CN116470923A - Method for constructing list search of PAC code or polarization code - Google Patents

Method for constructing list search of PAC code or polarization code Download PDF

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CN116470923A
CN116470923A CN202310387053.2A CN202310387053A CN116470923A CN 116470923 A CN116470923 A CN 116470923A CN 202310387053 A CN202310387053 A CN 202310387053A CN 116470923 A CN116470923 A CN 116470923A
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list
information set
code
path
pac
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王家豪
蒋世荣
夏春芳
李红慧
闫源滨
林雨润
刘澳
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China University of Geosciences
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/29—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 combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
    • H03M13/2957—Turbo codes and decoding
    • H03M13/296—Particular turbo code structure
    • H03M13/2972—Serial concatenation using convolutional component codes
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
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    • G06F16/22—Indexing; Data structures therefor; Storage structures
    • G06F16/2282—Tablespace storage structures; Management thereof
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
    • G06F16/24—Querying
    • G06F16/245—Query processing
    • G06F16/2455—Query execution
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention discloses a list searching construction method of PAC codes or polarization codes, which comprises the following steps: determining an initial information set, an alternative information set and a generalized information set according to the RM score; obtaining partial weight spectrum of the generalized information set through a list (or SCL) decoding algorithm, and storing a source word sequence, a code word sequence and code weight of the code word sequence; determining a list search metric, and initializing a list of the list search; and each list carries out path splitting and path pruning according to the initial information set and the alternative information set of the current list, if the initial information set in each list is equal to the information bit length, returning the initial information set in the list with the minimum list searching measurement as the information set constructed by the PAC code or the polarization code, otherwise, continuing path splitting and path pruning. Compared with the codes constructed by the most advanced PAC codes and the polarized code construction methods at present, the codes constructed by the list search construction method disclosed by the invention have better block error rate (BLER) performance, can solve the problem that the coding construction method deviates from a discrete boundary, and are simple in construction method.

Description

Method for constructing list search of PAC code or polarization code
Technical Field
The invention relates to the technical field of 5G mobile communication and channel coding, in particular to a list searching construction method of PAC codes or polarization codes.
Background
In 2012, the fifth generation mobile communication (5G) system has gradually become a major research hotspot in the field of mobile communication. A large number of scholars and engineers are striving to pursue shannon capacity limits to improve the error performance of channel coding. Although the performance of Turbo codes and LDPC codes has been very small from shannon capacity limits, capacity limits have not been reached at all times. Polarization codes are the first channel coding schemes that can be strictly proven to reach capacity limits in binary input symmetric discrete memory-less channels (BI-BDC). The polar code can reach the capacity limit when the code length is towards infinity by using a Serial Cancellation (SC) decoding algorithm, but the error code performance loss is serious when the channel polarization is insufficient in the middle and short code lengths. Although researchers have proposed Serial Cancellation List (SCL) decoding to address channel polarization inadequacies, discrete boundaries have not been approached. In order to obtain more excellent BLER performance, arikan uses a one-to-one convolution transformation as a precoding step before Polarization transformation, and the concatenated code is referred to as Polarization-adjusted convolution (PAC) code.
The construction of the polarization code is mainly based on the channel polarization theory to estimate the reliability of the sub-channels, and then the information set and the freezing set are selected. Channel polarization is achieved through two processes of channel combination and channel splitting, so that two stages of differentiation are generated on the split channels: one part becomes a noise-free channel with a capacity approaching 1 and the other part becomes a pure noise channel with a capacity approaching 0. The data to be transmitted is only required to be loaded into the noiseless channel, and the pure noise channel is not used, so that the reliable transmission of the data can be realized. The method for evaluating the reliability of the sub-channels by using the polarization codes is commonly as follows: the above-mentioned polarization code construction method is only applicable to SC decoding algorithm of polarization code, and SCL decoding algorithm and SC-Fano decoding algorithm are Maximum Likelihood (ML) decoding algorithm, so that research is mostly conducted from improving weight spectrum, and its bottleneck is the code weight of minimum weight codeword. Researchers at the Hua-Chen company use RM-polar construction methods to improve the weight spectrum, where the information set chooses as much as possible the sub-channels of great row weight, and for the sub-channels of minimum row weight can be chosen by either Gaussian construction or polar weight construction. Although the RM-polar construction method has superior BLER performance compared to the gaussian construction method and the polarization weight construction method, the optimal BLER performance of the polarization code is still not achieved. It is therefore a hotspot in polar code construction that needs to have better BLER performance.
PAC codes can solve the problems of slow channel polarization, serious channel capacity loss and the like of the polarized codes under the actual code length, so that the performance close to discrete boundaries can be realized after proper construction and decoding algorithm is selected. Although PAC codes are concatenated codes of convolutional codes and polarization codes, the construction is different from that of the polarization codes. Most of PAC code decoding algorithms are Maximum Likelihood (ML) decoding algorithms, so research is mostly conducted from improving weight spectrum, and the bottleneck is the code weight of the minimum weight codeword. The use of RM construction methods when Arikan proposes PAC codes makes it necessary to select as much as possible sub-channels of great row size as the information set, but RM construction methods are constructed only under specific parameters, so RM-polar construction methods, monte carlo construction methods, weighted sum construction methods, and the like appear. While RM-polar construction methods, monte carlo construction methods, and weighted sum construction methods can all be seen as generalizations of RM construction methods, although there is also good construction performance, the constructed codes still deviate from the discrete boundaries and the construction method is complex. An overview shows how to bring the codes of PAC code or polar code construction close to the discrete world (or better BLER performance) and simpler construction methods are current research hotspots.
Disclosure of Invention
In view of this, in order to make the codes of PAC code or polarization code construction approach to the discrete boundary and to obtain a simpler construction method, the present invention proposes a list search construction method of PAC code or polarization code, comprising the steps of:
s1, determining an initial information set, an alternative information set and a generalized information set of a list searching construction method according to an RM score of the RM construction method, returning the initial information set to serve as an information set constructed by PAC codes or polarization codes if the number of the initial information set is equal to the length of information bits, otherwise executing S2;
s2, obtaining a partial weight spectrum of the generalized information set through a decoding algorithm, and storing a source word sequence, a codeword sequence and code weights of the codeword sequence;
s3, determining a list searching measure, initializing a list searched by the list, and determining a list searched by the current list according to the partial weight spectrum, wherein the number of the list searched by the initial list is the number of the initial information sets, and each list searched by the list comprises the initial information sets and the alternative information sets;
s4, carrying out path splitting and path pruning on each list searched list according to the initial information set and the alternative information set of the list searched by the current list, returning the initial information set in the list searched by the list with the minimum list searching metric to serve as the information set constructed by the PAC code or the polarization code if the initial information set in the list searched by the list is equal to the information bit length, otherwise, continuing path splitting and path pruning.
The technical scheme provided by the invention has the beneficial effects that:
the code constructed by the list search construction method disclosed by the invention has more excellent BLER performance, can solve the problem that the PAC code and polarization code construction method deviate from discrete boundaries, and is simpler than other construction methods. Compared with the most advanced RM-polar construction method, monte Carlo construction method and weighting and construction method of PAC codes, the codes constructed by the list search construction method disclosed by the invention can have better BLER performance, and the codes constructed by the list search construction method disclosed by the invention can be close to the discrete boundary. Compared with the most advanced Gaussian approximation construction method, the polarization weight construction method and the RM-polar construction method of the polarized codes, the codes constructed by the list search construction method disclosed by the invention can have more excellent BLER performance.
Drawings
Fig. 1 is a flowchart of a list search construction method of PAC codes or polarization codes of the present invention;
FIG. 2 is a flowchart of acquiring partial weight spectrum of PAC code through list decoding according to the embodiment of the present invention;
FIG. 3 is a flowchart of a method for obtaining a partial weight spectrum of a polarization code by SCL decoding of the polarization code according to an embodiment of the present invention;
FIG. 4 is a diagram of path splitting and path pruning for a list search construction method according to an embodiment of the present invention;
FIG. 5 is a graph of bit error rate performance versus list decoded blocks in various configurations for PAC (64, 32) in accordance with embodiments of the present invention;
FIG. 6 is a graph of bit error rate performance versus Viterbi decoded blocks in various configurations for PAC (64, 32) in accordance with embodiments of the present invention;
FIG. 7 is a graph showing bit error rate performance versus tabulated Viterbi decoding blocks in various configurations for PACs (64, 32) according to embodiments of the present invention;
FIG. 8 is a graph comparing error rate performance and complexity of Fano decoding blocks in various configurations for PAC (64, 32) according to embodiments of the present invention;
FIG. 9 is a graph comparing error rate performance and complexity of a Fano decoded block in various configurations for PAC (256,128) in accordance with embodiments of the present invention;
FIG. 10 is a graph of stack decode block error rate performance and complexity versus various configurations for PAC (64, 32) in accordance with embodiments of the present invention;
FIG. 11 is a graph showing the bit error rate performance of SCL decoding blocks in various configurations for a PC (64, 32) according to an embodiment of the present invention;
FIG. 12 is a graph showing the comparison of the bit error rate performance and complexity of an SC-Fano decoded block in various configurations for a PC (64, 32) in accordance with an embodiment of the present invention;
FIG. 13 is a graph showing the comparison of error rate performance and complexity of a Fano decoded block in various configurations for a PC (256,128) in accordance with an embodiment of the present invention;
fig. 14 is a graph of RM scores for example n=64 according to the present invention;
fig. 15 is a RM score chart when n=256 according to the embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be further described with reference to the accompanying drawings.
Referring to fig. 1, fig. 1 is a flowchart of a method for constructing a list search of PAC codes and polarization codes according to the present invention, and an embodiment of the present invention provides a method for constructing a list search of PAC codes and polarization codes, which mainly includes the following steps:
s1, determining an initial information set, an alternative information set and a generalized information set of a list searching construction method according to the RM score of the RM construction method, returning the initial information set to serve as an information set constructed by PAC codes or polarization codes if the number of the initial information set is equal to the length of the information bits, and otherwise executing S2.
S1 specifically comprises the following steps:
s11, setting the code length of PAC code or polarization code as N, the information bit length as K, the list size of a list searching construction method as Lg, the list size of a decoding algorithm as L, and constructing the signal to noise ratio as E b N 0 ；
S12, let n=log 2 N is:
wherein, the value range of r is not less than 0 and not more than r<n，For taking out the combination number of m elements from n elements; the value of r can be calculated by the formula.
S13, making the serial number of the sub-channel be i, and i is more than or equal to 0<N, and the binary expression of the sequence number i isThe RM score s (i) is the number of 1 in the binary expression form of the subchannel number i, and then the RM score s (i) is: />The larger the RM score of index i, the greater the likelihood of being an information set. In this embodiment, the binary representation of subchannel number 5In the form of (1, 0, 1), the RM score s (5) =2.
S14, determining an initial information set a, an alternative information set B and a generalized information set C according to the RM score, wherein the initial information set a contains all indexes of RM score S (i) > r, the alternative information set B contains all indexes of RM score S (i) =r, the generalized information set C is a union set of the initial information set a and the alternative information set B, namely c=a=b, and a= { a (0), a (|a| -1) }, b= { B (0), B (|b| -1) }, c= { C (0), C (|c| -1) }, where |a|b|and |c| are numbers of corresponding set elements.
S15, if the number of the initial information sets |A| is equal to the information bit length K, returning the initial information set A as a construction information set of PAC codes or polarization codes, otherwise executing S2.
S2, obtaining partial weight spectrum of the generalized information set, namely code weight and code weight code word number of the code words in the L lists through a decoding algorithm. And saves the code weights of the L source word sequences, the L codeword sequences. In this embodiment, PAC codes are decoded by a list decoding method, and polarization codes are decoded by an SCL decoding method. S2 specifically comprises the following steps:
the PAC code is constructed:
s201, initializing list decoding the current decoding list size lb=1, transmitting all-zero codeword in noise-free Additive White Gaussian Noise (AWGN) channel, and performing BPSK modulation to obtain the channel Log Likelihood Ratio (LLR) of list decodingWherein->I=0, N-1, for the LLR of the nth stage i.
S202, if the convolution generator polynomial is g= [ g ] 0 ,...,g m ]M+1 is the convolution constraint length, and g 0 ＝g m =1. Decoding all Lb paths by adopting a Serial Cancellation (SC) decoding algorithm, and initializing the path metric value of each path, namelyFor the SC decoding algorithm, polarization-encoded source word bit estimation +.>By local Maximum Likelihood (ML) rulesThe decision is made by the following formula:
when the j-th bit is information bit, the decoding path is completely duplicated, one path of convolution coding source word bit estimationConvolutional encoded source word bit estimate for the other path>And lb=2·lb. The PM value of each path is calculated according to the following formula:
wherein, the liquid crystal display device comprises a liquid crystal display device,final LLR for the j-th stage of the l-th path, < >>Polarization-encoded source word bit estimate for the j-th level of the first path of the polarization code,/>Source word bit estimation, g, of j-i th level convolution coding for the first path of PAC code i Generating polynomial g= [ g ] for convolution in PAC code 0 ,...,g m ]Is a combination of the above-mentioned elements,m+1 is the convolution constraint length, and g 0 ＝g m ＝1；
If Lb > L, L paths with smaller PM values in all Lb paths are selected for reservation, and the rest paths are deleted, so that lb=l.
When the j-th bit is the frozen bit in the list decoding, the convolution coding source word bits of all paths are estimated asAnd calculates the PM value of each path according to the following formula:
wherein, the liquid crystal display device comprises a liquid crystal display device,for the final LLR sequence of the jth level of the ith path,/for the final LLR sequence of the jth level of the jth path,>polarization-encoded source word bit estimate for the j-th level of the first path of the polarization code,/>Source word bit estimation, g, of j-i th level convolution coding for the first path of PAC code i Generating polynomial g= [ g ] for convolution in PAC code 0 ,...,g m ]M+1 is the convolution constraint length, and g 0 ＝g m ＝1。
S203, when the list decoding is finished, L source word estimated values can be obtainedFor each source word estimate sequenceAccording to the formula->Obtaining a polarization-encoded source word estimation sequence +.>And according to the formulaObtaining L bar code word estimated value sequence +.>Wherein->And initial value->And codeword estimation sequence +.>The code weight of (2) is w [ l ]]And the code weight is the number of 1 in the estimated value of the code word, thereby obtaining the code weight w [ L ] of the L code word sequences]。
Constructing a polarization code:
s211, S11 indicates that L is the list size of the polar SCL decoding algorithm, i.e. the maximum list size. Initializing SCL decoding of polar codes with current decoding list size Lb=1, transmitting all-zero code words in noiseless Additive White Gaussian Noise (AWGN) channel, and performing BPSK modulation to obtain SCL decoding of polar codes with channel Log Likelihood Ratio (LLR) of 1Wherein->I=0, N-1, for the LLR of the nth stage i.
S212, decoding all Lb paths by adopting a Serial Cancellation (SC) decoding algorithm, and initializing the path metric value of each path, namelyFor the SC decoding algorithm, polarization-encoded source word bit estimation +.>By local Maximum Likelihood (ML) rule +.>The decision is made by the following formula:
when SCL decoding algorithm of polarization code decodes the jth bit as information bit, the decoding path is completely copied once, wherein the polarization coding source word bit of one path is estimatedPolarization-encoded source word bit estimation of the other path>And lb=2·lb. The PM value of each path is calculated according to the following formula:
wherein, the liquid crystal display device comprises a liquid crystal display device,final LLR for the j-th stage of the l-th path, < >>Source word bit estimates are encoded for the polarization of the jth stage of the ith path. If Lb>And when L is detected, selecting L paths with smaller PM values from all Lb paths to be reserved, and deleting the rest paths to ensure that lb=l.
When SCL decoding algorithm of the polarization code decodes the jth bit to be a frozen bit, estimating polarization coding source word bits of all pathsIs thatAnd calculates the PM value of each path according to the following formula:
wherein, the liquid crystal display device comprises a liquid crystal display device,for the final LLR sequence of the jth level of the ith path,/for the final LLR sequence of the jth level of the jth path,>source word bit estimates are encoded for the polarization of the jth stage of the ith path.
S213, when SCL decoding of the polarization code is finished, L source word estimated values can be obtainedFor each source word evaluation value sequence +.>According to the formula->Obtaining L bar code word estimated value sequence +.>Wherein the method comprises the steps ofAnd initial value->And codeword estimation sequenceThe code weight of (2) is w [ l ]]And the code weight is the number of 1 in the estimated value of the code word, thereby obtaining L codesCode weight w [ l ] of word sequence]。
S3, determining list searching measurement, initializing list searching lists, determining current list searching lists according to the partial weight spectrum, wherein the number of the list searching lists is the number of initial information sets, and each list searching list comprises respective initial information sets and candidate information sets.
The method comprises the following steps:
s31, confirmationThe list search metric for the lm-th list can be considered to be a statistical partial weight spectrum, with all elements initially being 0. If the elements of the corresponding positions in the two list search metrics are equal, otherwise, the list search metric of the first unequal element is large.
In this embodiment, a list search metric (0,2,3,6) and a list search metric (0,2,3,6) are equal. And a list search metric (3,3,5,0) and a list search metric (3,4,5,0), the list search metric (3,4,5,0) being greater than the list search metric (3,3,5,0).
S32, enabling the current list size of the list searching construction method to be Lm, and enabling the initial information set A of each list i Sequentially adding elements B (i), namely A, in the alternative information set B on the basis of the initial information set A i =a u B (i). While the alternative information set B of each list i Satisfy A i ∪B i ＝C。
S33, searching measurement for each list is needed when initializing the listUpdating, in L source word estimated value sequences +.>If the first source word estimated value sequence +.>Medium element cableThe index B (i) is 1 and the first source word estimate sequence +.>Initial information of index in current list among other values of 1
Set A i In, then the list search metrics for the current listW [ l ] of (E)]Individual element->1 is added. Setting a list construction method a current list size lm= |b|.
S4, carrying out path splitting and path pruning on each list searched list according to the initial information set and the alternative information set of the list searched by the current list, returning the initial information set in the list searched by the list with the minimum list searching metric to serve as the information set constructed by the PAC code or the polarization code if the initial information set in the list searched by the list is equal to the information bit length, otherwise, continuing path splitting and path pruning. The method comprises the following steps:
s41, the current number of cycles num=0 is set.
S42, if num < (K- |A| -1), executing S43; otherwise, returning the initial information set in the list with the minimum list searching metric as the information set constructed by the PAC code or the polarization code.
S43, carrying out path splitting on the Lm lists, wherein each list is split into |B| -num-1 lists. If it isFor list initial information set A i An initial information set of the j-th list after splitting; />Alternative information set B for list i An alternative information set of the j-th list after splitting; />Search metrics +.>List search metrics for post-split jth list. Initial information set of post-split list +.>At list initial information set A i Sequentially adding list alternative information set B on the basis of i Element B of (3) i (j) I.e.Whereas the information set alternative after splitting +.>Satisfy->
S44, searching measurement of each list is needed for the split listUpdating, in L source word estimated value sequencesIf the first source word estimated value sequence +.>Index B of medium element i (j) 1, and the first source word estimate sequence +.>The index in the remaining 1 values is located in the initial information set of the current post-split list +.>In, then list search metric of the current list +.>W [ l ] of (E)]Individual element->1 is added. After each list is subjected to path splitting in sequence, setting the current list size lm=lm· (|b| -num-1) of the list construction method, and merging the split paths to obtain Lm lists.
S45, carrying out path pruning on a list with the same path in Lm lists obtained by path splitting, keeping one list in the list with the same initial information set, and then updating Lm.
To aid understanding, it is assumed that there are eight lists after splitting, the initial information sets of each of which are: (0, 1,2, 4), (0,1,4,5), (0,1,5,6), (2,1,5,7), (0, 1,2, 4), (2,1,5,7), (0, 1,2, 4), (0,1,5,6), it can be known that after one list is kept for the same initial information set, the list remains four: (0, 1,2, 4), (0,1,4,5), (0,1,5,6), (2,1,5,7).
S46, obtaining a cut-off rate by using a Gaussian approximation structure, and calculating the Gaussian distribution variance sigma of the AWGN channel according to each parameter of S11 2 The method comprises the following steps:
and in the AWGN channel, the LLR mean value of the receiving endFor the ith element of the N-dimensional vector, the mean value ++of the LLR at the receiving end can be calculated by a recursive formula>
Wherein the initial value isIs->And->The expression of (2) is:
parameters of PasteurThe following formula can be used to calculate the value:
finally, the cut-off rate of each sub-channel is obtainedThe method comprises the following steps:
s47, if the initial information set A of the ith list i Rate of jth sub-channelIs obtainable by the following formula:
if r=0,..n-1, the following conditions are satisfied for all r:
then this list is kept; otherwise discard the list. And updating Lm after path pruning, if Lm > Lg, reserving an Lg list with the maximum path search metric, and updating lm=lg. And num=num+1 is updated, and then returns to step S42.
The implementation effect of the invention is further described below with reference to the accompanying drawings:
fig. 2 is a flowchart of acquiring a PAC code partial weight spectrum by list decoding. The method comprises the following specific steps: transmitting all-zero codewords in a noiseless AWGN channelObtaining the estimated value of the source word in the L lists from the list decoding>PAC code coding (convolution coding and polarization coding) is carried out on the estimated values of the source words in the L lists to obtain code words in the L listsFinally, counting the code weight and the code weight code word number of the code words in the L lists, A d I.e. a partial weight spectrum, representing the code weights and the number of code-weight codewords of the L lists.
Fig. 3 is a flowchart of obtaining a weight spectrum of a polarized code portion by SCL decoding of the polarized code. The method comprises the following specific steps: transmitting all-zero codewords in a noiseless AWGN channelObtaining estimated value +.f of source word in L list from SCL decoding of polarization code>Performing polarization code encoding on the estimated values of the source words in the L lists to obtain code words +.>Finally, counting the code weight and the code weight code word number of the code words in the L lists, A d I.e. a partial weight spectrum, representing the code weights and the number of code-weight codewords of the L lists.
FIG. 4 is a diagram of path splitting and path pruning for the list search construction method of the present invention. As shown in fig. 4, one list path may be split into a plurality of list paths, and the number of paths split by each list path is the same; performing path pruning on the list paths after path splitting, namely cutting off repeated paths and paths which do not meet the limited average calculation complexity of sequence decoding; and finally, obtaining a list path after path pruning.
The error rate performance versus the PAC (64, 32) list-decoded blocks in various configurations is shown in fig. 5. The construction signal-to-noise ratio of the gaussian approximation construction and the RM-polar construction as in fig. 5 is 4dB; in the invention, the list searching structure has a structure signal-to-noise ratio of 2.5dB, a list size of 40000 and a maximum list size of 400; the construction signal to noise ratio of the Monte Carlo construction is 5dB, which is the best BLER performance construction of the Monte Carlo construction. The convolution polynomial of the Monte Carlo construction is 0o3211, and the remaining construction convolution polynomials are 0o133. The list coding list is L in size. It can be seen from the figure that the list search construction method of the present invention has BLER performance in list decoding close to the most advanced monte carlo construction at present and significantly better than gaussian approximation construction and RM-polar construction. And the BLER performance of the list search construction method at the list size of 8 is superior to that of the Gaussian approximation construction and the RM-polar construction at the list size of 32, and the BLER performance is superior to that of the most advanced Monte Carlo construction at present at the list size of 8.
The viterbi decoding block error rate performance versus diagram for PAC (64, 32) in various configurations is shown in fig. 6. The construction signal-to-noise ratio of the gaussian approximation construction and the RM-polar construction as in fig. 6 is 4dB; in the invention, the list searching structure has a structure signal-to-noise ratio of 2.5dB, a list size of 40000 and a maximum list size of 400; the construction signal to noise ratio of the Monte Carlo construction is 5dB, which is the best BLER performance construction of the Monte Carlo construction. The convolution polynomial of the Monte Carlo construction is 0o3211, and the remaining construction convolution polynomials are 0o133. The number of viterbi decoding states is Ns. It can be seen from the figure that the list search construction method of the present invention has a significantly better BLER performance in viterbi decoding than the most advanced monte carlo constructions at present, and significantly better gaussian approximation and RM-polar constructions. And the BLER performance of the list search construction method at the state number of 16 is close to that of a Gaussian construction and an RM-polar construction at the state number of 64, and is superior to that of the most advanced Monte Carlo construction at present at the state number of 16.
The table viterbi decoding block error rate performance versus diagram for PAC (64, 32) in various configurations is shown in fig. 7. The construction signal-to-noise ratio of the gaussian approximation construction and the RM-polar construction as in fig. 7 is 4dB; in the invention, the list searching structure has a structure signal-to-noise ratio of 2.5dB, a list size of 40000 and a maximum list size of 400; the construction signal to noise ratio of the Monte Carlo construction is 5dB, which is the best BLER performance construction of the Monte Carlo construction. The convolution polynomial of the Monte Carlo construction is 0o3211, and the remaining construction convolution polynomials are 0o133. The number of list viterbi decoding states is Ns, the list size is L, and the number of states ns=2 is fixed in fig. 7. It can be seen from the figure that the list search construction method of the present invention has BLER performance in list viterbi decoding that is close to the most advanced monte carlo construction at present, and significantly better than gaussian approximation construction and RM-polar construction. And the BLER performance of the list search construction method at the list size of 4 is superior to that of the Gaussian approximation construction and the RM-polar construction at the list size of 16, and the BLER performance is superior to that of the most advanced Monte Carlo construction at present at the list size of 4.
The Fano decoding block error rate performance and complexity versus various configurations for PACs (64, 32) are shown in fig. 8. The construction signal-to-noise ratio of the gaussian approximation construction and the RM-polar construction as in fig. 8 is 4dB; in the invention, the list searching structure has a structure signal-to-noise ratio of 2.5dB, a list size of 40000 and a maximum list size of 400; the construction signal to noise ratio of the Monte Carlo construction is 5dB, which is the best BLER performance construction of the Monte Carlo construction. The convolution polynomial of the Monte Carlo construction is 0o3211, and the remaining construction convolution polynomials are 0o133. The Fano decoding threshold pitch is Δ, and in fig. 8, the fixed threshold pitch Δ=2. It can be seen in fig. 8 that the BLER performance of the list search configuration is close to that of the monte carlo configuration and significantly better than the gaussian approximation configuration and the RM-polar configuration. While the complexity of the list search construct is lower than the monte carlo construct in terms of average computational complexity, this also demonstrates the superiority of the list search construct.
The Fano decoding block error rate performance and complexity versus various configurations for PAC (256,128) is shown in fig. 9. The construction signal-to-noise ratio of the RM-polar construction as in FIG. 9 is 4dB; in the invention, the list searching structure has a structure signal-to-noise ratio of 3.2dB, a list size of 40000 and a maximum list size of 400; the construction signal to noise ratio of both the Monte Carlo construction and the weighted sum construction is 3dB, which is the best BLER performance construction for both the Monte Carlo construction and the weighted sum construction. The convolution polynomials for the Monte Carlo construction and the weighted sum construction are 0o3211, and the remaining construction convolution polynomials are 0o133. The Fano decoding threshold pitch is Δ, and in fig. 9, the fixed threshold pitch Δ=2. As can be seen from fig. 9, the BLER performance of the list search construction coincides with the discrete bound, whereas the BLER performance of the current most advanced monte carlo construction and the weighted sum construction deviates significantly from the discrete bound.
The PAC (64, 32) is shown in fig. 10 as a comparison of stack coded block bit error rate performance and complexity in various configurations. The construction signal-to-noise ratio of the gaussian approximation construction and the RM-polar construction as in fig. 10 is 4dB; in the invention, the list searching structure has a structure signal-to-noise ratio of 2.5dB, a list size of 40000 and a maximum list size of 400; the construction signal to noise ratio of the Monte Carlo construction is 5dB, which is the best BLER performance construction of the Monte Carlo construction. The convolution polynomial of the Monte Carlo construction is 0o3211, and the remaining construction convolution polynomials are 0o133. Further, the stack coding maximum depth is D, and the maximum depth d=1024 is fixed in fig. 8. It can be seen in fig. 10 that the BLER performance of the list search configuration is close to that of the monte carlo configuration and significantly better than the gaussian approximation configuration and the RM-polar configuration. While the complexity of the list search construct is lower than the monte carlo construct in terms of average computational complexity, this also demonstrates the superiority of the list search construct.
FIG. 11 is a graph of SCL decoding block error rate performance versus PC (64, 32) in various configurations. The construction signal-to-noise ratio of the gaussian approximation, polarization weights and RM-polar constructions as in fig. 11 is 4dB; in the invention, the list search structure has a structure signal-to-noise ratio of 2.5dB, a list size of 100000 and a maximum list size of 400. The list coding list is L in size. It can be seen from the figure that the BLER performance in list decoding is significantly better than gaussian approximation, polarization weight and RM-polar constructions in the list search construction method of the present invention, and the construction method of the present invention is simpler.
FIG. 12 is a graph of SC-Fano decoding block error rate performance and complexity versus various configurations for a PC (64, 32). The construction signal-to-noise ratio of the gaussian approximation, polarization weights and RM-polar constructions as in fig. 12 is 4dB; in the invention, the list search structure has a structure signal-to-noise ratio of 2.5dB, a list size of 100000 and a maximum list size of 400. Furthermore, the SC-Fano decoding threshold spacing is Δ. It can be seen from the figure that the list search construction method of the present invention has better BLER performance than gaussian approximation construction, polarization weight construction and RM-polar construction in viterbi decoding, but with a modest increase in complexity.
The Fano decoding block error rate performance and complexity versus various configurations of the PC (256,128) is shown in fig. 13. The construction signal-to-noise ratio of the gaussian approximation, polarization weights and RM-polar constructions as in fig. 13 is 4dB; in the invention, the list search structure has a structure signal-to-noise ratio of 3.2dB, a list size of 200000 and a maximum list size of 400. Furthermore, the SC-Fano decoding threshold spacing is Δ. It can be seen from the figure that the list search construction method of the present invention has better BLER performance than gaussian approximation construction, polarization weight construction and RM-polar construction in viterbi decoding, but with a modest increase in complexity. This confirms the superiority of the list search construction of the polarization code, and furthermore, the list search construction method of the polarization code is simpler.
As shown in fig. 14, the RM score chart when n=64. In the figure it can be seen that there are many sub-channels with the same RM score, whereas the list search construction method is to select sub-channels with a large RM score as much as possible, after which a suitable number of sub-channels are selected from the candidate information set.
The RM score plot is shown as n=256 in fig. 15. In the figure, it can be seen that there are many sub-channels with the same RM score, and the list search construction method is to select sub-channels with large RM scores as much as possible, and then select a proper number of sub-channels from the alternative information set.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (8)

  1. The list searching construction method of PAC codes or polarization codes is characterized by comprising the following steps:
    s1, determining an initial information set, an alternative information set and a generalized information set of a list searching construction method according to an RM score of the RM construction method, returning the initial information set to serve as an information set constructed by PAC codes or polarization codes if the number of the initial information set is equal to the length of information bits, otherwise executing S2;
    s2, obtaining a partial weight spectrum of the generalized information set through a decoding algorithm, and storing a source word sequence, a codeword sequence and code weights of the codeword sequence;
    s3, determining a list searching measure, initializing a list searched by the list, and determining a list searched by the current list according to the partial weight spectrum, wherein the number of the list searched by the initial list is the number of the initial information sets, and each list searched by the list comprises the initial information sets and the alternative information sets;
    s4, carrying out path splitting and path pruning on each list searched list according to the initial information set and the alternative information set of the list searched by the current list, returning the initial information set in the list searched by the list with the minimum list searching metric to serve as the information set constructed by the PAC code or the polarization code if the initial information set in the list searched by the list is equal to the information bit length, otherwise, continuing path splitting and path pruning.
  2. 2. The PAC code or the list search construction method of the polarization code according to claim 1, wherein the PAC code is decoded by a list decoding algorithm, and the polarization code is decoded by an SCL decoding algorithm.
  3. 3. The method for constructing a list search of PAC codes or polarization codes according to claim 2, wherein step S1 specifically comprises:
    s11, setting the code length of PAC code or polarization code as N, the information bit length as K, the list size of a list searching construction method list as Lg, the list size of a decoding algorithm list as L, and the construction signal-to-noise ratio as E b N 0 ；
    S12, let n=log 2 N is:
    wherein, the liquid crystal display device comprises a liquid crystal display device,calculating the value of r for taking out the combined number of m elements from n elements;
    s13, binary expression form of serial number i of sub-channel is0≤i<N, RM score s (i) is the number of 1 in the binary expression of subchannel number i, RM score s (i) is: />
    S14, determining an initial information set a, an alternative information set B and a generalized information set C according to the RM score, wherein the initial information set a contains all indexes of RM score S (i) > r, the alternative information set B contains all indexes of RM score S (i) =r, the generalized information set C is a union set of the initial information set a and the alternative information set B, namely c=a_b, and a= { a (0), a (|a| -1) }, b= { B (0), B (|b| -1) }, c= { C (0), C (|c| -1) }, wherein |a|b| and |c| are numbers of corresponding set elements thereof;
    s15, if the number of the initial information sets |A| is equal to the information bit length K, returning the initial information set A as a construction information set of PAC codes or polarization codes, otherwise executing S2.
  4. 4. The PAC code or the list search construction method of the polarization code of claim 3, wherein the step S2 specifically comprises:
    s21, initializing the list size Lb=1 of the current decoding algorithm, transmitting all-zero code words in an AWGN channel, and performing BPSK modulation to obtain LLR (binary phase shift keying) as followsWherein->LLR for stage i of stage N, i=0,..n-1;
    s22, decoding all Lb paths by adopting an SC decoding algorithm, and initializing path metric values of each path:and calculating PM values of the paths;
    s23, when decoding is finished, obtaining L polarization coding source word estimated valuesFor each source word estimate sequenceAccording to the formula->Obtaining L bar code word estimated value sequence +.>Wherein the method comprises the steps ofAnd initial value->Code word estimation value sequence->The code weight of (2) is w [ l ]]The code weight is the number of 1 in the codeword estimation value.
  5. 5. The PAC code or the list search construction method of the polarization code of claim 4, wherein in step S22, the PM value of each path is calculated specifically as:
    when decoding to the j-th bit as an information bit, the decoding path is completely copied once, wherein the encoding source word bit of one path is estimated to be 0, the encoding source word bit of the other path is estimated to be 1, and lb=2·lb is made, and the PM value of each path is calculated according to the following formula, namely:
    wherein, the liquid crystal display device comprises a liquid crystal display device,final LLR for the j-th stage of the l-th path, < >>Polarization-encoded source word bit estimate for the j-th level of the first path of the polarization code,/> Source word bit estimation, g, of j-i th level convolution coding for the first path of PAC code i Generating polynomial g= [ g ] for convolution in PAC code 0 ,...,g m ]M+1 is the convolution constraint length, and g 0 ＝g m ＝1；
    If Lb > L, selecting L reservations with PM values smaller than the threshold value in Lb paths, and deleting the rest paths to enable lb=l;
    when decoding to the j-th bit is a frozen bit, estimating the coded source word bits of all paths as 0, and calculating the PM value of each path according to the following formula, namely:
    wherein, the liquid crystal display device comprises a liquid crystal display device,for the final LLR sequence of the jth level of the ith path,/for the final LLR sequence of the jth level of the jth path,>polarization-encoded source word bit estimate for the j-th level of the first path of the polarization code,/> Source word bit estimation is convolutionally encoded for the j-i th level of the first path of PAC code.
  6. 6. The method for constructing a list search of PAC codes or polarization codes according to claim 4, wherein step S3 is specifically:
    s31, determiningSearching the metric for the list of the lm-th list, wherein all elements are initially 0;
    s32, list searching construction method, wherein the current list size is Lm, so that the initial information set A of each list i Sequentially adding elements B (i) in the alternative information set B on the basis of the initial information set A: a is that i =a ≡b (i), alternative information set B of each list i Satisfy A i ∪B i ＝C；
    S33, searching and measuring the respective listsUpdating, searching in L source word estimated value sequences, and if the element index in the first source word estimated value sequence is 1, and the index in the rest values of 1 in the first source word estimated value sequence is positioned in the initial information set A of the current list i In, then list search metric of the current list +.>W [ l ] of (E)]Individual element->Adding 1, setting the current list size lm= |b| of the list construction method.
  7. 7. The method for constructing a list search of PAC codes or polarization codes according to claim 6, wherein step S4 is specifically:
    s41, setting the current number of cycles num=0;
    s42, if num < (K- |A| -1), executing S43; otherwise, returning the initial information set in the list with the minimum list searching measurement as the information set constructed by the PAC code or the polarization code;
    s43, carrying out path splitting on Lm lists, wherein each list is split into an I B I-num-1 list, and the initial information set of the split list is obtainedAt list initial information set A i Sequentially adding list alternative information set B on the basis of i Element B of (3) i (j)：Alternative information set after division +.>Satisfy->Wherein (1)>For list initial information set A i Initial information set of post-split jth list, < >>Alternative information set B for list i An alternative information set of the j-th list after splitting;
    s44, searching and measuring respective lists by the split listsUpdate (F)>Search metrics +.>Searching in the L source word estimated value sequences by using the list searching measurement of the j-th list after splitting, if the element index in the first source word estimated value sequence is 1, and the index in the rest values of 1 in the first source word estimated value sequence is positioned in the initial information set of the list after splitting currently>In, list search metric of the current list +.>W [ l ] of (E)]Individual element->Adding 1, after sequentially splitting paths of each list, setting the current list size lm=lm· (|b| -num-1) of a list construction method, and merging the split paths to obtain Lm lists;
    s45, carrying out path pruning on a list with the same path in Lm lists obtained by path splitting, reserving one list in the list with the same initial information set in the Lm lists, and updating Lm;
    s46, calculating LLR mean value of the receiving end through a recursive formula, and solving the cut-off rate of each sub-channel by using a Gaussian approximation construction method
    S47 initial information set A of ith list i Rate of jth subchannelIs obtainable by the following formula:
    wherein A is i Initial information set A for the ith list i ，
    r=0..n-1, the following conditions are satisfied for all r:
    then this list is kept; otherwise, discarding the list, updating Lm after pruning the path, if Lm > Lg, reserving an Lg list with the maximum path search metric, updating lm=lg, wherein Lg is the size of the PAC code list search construction method list, updating num=num+1, and returning to step S42.
  8. 8. The method of constructing a list search of PAC codes or polarization codes according to claim 7, wherein step S46 is specifically:
    computing the Gaussian distribution variance sigma of an AWGN channel 2 The method comprises the following steps:
    the LLR mean value of the receiving end can be calculated by a recursive formula
    Wherein the initial value The i element of the N-dimensional vector is represented as the mean value of LLR at the receiving end in the AWGN channel,/I>Is->Is an inverse function of +.>The expression of (2) is:
    parameters of PasteurThe following formula can be used to calculate the value: />Determining the cut-off rate of each sub-channel>The method comprises the following steps: />
CN202310387053.2A 2023-04-07 2023-04-07 Method for constructing list search of PAC code or polarization code Pending CN116470923A (en)

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