parameter information, the channel log-likelihood ratio information and the index information, and inputting all information into an information storage unit in a parameter configuration module for a subsequent module to read at any time.
Step (2) the permutation and arrangement selection module reads index information from the parameter configuration module and defines the arrangement pi with the length of N 00,1, …, N-1 }; will arrange pi0The middle elements are arranged and combined to obtain N! In different arrangements i.e. { π0,π1,…,πN！-1Comparing Hamming distances among the arrays, selecting the first L arrays with large Hamming distances to form an array set pi (pi) ═ pi0,π1,…,πL-1}。
And (3) reading the permutation set pi (pi) ═ pi in the permutation and arrangement selection module by the preprocessing module0,π1,…,πL-1And polarization code parameter information (N, K, F) and channel log likelihood ratio information LLRs ═ LLR { (LLR) } in the parameter configuration module0,LLR1,…,LLRN-1And permutation is performed on the LLRs according to the permutation set pi (pi), and a permutation log likelihood ratio information set pi (LLRs) is obtained0,LLRs1,…,LLRsL-1}＝Π[π(LLRs)]。
And (4) correspondingly inputting elements in the replacement log-likelihood ratio information set Π (LLRs) into L simplified soft elimination decoding modules with the same factor graph form for parallel decoding, and reading the polarization code parameter information (N, K and F) from the preprocessing module by the simplified soft elimination decoding modules. Wherein:
(4-1) the initialization submodule carries out initial parameter setting on the decoding factor graph by utilizing the permutation log likelihood ratio information and the polarization code parameter information (N, K, F), and sets left information lambda on the rightmost column node of the decoding factor graphi nThe initial parameter is the information of the replacement log likelihood ratio, and the right information beta on the node corresponding to the freezing position of the leftmost column of the factor graph is seti 0The initial parameter gamma is a positive integer, and the right information initial parameters on the other nodes are set to be 0:
Figure BDA0003415810900000033
i is more than or equal to 0 and less than or equal to N-1, and F is a frozen bit index set;
(4-2) the iterative decoding submodule carries out soft information updating and transmitting operation based on a decoding factor graph structure, and simplification is carried out by deleting decoding nodes in the soft information updating process;
calculating a path metric value PM, initializing the PM to be 0, and updating the path metric value when a node corresponding to a frozen bit is encountered, wherein the rule is updatedComprises the following steps: PM- λi,i∈F，λiLeft information on the corresponding node of the frozen bit; when the left information and the right information respectively reach the left side and the right side of the decoding factor graph, the iterative decoding submodule completes decoding to obtain path metric value information;
(4-3) the decoding bit decision sub-module carries out bit decision operation according to the soft information on the leftmost node of the decoding factor graph, and the decoding sequence of the ith node
Figure BDA0003415810900000034
λi 0、βi 0Left and right information on the node, respectively.
Step (5) when the parallel decoding of the L simplified soft elimination decoding modules is completed, the decision device module reads the decoding sequence information and the corresponding path metric value information from the L simplified soft elimination decoding modules in sequence and uses the decoding sequence set to collect
Figure BDA0003415810900000036
And the path metric set Pi (PM) { PM }0,PM1,…,PML-1Storing in the form of II, selecting the smallest path metric value PM in II (PM) setmin＝min{PM0,…,PML-1According to the minimum path metric value PMminAt index positions in the collection, obtaining the collection
Figure BDA0003415810900000037
Coding sequence of middle corresponding index position
Figure BDA0003415810900000038
Step (6) from the decoded sequence
Figure BDA0003415810900000039
Taking out K bit long initial information sequence
Figure BDA00034158109000000310
And finishing decoding.
Further, in the step (2),array piaAnd pibHamming distance therebetween
Figure BDA00034158109000000311
δ is the kronecker pulse function.
Further, the simplification by the decoding node deletion described in (4-2) is specifically as follows,
Figure BDA00034158109000000312
for the value of the soft information to be transferred, t is more than or equal to 0 and less than or equal to (log)2N-1)：
(a) If node
Figure BDA0003415810900000041
And node
Figure BDA0003415810900000042
Upper right information
Figure BDA0003415810900000043
All are less than gamma, then the node is judged
Figure BDA0003415810900000044
And node
Figure BDA0003415810900000045
Is an information bit node; the soft information updating calculation process comprises the following steps:
Figure BDA0003415810900000046
Figure BDA0003415810900000047
function(s)
Figure BDA00034158109000000434
(b) If node
Figure BDA0003415810900000048
Upper right information
Figure BDA0003415810900000049
Node point
Figure BDA00034158109000000410
Upper right information
Figure BDA00034158109000000411
Then the decision node
Figure BDA00034158109000000412
To freeze a bit node, a node
Figure BDA00034158109000000413
Is an information bit node; and betai tThe related soft information updating calculation process is simplified as follows:
Figure BDA00034158109000000415
Figure BDA00034158109000000416
(c) if node
Figure BDA00034158109000000417
Upper right information
Figure BDA00034158109000000418
Node point
Figure BDA00034158109000000419
Upper right information
Figure BDA00034158109000000420
Then the decision node
Figure BDA00034158109000000421
Being information bit nodes, nodes
Figure BDA00034158109000000422
Is a frozen bit node; and
Figure BDA00034158109000000423
the related soft information updating calculation process is simplified as follows:
Figure BDA00034158109000000424
Figure BDA00034158109000000425
(d) if node
Figure BDA00034158109000000426
And node
Figure BDA00034158109000000427
Upper right information
Figure BDA00034158109000000428
Are all more than or equal to gamma, then the node is judged
Figure BDA00034158109000000429
And node
Figure BDA00034158109000000430
Is a frozen bit node; the soft information updating calculation process comprises the following steps:
Figure BDA00034158109000000431
compared with the prior art, the invention has the following beneficial effects: the decoding module in the soft elimination list decoder is improved by using a decoding node deleting technology, the calculation process related to the soft information on the frozen bit node in the decoding process is simplified, and the frozen bit node is approximately deleted, so that the calculation complexity of the decoder is reduced.
Drawings
FIG. 1 is a schematic diagram of a decoder according to the present invention;
FIG. 2 is a diagram illustrating initial parameter settings in an initialization submodule;
FIG. 3 is a diagram of soft information transfer in a soft erasure coding unit factor graph;
FIG. 4 is a diagram of approximate deleted nodes
Figure BDA00034158109000000432
A post-soft information transfer diagram;
FIG. 5 is a diagram of approximate deleted nodes
Figure BDA00034158109000000433
And (4) a rear soft information transmission schematic diagram.
Detailed Description
The technical scheme of the invention is further specifically described by the following embodiments and the accompanying drawings.
A low complexity decoding method for simplified soft erasure list of polar codes, using a decoder as shown in fig. 1, comprising: the device comprises a parameter configuration module, a permutation and arrangement selection module, a preprocessing module, a plurality of simplified soft elimination decoding modules and a decision device module; the simplified soft cancellation decoding module includes: the device comprises an initialization sub-module, an iterative decoding sub-module and a decoding bit judgment sub-module.
The parameter configuration module is used for providing required information for the subsequent module before decoding begins;
the permutation and arrangement selection module is used for providing a required permutation and arrangement set for a subsequent module;
the preprocessing module is used for carrying out corresponding replacement on the channel receiving information according to the replacement arrangement set;
the simplified soft elimination decoding modules have the same factor graph form, and the simplified soft elimination decoding modules decode in parallel, wherein: the initialization sub-module carries out initial parameter setting on the decoding factor graph; the iterative decoding submodule is used for soft information updating and transmitting operation, decoding nodes are deleted, and nodes in a factor graph are classified by taking initial parameters set on nodes corresponding to freezing positions in the initialization submodule as standards; the decoding bit decision submodule is used for acquiring decoding sequence information;
the decision device module is used for selecting the decoding sequence corresponding to the minimum path metric value and taking out the initial information sequence from the decoding sequence.
The specific decoding method is as follows:
step (1) inputs given polarization code parameter information (N, K, F) and received channel log likelihood ratio information LLRs into a parameter configuration module, wherein LLRs is { LLR }0,LLR1,…,LLRN-1Determining index information pos as (0,1, …, N-1) according to the channel log-likelihood ratio information LLRs, wherein N represents a polar code length, K represents an initial information sequence length, F represents a frozen bit index set, and the length is N-K;
and performing parameter configuration according to the polarization code parameter information, the channel log-likelihood ratio information and the index information, and inputting all information into an information storage unit in a parameter configuration module for a subsequent module to read at any time.
Step (2) the permutation and arrangement selection module reads index information from the parameter configuration module and defines the arrangement pi with the length of N 00,1, …, N-1 }; will arrange pi0The middle elements are arranged and combined to obtain N! In different arrangements i.e. { π0,π1,…,πN！-1Comparing Hamming distances among the arrays, selecting the first L arrays with large Hamming distances to form an array set pi (pi) ═ pi0,π1,…,πL-1}; array piaAnd pibHamming distance therebetween
Figure BDA0003415810900000051
δ is the kronecker pulse function.
And (3) reading the permutation set pi (pi) ═ pi in the permutation and arrangement selection module by the preprocessing module0,π1,…,πL-1And polarization code parameter information (N, K, F) and channel log likelihood ratio information LLRs ═ LLR { (LLR) } in the parameter configuration module0,LLR1,…,LLRN-1And permutation is performed on the LLRs according to the permutation set pi (pi), and a permutation log likelihood ratio information set pi (LLRs) is obtained0,LLRs1,…,LLRsL-1}＝Π[π(LLRs)]。
And (4) correspondingly inputting elements in the replacement log-likelihood ratio information set Π (LLRs) into L simplified soft elimination decoding modules with the same factor graph form for parallel decoding, and reading the polarization code parameter information (N, K and F) from the preprocessing module by the simplified soft elimination decoding modules. The simplified soft cancellation decoding module includes: the device comprises an initialization sub-module, an iterative decoding sub-module and a decoding bit judgment sub-module.
The initialization submodule carries out initial parameter setting on the decoding factor graph by utilizing the permutation log likelihood ratio information and the polarization code parameter information (N, K, F). Taking the decoding factor graph shown in fig. 2 as an example, the initialization sub-module sets left information λ on the rightmost column node of the decoding factor graphi nThe initial parameter is the information of the replacement log likelihood ratio, and the right information beta on the node corresponding to the freezing position of the leftmost column of the factor graph is seti 0The initial parameter gamma is a positive integer, and the right information initial parameters on the other nodes are set to be 0:
Figure BDA0003415810900000063
i is more than or equal to 0 and less than or equal to N-1, and F is a frozen bit index set.
And after the initialization setting is completed, the iterative decoding submodule starts to operate. The iterative decoding submodule carries out soft information updating and transmitting operation based on a decoding factor graph structure, and a decoding node deleting technology is adopted to simplify the soft information updating process. The decoding node deletion technique is described below, taking the decoding unit factor graph shown in FIG. 3 as an example, where delivery is required
Figure BDA0003415810900000064
Figure BDA0003415810900000065
Four soft information values, t is more than or equal to 0 and less than or equal to (log)2N-1), the remaining soft information values are known. And classifying the nodes in the unit factor graph according to the initial parameter gamma set on the nodes corresponding to the freezing bits in the initialization submodule. The frozen bit nodes are represented as black nodes, the information bit nodes are represented as white nodes, and the non-decision nodes are represented as shaded nodes. Nodes in the unit factor graph shown in FIG. 3
Figure BDA0003415810900000066
And node
Figure BDA0003415810900000067
Upper right information
Figure BDA0003415810900000068
For the soft information sought, its value is unknown, so the node
Figure BDA0003415810900000069
And node
Figure BDA00034158109000000610
I.e. non-decision nodes and represented by shaded nodes, and nodes
Figure BDA00034158109000000611
And node
Figure BDA00034158109000000612
Upper right information
Figure BDA00034158109000000613
Are known, and therefore can be paired with nodes
Figure BDA00034158109000000614
And node
Figure BDA00034158109000000615
The classification decision is made as follows:
(a) if node
Figure BDA00034158109000000616
And node
Figure BDA00034158109000000617
Upper right information
Figure BDA00034158109000000618
All are less than gamma, then the node is judged
Figure BDA00034158109000000619
And node
Figure BDA00034158109000000620
Is an information bit node; the soft information updating calculation process comprises the following steps:
Figure BDA00034158109000000621
Figure BDA00034158109000000622
function(s)
Figure BDA00034158109000000628
(b) If node
Figure BDA00034158109000000623
Upper right information
Figure BDA00034158109000000624
Node point
Figure BDA00034158109000000625
Upper right information
Figure BDA00034158109000000626
Then the decision node
Figure BDA00034158109000000627
To freeze a bit node, a node
Figure BDA0003415810900000071
Is an information bit node; at the moment, the soft information is updated and calculated in the process of the node
Figure BDA0003415810900000072
The calculation steps related to the above right information are simplified and approximated as nodes
Figure BDA0003415810900000073
The deletion processing of (1). Approximate deletion node
Figure BDA0003415810900000074
The post-soft information transfer scheme is shown in FIG. 4, which is derived from FIG. 4, and βi tThe related soft information updating calculation process is simplified as follows:
Figure BDA0003415810900000076
Figure BDA0003415810900000077
(c) if node
Figure BDA0003415810900000078
Upper right information
Figure BDA0003415810900000079
Node point
Figure BDA00034158109000000710
Upper right information
Figure BDA00034158109000000711
Then the decision node
Figure BDA00034158109000000712
Being information bit nodes, nodes
Figure BDA00034158109000000713
Is a frozen bit node; approximating the nodes by the same way as (b)
Figure BDA00034158109000000714
And (5) deleting. Approximate deletion node
Figure BDA00034158109000000715
The post-soft information transfer scheme is shown in FIG. 5, which is obtainable from FIG. 5, and
Figure BDA00034158109000000716
the related soft information updating calculation process is simplified as follows:
Figure BDA00034158109000000717
(d) if node
Figure BDA00034158109000000718
And node
Figure BDA00034158109000000719
Upper right information
Figure BDA00034158109000000720
Are all more than or equal to gamma, then the node is judged
Figure BDA00034158109000000721
And node
Figure BDA00034158109000000722
Is a frozen bit node; the soft information updating calculation process comprises the following steps:
Figure BDA00034158109000000723
as can be seen from the simplified soft information update calculation process, approximately deleting a frozen bit node can reduce twice
Figure BDA00034158109000000732
And (6) operation.
The more frozen nodes, the better the computational complexity reduction effect.
In the iterative updating process of the soft information, a path metric value PM is also required to be calculated, the PM is initialized to be 0, when a node corresponding to a frozen bit is encountered, the path metric value is updated, and the updating rule is as follows: PM- λi,i∈F，λiThe left information on the corresponding node is frozen. And when the left information and the right information respectively reach the left side and the right side of the decoding factor graph, the iterative decoding submodule completes decoding to obtain path metric value information.
The decoding bit decision sub-module carries out bit decision operation according to the soft information on the leftmost node of the decoding factor graph,decoding sequence of ith bit node
Figure BDA00034158109000000724
λi 0、βi 0Left and right information on the node, respectively.
Step (5) when the parallel decoding of the L simplified soft elimination decoding modules is completed, the decision device module reads the decoding sequence information and the corresponding path metric value information from the L simplified soft elimination decoding modules in sequence and uses the decoding sequence set to collect
Figure BDA00034158109000000726
And the path metric set Pi (PM) { PM }0,PM1,…,PML-1Storing in the form of II, selecting the smallest path metric value PM in II (PM) setmin＝min{PM0,…,PML-1According to the minimum path metric value PMminAt index positions in the collection, obtaining the collection
Figure BDA00034158109000000727
Coding sequence of middle corresponding index position
Figure BDA00034158109000000728
Step (6) from the decoded sequence
Figure BDA00034158109000000729
Taking out K bit long initial information sequence
Figure BDA00034158109000000730
And finishing decoding.

Claims (4)

1. A low complexity reduced soft erasure list decoder for a polar code, comprising:
the device comprises a parameter configuration module, a permutation and arrangement selection module, a preprocessing module, a plurality of simplified soft elimination decoding modules and a decision device module; the simplified soft cancellation decoding module includes: initializing a sub-module, iterating a decoding sub-module and decoding a bit judgment sub-module;
the parameter configuration module is used for providing required information for the subsequent module before decoding begins;
the permutation and arrangement selection module is used for providing a required permutation and arrangement set for a subsequent module;
the preprocessing module is used for carrying out corresponding replacement on the channel receiving information according to the replacement arrangement set;
the simplified soft elimination decoding modules have the same factor graph form, and the simplified soft elimination decoding modules decode in parallel, wherein: the initialization sub-module carries out initial parameter setting on the decoding factor graph; the iterative decoding submodule is used for soft information updating and transmitting operation, decoding nodes are deleted, and nodes in a factor graph are classified by taking initial parameters set on nodes corresponding to freezing positions in the initialization submodule as standards; the decoding bit decision submodule is used for acquiring decoding sequence information;
the decision device module is used for selecting the decoding sequence corresponding to the minimum path metric value and taking out the initial information sequence from the decoding sequence.
2. The method for decoding a reduced soft erasure list using a decoder according to claim 1, wherein the method is embodied as:
step (1) inputs given polarization code parameter information (N, K, F) and received channel log likelihood ratio information LLRs into a parameter configuration module, wherein LLRs is { LLR }0,LLR1,…,LLRN-1Determining index information pos as (0,1, …, N-1) according to the channel log-likelihood ratio information LLRs, wherein N represents a polar code length, K represents an initial information sequence length, F represents a frozen bit index set, and the length is N-K;
carrying out parameter configuration according to the polarization code parameter information, the channel log-likelihood ratio information and the index information, and inputting all information into an information storage unit in a parameter configuration module for a subsequent module to read at any time;
step (2) the permutation and arrangement selection module reads index information from the parameter configuration module and defines the arrangement pi with the length of N00,1, …, N-1 }; will arrange pi0Middle elementPerforming permutation and combination to obtain N! In different arrangements i.e. { π0,π1,…,πN！-1Comparing Hamming distances among the arrays, selecting the first L arrays with large Hamming distances to form an array set pi (pi) ═ pi0,π1,…,πL-1}；
And (3) reading the permutation set pi (pi) ═ pi in the permutation and arrangement selection module by the preprocessing module0,π1,…,πL-1And polarization code parameter information (N, K, F) and channel log likelihood ratio information LLRs ═ LLR { (LLR) } in the parameter configuration module0,LLR1,…,LLRN-1And permutation is carried out on the LLRs according to the permutation set pi (pi), and a permutation log likelihood ratio information set pi (LLRs) is obtained0,LLRs1,…,LLRsL-1}＝Π[π(LLRs)]；
Correspondingly inputting elements in a replacement log-likelihood ratio information set Π (LLRs) into L simplified soft elimination decoding modules with the same factor graph form for parallel decoding, and reading polarization code parameter information (N, K and F) from a preprocessing module by the simplified soft elimination decoding modules; wherein:
(4-1) the initialization submodule carries out initial parameter setting on the decoding factor graph by utilizing the replacement log likelihood ratio information and the polarization code parameter information (N, K, F), and sets left information on the rightmost column node of the decoding factor graph
Figure FDA0003415810890000021
The initial parameter is the information of the replacement log likelihood ratio, and the right information on the node corresponding to the freezing position of the leftmost column of the factor graph is set
Figure FDA0003415810890000022
The initial parameter gamma is a positive integer, and the right information initial parameters on the other nodes are set to be 0:
Figure FDA0003415810890000023
i is more than or equal to 0 and less than or equal to N-1, and F is a frozen bit index set;
(4-2) the iterative decoding submodule carries out soft information updating and transmitting operation based on a decoding factor graph structure, and simplification is carried out by deleting decoding nodes in the soft information updating process;
calculating a path metric value PM, initializing the PM to be 0, and updating the path metric value when a node corresponding to a frozen bit is encountered, wherein the updating rule is as follows: PM- λi,i∈F，λiLeft information on the corresponding node of the frozen bit; when the left information and the right information respectively reach the left side and the right side of the decoding factor graph, the iterative decoding submodule completes decoding to obtain path metric value information;
(4-3) the decoding bit decision sub-module carries out bit decision operation according to the soft information on the leftmost node of the decoding factor graph, and the decoding sequence of the ith node
Figure FDA0003415810890000024
Figure FDA0003415810890000025
Left information and right information on the node respectively;
step (5) when the parallel decoding of the L simplified soft elimination decoding modules is completed, the decision device module reads the decoding sequence information and the corresponding path metric value information from the L simplified soft elimination decoding modules in sequence and uses the decoding sequence set to collect
Figure FDA0003415810890000026
And the path metric set Pi (PM) { PM }0,PM1,…,PML-1Storing in the form of II, selecting the smallest path metric value PM in II (PM) setmin＝min{PM0,…,PML-1According to the minimum path metric value PMminAt index positions in the collection, obtaining the collection
Figure FDA0003415810890000027
Coding sequence of middle corresponding index position
Figure FDA0003415810890000028
Step (6) from the decoded sequence
Figure FDA0003415810890000029
Taking out K bit long initial information sequence
Figure FDA00034158108900000210
And finishing decoding.
3. The method of reduced soft erasure list decoding of polar codes according to claim 2, wherein: in step (2), n is arrangedaAnd pibHamming distance therebetween
Figure FDA0003415810890000031
δ is the kronecker pulse function.
4. The reduced soft erasure list decoding method of polar codes according to claim 2, wherein said reduction by decoding node erasure in (4-2) is as follows,
Figure FDA0003415810890000032
for the value of the soft information to be transferred, t is more than or equal to 0 and less than or equal to (log)2N-1)：
(a) If node
Figure FDA0003415810890000033
And node
Figure FDA0003415810890000034
Upper right information
Figure FDA0003415810890000035
All are less than gamma, then the node is judged
Figure FDA0003415810890000036
And node
Figure FDA0003415810890000037
As information bitsA node; the soft information updating calculation process comprises the following steps:
Figure FDA0003415810890000038
Figure FDA0003415810890000039
function(s)
Figure FDA00034158108900000334
(b) If node
Figure FDA00034158108900000310
Upper right information
Figure FDA00034158108900000311
Node point
Figure FDA00034158108900000312
Upper right information
Figure FDA00034158108900000313
Then the decision node
Figure FDA00034158108900000314
To freeze a bit node, a node
Figure FDA00034158108900000315
Is an information bit node; and
Figure FDA00034158108900000316
the related soft information updating calculation process is simplified as follows:
Figure FDA00034158108900000317
Figure FDA00034158108900000318
(c) if node
Figure FDA00034158108900000319
Upper right information
Figure FDA00034158108900000320
Node point
Figure FDA00034158108900000321
Upper right information
Figure FDA00034158108900000322
Then the decision node
Figure FDA00034158108900000323
Being information bit nodes, nodes
Figure FDA00034158108900000324
Is a frozen bit node; and
Figure FDA00034158108900000325
the related soft information updating calculation process is simplified as follows:
Figure FDA00034158108900000326
Figure FDA00034158108900000327
(d) if node
Figure FDA00034158108900000328
And node
Figure FDA00034158108900000329
Upper right information
Figure FDA00034158108900000330
Are all more than or equal to gamma, then the node is judged
Figure FDA00034158108900000331
And node
Figure FDA00034158108900000332
Is a frozen bit node; the soft information updating calculation process comprises the following steps:
Figure FDA00034158108900000333
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117375635A (en) * 2023-11-09 2024-01-09 中国人民解放军军事科学院系统工程研究院 Geometric representation method and device for BP decoding of satellite communication polarization code

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117375635A (en) * 2023-11-09 2024-01-09 中国人民解放军军事科学院系统工程研究院 Geometric representation method and device for BP decoding of satellite communication polarization code
CN117375635B (en) * 2023-11-09 2024-05-03 中国人民解放军军事科学院系统工程研究院 Geometric representation method and device for BP decoding of satellite communication polarization code

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