CN108282264B - Polar code decoding method based on bit flipping serial elimination list algorithm - Google Patents

Polar code decoding method based on bit flipping serial elimination list algorithm Download PDF

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CN108282264B
CN108282264B CN201810010667.8A CN201810010667A CN108282264B CN 108282264 B CN108282264 B CN 108282264B CN 201810010667 A CN201810010667 A CN 201810010667A CN 108282264 B CN108282264 B CN 108282264B
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CN108282264A (en
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相征
孙五星
任鹏
刘明辉
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Xian University of Electronic Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0045—Arrangements at the receiver end
    • H04L1/0054—Maximum-likelihood or sequential decoding, e.g. Viterbi, Fano, ZJ algorithms
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    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/09—Error detection only, e.g. using cyclic redundancy check [CRC] codes or single parity bit
    • H03M13/095—Error detection codes other than CRC and single parity bit codes
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13—Linear codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
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Abstract

The invention discloses a polarization code decoding method based on a bit reversal serial elimination list algorithm, which solves the problem that the traditional SCL algorithm has higher time complexity and comprises the steps of (1) receiving a sequence to be decoded by a communication terminal, (2) carrying out SC decoding on the received sequence to be decoded, (3) judging whether the SC decoding sequence passes CRC (cyclic redundancy check), initializing the list width and the bit reversal times, (5) selecting a judgment error position set, (6) selecting elements from the judgment error position set, (7) carrying out decoding by using the bit reversal serial elimination list algorithm, (8) judging whether the elements in the judgment error position set are selected, (9) successfully decoding, (10) failing decoding, combining bit reversal and list decoding to carry out re-decoding when the decoding fails, thereby improving the decoding performance and reducing the time complexity of the decoding algorithm.

Description

Polar code decoding method based on bit flipping serial elimination list algorithm
Technical Field
The invention belongs to the technical field of communication, and further relates to polarization code decoding methods based on a bit reversal serial elimination list algorithm in the technical field of channel coding.
Background
The polarization code can reach the shannon limit theoretically, has low coding and decoding computation complexity, and has a deterministic construction method, so that the polarization code can be used for a channel coding scheme in the communication system, and the problem of transmission errors of information in a wireless channel is solved.
Although the serial elimination SC decoding can obtain good asymptotic performance under the condition of long code length N and approaches to Shannon limit, when the code length N is short or medium, because Polar codes still have partial unpolarized channels, the information bits are transmitted on the unpolarized channels, decoding errors are easily caused, secondly, the serial elimination SC decoding method can generate error propagation in the decoding process, so that the performance of the serial elimination SC decoding method does not exceed the performance of Turbo codes and Low-density Parity check (Low-Parity-check) codes, and steps are needed to improve the decoding performance.
ORION A, BALASUOKAS-STIMMING A, ANDREAS B. paper "A Low-complexity Improved statistical Decoder for Polar Codes" ([ C)] decoding methods of polarization code are disclosed in// Proceedings of IEEE 48th orthogonal reference on Signals, Systems and communications, Pacific Grove: IEEE,2014:2116-
Figure GDA0002265545590000011
Selecting T minimum judgment bits as estimation of unreliable information bits, forming set M with index values corresponding to the bits, taking values from the set M each time, then re-executing serial elimination SC algorithm decoding, and judging sequence
Figure GDA0002265545590000012
And carrying out bit reversal on unreliable information bits corresponding to the index marks, and taking the reversal result as a decoding result of the index position. If the new codeword estimates
Figure GDA0002265545590000021
The decoding method is improved by to a certain degree on decoding performance, and time complexity is greatly reduced compared with a serial elimination list SCL (successful cancellation List) decoding method.
The invention discloses serial List decoding algorithms based on bit flipping in the patent document ' of the university of Western Ann electronic technology' (application published: 2016, 28.9.2016, application published: CN 105978557A). The inventive embodiment proposes new serial List decoding algorithms based on bit flipping, which are directed at the problem of error propagation in the cyclic redundancy Check-assisted serial Cancellation List CA-SCL decoding algorithm (cyclic redundancy Check-assisted serial Cancellation List CA-SCL), and flip the error bit appearing at the th time on the original error path to make it become the correct path.
Disclosure of Invention
The invention aims to provide polar code decoding methods based on the bit reversal serial elimination list algorithm aiming at the defects of the prior art, so that the decoding performance of the polar code is improved, the complexity is relatively low, and the time complexity of the decoding method gradually tends to the complexity of the serial elimination SC algorithm under the environment of high signal-to-noise ratio.
The method comprises the steps of firstly carrying out serial elimination SC decoding on a polarization code, if the decoding result can pass cyclic redundancy check, directly outputting a correct result, otherwise finding out a position where the judgment is possible to make an error by using an absolute value of a log Likelihood ratio LLR (Log Likelihood ratio) of a polarization channel corresponding to an information bit in a judgment layer, then starting to carry out serial elimination list decoding of bit inversion, when the decoding is carried out to the position where the judgment is possible to make an error, directly inverting the bit corresponding to the position where the judgment is made to make an error in an SC decoding sequence to be used as the decoding result of the position, continuing to carry out the rest decoding until leaves in a decoding node are carried out, when paths in a candidate path can pass cyclic redundancy check, ending the decoding, otherwise, selecting elements from the position where the judgment is possible to make an error, and carrying out the serial elimination list decoding of bit inversion again.
The invention has the following implementation steps:
(1) receiving a sequence to be decoded from a communication terminal:
(2) the serial elimination SC decoding is firstly carried out on the sequence to be decoded:
(2a) calculating the log-likelihood ratio of the polarized channel;
(2b) judging the sequence received by the communication terminal according to the positive and negative of the log-likelihood ratio of each polarized channels corresponding to the information bits in the decoding structure judgment layer, if the sequence is positive, judging the sequence to be 0, if the sequence is negative, judging the sequence to be 1, and directly judging the position bits corresponding to each non-information bits in the sequence received by the communication terminal to be 0;
(2c) judging whether the serial number of the current decoding sequence is larger than the code length of the polarization code, if so, executing the step (3) after taking the current decoding sequence as a serial elimination SC decoding sequence, otherwise, executing the step (2a) after adding 1 to the serial number of the current decoding sequence;
(3) judging whether the serial elimination SC decoding sequence passes through cyclic redundancy CRC (cyclic redundancy check), if so, executing the step (9), otherwise, executing the step (4):
(4) initializing the list width and the bit flipping times of the serial elimination list algorithm by using values of 2 to the power of an integer;
(5) selecting a position set with a wrong judgment:
according to a sorting method from small to large, sequentially selecting the positions with decoding judgment errors corresponding to the information bit set from a serial elimination SC decoding sequence which does not pass through cyclic redundancy CRC (cyclic redundancy check), and forming the positions with errors into a position set with serial elimination SC decoding judgment errors;
(6) elements are selected from a position set for serially eliminating SC decoding judgment errors in sequence;
(7) decoding by using a bit flipping serial elimination list algorithm:
(7a) judging whether the sequence number of the current decoding sequence is equal to the value of the selected error position set element, if so, executing the step (7b), otherwise, executing the step (7 c);
(7b) calculating the metric value of each expansion paths at the position where each decoding sequence numbers in the decoding tree are equal to the element value in the position set with decoding judgment errors by using a penalty factor according to the following formula so as to indirectly realize bit flipping;
Figure GDA0002265545590000031
wherein,
Figure GDA0002265545590000032
indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to ith bitiThe values of the metrics of the constructed extension paths,
Figure GDA0002265545590000033
indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to i-1 biti-1Metric values of the formed extension paths, ueIndicating the bit value corresponding to the e-th bit in the serial elimination SC decoding sequence, e indicating the value of an element selected from the set of serial elimination SC decoding decision error positions, LiRepresenting the absolute value of the log-likelihood ratio of the ith polarization channel in the decision layer of the decoding structure, and α representing a penalty factor, wherein the value range of the penalty factor is more than or equal to 100 and less than or equal to α and less than or equal to 2000;
(7c) calculating the metric value of each expansion paths at the sequence number of each decoding sequences in the decoding tree according to the following formula;
Figure GDA0002265545590000041
wherein,indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to ith bitiThe values of the metrics of the constructed extension paths,
Figure GDA0002265545590000043
indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to i-1 biti-1The metric value of the formed extended path belongs to operation, wherein the epsilon represents the selected information bit set during coding, the lambda represents the correct frozen bit value, the value of which is 0, and the value of LiRepresenting the absolute value of the log-likelihood ratio of the ith bit polarization channel in the decision layer;
(7d) judging whether the metric value of the extended path is less than or equal to the list width value of the serial elimination list algorithm, if so, executing the step (7e), otherwise, executing the step (7 f);
(7e) reserving all the extension paths;
(7f) sorting the metric values of the extended paths from large to small, and taking the first Q extended paths in the sorting as candidate paths, wherein the value of Q is equal to the list width value of a serial elimination list algorithm;
(7g) judging whether the serial number of the current decoding sequence is larger than the code length of the polarization code, if so, executing the step (7h), otherwise, adding 1 to the serial number of the current decoding sequence and executing the step (7 a);
(7h) judging whether the candidate paths have paths passing the cyclic redundancy check, if so, selecting paths with the maximum path metric from the candidate paths passing the cyclic redundancy check as a decoding sequence, and then executing the step (9), otherwise, executing the step (8);
(8) judging whether all elements in the position set with errors in serial elimination SC decoding judgment are selected, if so, executing the step (10), otherwise, executing the step (6);
(9) decoding is successful, and a successfully decoded sequence is output;
(10) if the decoding fails, the serial cancellation SC decoding sequence is output.
Compared with the prior art, the invention has the following advantages:
, because the invention uses punishment factor, calculate the metric value of every decoding serial numbers in the decoding tree equal to every extension paths at the element value in the position set of the decoding decision making mistakes, to realize the bit reversal indirectly, overcome the problems that the single bit reversal serial elimination decoding algorithm in the prior art only tries to reverse unreliable information bits each time, the decoding performance is not good, and the algorithm can not be used for the communication system with high performance requirement, so the invention obviously improves the error correction performance of the decoding by using the serial elimination list decoding algorithm.
Secondly, because the serial elimination SC decoding is firstly carried out on the sequence to be decoded, when the serial elimination SC decoding sequence does not pass the cyclic redundancy CRC check, the serial elimination list algorithm is used for decoding, the problem that the serial list decoding algorithm based on bit inversion in the prior art improves the decoding performance at the cost of increasing the decoding complexity, and the decoding complexity is still very high even under the environment of high signal-to-noise ratio and cannot be used in an actual communication system is solved, so that the serial elimination SC decoding method and the serial elimination SC decoding method realize that the decoding complexity gradually tends to the serial elimination SC complexity under the environment of high signal-to-noise ratio, and obviously reduce the time complexity of the decoding algorithm.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph comparing the frame error rate curves of the improved decoding algorithm SFSCL with the existing serial elimination SC, CRC-SC and SFSC decoding method based on single-bit flipped serial elimination;
FIG. 3 is a comparison graph of the average decoding complexity curve of the improved decoding algorithm SFSCL and the existing SC, CRC-SCL, SFSC decoding method classified as .
Detailed Description
The invention is further described with reference to the drawings.
Referring now to FIG. 1, the steps involved in the present invention are further illustrated at .
Step 1, receiving a sequence to be decoded from a communication terminal.
And 2, performing serial elimination SC decoding on the sequence to be decoded.
Log-likelihood ratios of the polarized channels are calculated.
Respectively calculating the log-likelihood ratio of the polarized channel in the decision layer of the decoding structure according to the parity of the polarized channel sequence number:
calculating the log-likelihood ratio of each polarized channel with odd serial number in the decision layer of the decoding structure according to the following formula;
Figure GDA0002265545590000051
wherein,
Figure GDA0002265545590000052
the input of the polarization channel of the kth odd-numbered sequence number in the decoding structure decision layer which represents the length of the code word after the polarization code coding is N isK represents the serial number of the polarized channel in the decision layer of the decoding structure, the value of the serial number is 2j-1, j is more than or equal to 1 and less than or equal to N/2, N represents the code word length after the code coding of the polarized code,
Figure GDA0002265545590000062
representing the input of the polarized channel, y represents the sequence received by the communication terminal,
Figure GDA0002265545590000063
represents the decoded first k-1 bit code word sequence, sign (h) represents code words1And L2When the product of (A) is positive, the function value is 1, and when L is positive1And L2When the product of (A) is negative, the function valueA function of-1, L1Representing the log-likelihood ratio, L, of the polarized channel of the upper branch in the adjacent layers of the decoding structure2Represents the log-likelihood ratio of the polarized channel of the lower branch in the adjacent layer of the decoding structure, min (-) represents the function of solving the minimum value of the two real numbers, | - | represents the operation of solving the absolute value.
And calculating the log-likelihood ratio of each polarized channel with even number in the decision layer of the decoding structure according to the following formula.
Wherein,
Figure GDA0002265545590000065
the input of the polarization channel of the mth even serial number in the decoding structure decision layer which represents the length of the code word after the polarization code coding is N is
Figure GDA0002265545590000066
M represents the serial number of the polarized channel in the decision layer of the decoding structure, the value of the serial number is 2j, j is more than or equal to 1 and less than or equal to N/2, N represents the code word length after the polarized code is coded,
Figure GDA0002265545590000067
represents the input of the polarized channel, y represents the sequence received by the receiving end of the communication terminal,
Figure GDA0002265545590000068
representing the first m-1 bit codeword sequence that has been decoded,
Figure GDA0002265545590000069
indicating the m-1 bit codeword that has been decoded.
And judging the sequence received by the communication terminal according to the positive and negative of the log-likelihood ratio of each polarized channels corresponding to the information bits in the decoding structure judgment layer, if the value is positive, judging the value to be 0, if the value is negative, judging the value to be 1, directly judging the value to be 0 for the position bits corresponding to each non-information bits in the sequence received by the communication terminal, and finally obtaining the serial elimination SC decoding sequence when the decoding is carried out to the final bits.
Wherein, the bit corresponding to the information bit is judged according to the following formula.
Figure GDA00022655455900000610
Wherein,
Figure GDA00022655455900000611
representing the value of the ith bit decoded in the decoded sequence,
Figure GDA00022655455900000612
representing the log-likelihood ratio of the i-th bit-polarized channel in the decision layer, and Λ representing the set of information bits.
The information bit set Λ is selected as follows:
computing mean values of polarized channels from gaussian approximations
Figure GDA0002265545590000071
In BAWGN, probability density function of LLR value in density evolution can be approximated by Gaussian distribution with mean value of 2 times variance, noise variance is sigma2Gaussian white channel AWGN, the received signal acquired by the receiving end is y:
y＝(1-2x)+z
where y represents the sequence received by the receiver, x represents the transmitted bits, x belongs to {0,1}, z represents the mean 0, and the variance σ represents2Gaussian white noise, the source bit sequence is modulated by BPSK, and the probability density function is:
Figure GDA0002265545590000072
wherein, p (y | x)Probability density function, sigma, representing x sent by the sending end and y received by the receiving end2Representing the variance of gaussian white noise.
Assuming that the transmitted bits are all-zero sequences, the corresponding LLR values are
Wherein LLR (y) represents the log-likelihood ratio of the polarized channel of the channel layer, ln () represents the natural logarithm operation, p (-) represents the transition probability of the channel layer, y represents the sequence received by the receiving end, σ represents2Representing the variance of gaussian white noise.
According to the setting in the density evolution, let
Figure GDA0002265545590000074
To representA probability density function of, then
Figure GDA0002265545590000076
Is also obey
Figure GDA00022655455900000710
A gaussian distribution of (a). Then according to the Gaussian approximation construction theory, the calculation of density evolution is converted into a mean value
Figure GDA0002265545590000077
The recursive calculation of (2):
when the serial number of the polarized channel in the decision layer is odd, the average value is calculated according to the following formula
Figure GDA0002265545590000079
Wherein,
Figure GDA0002265545590000081
represents the mean of the probability density function of the 2i-1 th polarized channel in the decision layer,
Figure GDA0002265545590000082
represents the mean of the probability density functions of the polarized channels in the adjacent layers,
Figure GDA0002265545590000083
to represent
Figure GDA0002265545590000084
The inverse function of (a) is,
Figure GDA0002265545590000085
the definition is as follows:
Figure GDA0002265545590000086
when the serial number of the polarized channel in the decision layer is even, the average value is calculated according to the following formula
Figure GDA0002265545590000087
Wherein,
Figure GDA0002265545590000089
represents the mean of the probability density function of the 2 i-th polarized channel in the decision layer,
Figure GDA00022655455900000810
representing the mean of the probability density functions of the polarized channels in the adjacent layers.
At the end of the recursion, the mean is:
wherein,
Figure GDA00022655455900000812
representing the mean, σ, of the probability density function in the channel layer2Representing the variance of gaussian white noise.
Calculating the error probability of the polarized sub-channel according to the following formula
Figure GDA00022655455900000813
Figure GDA00022655455900000814
Wherein,
Figure GDA00022655455900000815
representing the error probability of the ith polarized channel in the decision layer,
Figure GDA00022655455900000816
represents the mean of the ith polarization channel in the decision layer, and the q (x) function is defined as follows:
Figure GDA00022655455900000817
error probability for polarized sub-channels
Figure GDA00022655455900000818
Sorting in ascending order to select an information bit set lambda;
sequencing the error probability of each polarization sub-channel in an ascending order, selecting k sub-channels with the minimum error probability of the polarization channels for transmitting bit information, wherein the set is marked as Λ, the set is the index position of the information bit, the other sub-channels are used for transmitting frozen bits, and the set is marked as ΛcThe frozen bit set is typically transmitted as an all-zero bit set.
And 3, judging whether the serial elimination SC decoding sequence passes through cyclic redundancy CRC (cyclic redundancy check), if so, executing the step 9, otherwise, executing the step 4.
Step 4, initializing the list width and the bit flipping times of the serial elimination list algorithm with values of integer power of 2.
And 5, selecting a position set with an error judgment.
Sorting the absolute values of the log-likelihood ratios of the polarized channels corresponding to the information bits in the decision layers in a descending order, and sequentially selecting the index positions of the polarized channels corresponding to the absolute values of the log-likelihood ratios of the polarized channels in the first T decision layers to form a serial elimination SC decoding decision error position set, wherein T is values equal to the bit flipping times.
And 6, sequentially selecting elements from the position set in which the serial elimination SC decoding decision is wrong.
And 7, decoding by using a bit flipping serial elimination list algorithm.
The metric values for each spreading paths are calculated two times depending on whether the sequence number of the currently decoded sequence is equal to the value of the selected error location set element.
Case when the sequence number of the current decoded sequence is equal to the value of the selected error position set element, a penalty factor is used to calculate the metric value of every decoded sequence numbers in the decoding tree equal to every extended paths at the element value in the position set where the decoding decision is erroneous, according to the following formula, to indirectly achieve bit flipping.
Figure GDA0002265545590000091
Wherein,
Figure GDA0002265545590000092
indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to ith bitiThe values of the metrics of the constructed extension paths,
Figure GDA0002265545590000093
indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to i-1 biti-1Metric values of the formed extension paths, ueRepresenting serial erasureDividing the bit value corresponding to the e-th bit in the SC decoded sequence, e representing the value of an element selected from the set of serial erasure SC decoded decision error locations, LiRepresenting the absolute value of the log-likelihood ratio of the ith polarization channel in the decision layer of the decoding structure, and α representing a penalty factor, wherein the value range of the penalty factor is more than or equal to 100 and less than or equal to α and less than or equal to 2000;
when the sequence number of the current decoding sequence is not equal to the value of the selected error position set element, calculating the metric value of each expansion paths at the sequence number of each decoding sequences in the decoding tree according to the following formula;
Figure GDA0002265545590000094
wherein,
Figure GDA0002265545590000101
indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to ith bitiThe values of the metrics of the constructed extension paths,indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to i-1 biti-1The metric value of the formed extended path belongs to operation, wherein the epsilon represents the selected information bit set during coding, the lambda represents the correct frozen bit value, the value of which is 0, and the value of LiRepresenting the absolute value of the log-likelihood ratio of the i-th bit-polarized channel in the decision layer.
And when the value of the extended path is not more than the list width value of the serial elimination list algorithm, reserving all the extended paths, otherwise, sequencing the metric values of the extended paths from large to small, and taking the first M extended paths in the sequencing as candidate paths, wherein the value of M is equal to the list width value of the serial elimination list algorithm.
And continuing the above processes until the decoding is carried out to leaf nodes in the decoding tree, finally obtaining candidate paths, judging whether the candidate paths have paths passing the cyclic redundancy check, if so, selecting paths with the maximum path metric from the candidate paths passing the cyclic redundancy check as a decoding sequence, and then executing the step 9, otherwise, executing the step 8, wherein the value of Q is equal to the list width value of the serial elimination list algorithm.
And 8, judging whether all elements in the position set with errors in serial elimination SC decoding judgment are selected, if so, executing the step 10, and otherwise, executing the step 6.
And 9, successfully decoding, and outputting a successfully decoded sequence.
And step 10, outputting a serial elimination SC decoding sequence when the decoding fails.
The effect of the present invention will be further illustrated in with the simulation experiment.
1. Simulation conditions are as follows:
the simulation experiment of the invention is carried out under MATLAB 16.0 software. In the simulation experiment of the invention, in order to truly simulate an additive white Gaussian noise channel, a pseudo-random sequence is adopted to simulate the white Gaussian noise and BPSK is used to modulate signals, an information sequence at the output end of an information source is generated by random numbers, the code rate is 0.5, the code length is 1024, and the selection of information bits of a polarization code adopts a Gaussian approximation method.
2. Simulation content and result analysis:
simulation experiment 1:
the simulation experiment 1 of the invention is a frame error rate comparison experiment adopting the polar code decoding method of the invention and three existing polar code decoding methods (a serial elimination SC method, a cyclic redundancy check-assisted serial elimination list CRC-SCL method, and a single-bit upset serial elimination SFSC-based method).
Fig. 2 is a comparison graph of frame error rate curves of the polar code decoding method of the present invention and three existing polar code decoding methods (serial elimination SC algorithm, CRC-SCL algorithm for cyclic redundancy check-assisted serial elimination list, SFSC algorithm based on single-bit flip serial elimination). In fig. 2, the horizontal axis represents the signal-to-noise ratio and the vertical axis represents the frame error rate. The curve marked by the open circles in fig. 2 represents the frame error rate curve of the polar code decoding method using the conventional serial erasure decoding algorithm. The curve marked by a square in fig. 2 represents a frame error rate curve of a polar code decoding method based on the single-bit-flipping serial erasure SFSC algorithm in the prior art, and the number of flips is equal to 4. The curve marked by diamonds in fig. 2 represents the frame error rate curve of the polar code decoding method based on the single-bit-flipping serial erasure SFSC algorithm in the prior art, and the number of flips is equal to 8. The curve marked with triangles in fig. 2 represents the frame error rate curve of the polar code decoding method using the CRC-SCL algorithm assisted by the CRC in the prior art and the list width is equal to 2. The curve marked by a five-pointed star in fig. 2 represents the frame error rate curve of the polar code decoding method using the method of the present invention, and the list width is equal to 2 and the number of flipping times is equal to 4. The curve marked by asterisk in fig. 2 represents the frame error rate curve of the polar code decoding method using the method of the present invention, and the list width is equal to 2 and the number of flipping times is equal to 8.
As can be seen from the comparison between the astroid curve in fig. 2 and the rhomboid curve and the triangular curve, the frame error rate of the astroid curve is lower than that of the rhomboid curve and that of the triangular curve under the condition of equal signal-to-noise ratio.
Simulation experiment 2:
the simulation experiment 2 of the invention is an -classified average complexity contrast experiment adopting the polar code decoding method of the invention and three existing polar code decoding methods (a serial elimination SC method, a cyclic redundancy check-assisted serial elimination list CRC-SCL method, and a single-bit upset serial elimination SFSC-based method).
Fig. 3 is a comparison graph of average decoding complexity normalized to between the polar code decoding method of the present invention and three existing polar code decoding methods (serdes SC algorithm, CRC-SCL algorithm for cyclic redundancy check assistance, SFSC algorithm based on single bit flipping), the horizontal axis in fig. 3 represents the signal-to-noise ratio, the vertical axis represents the average decoding complexity normalized to , the curve marked with open circles in fig. 3 represents the average decoding complexity curve normalized to of the polar code method using the prior art serdes method, the curve marked with squares in fig. 3 represents the average decoding complexity curve normalized to of the polar code decoding method using the prior art SFSC algorithm based on single bit flipping, and the number of flips is equal to 4, the curve marked with diamonds in fig. 3 represents the average decoding complexity curve normalized to of the polar code decoding method using the prior art, the number of flips is equal to SFSC decoding method based on single bit flipping, the number of flips is equal to 8, the average decoding complexity curve marked with star map 3, the number of the flip times is equal to 389 curve of the polar code decoding method using the average decoding method of the polar code decoding method based on the list , and the average decoding method using star-srep algorithm, and the flip times of the polar code decoding method of the present invention is equal to the average decoding method, the triangular curve marked with the average decoding method of the triangular curve marked srep, and the width of the flip times of the polar code decoding method of the star map 3, and the flip of the polar code decoding method of the average decoding method of the present invention is equal to the average decoding method of the polar code of the star marks of the polar code.
As can be seen from the comparison between the star curve and the circular curve in fig. 3, the star curve is gradually overlapped with the diamond curve under the condition of high signal-to-noise ratio, so that the complexity of the decoding method gradually approaches to the complexity of serial elimination of SC decoding along with the improvement of the signal-to-noise ratio, and the decoding complexity is obviously reduced.

Claims (3)

1, polar code decoding method based on bit reversal serial elimination list algorithm, characterized in that, the concrete steps include the following:
(1) receiving a sequence to be decoded from a communication terminal:
(2) performing serial elimination SC decoding on a sequence to be decoded:
(2a) calculating the log-likelihood ratio of the polarized channel;
(2b) judging the sequence received by the communication terminal according to the positive and negative of the log-likelihood ratio of each polarized channels corresponding to the information bits in the decoding structure judgment layer, if the sequence is positive, judging the sequence to be 0, if the sequence is negative, judging the sequence to be 1, and directly judging the position bits corresponding to each non-information bits in the sequence received by the communication terminal to be 0;
(2c) judging whether the serial number of the current decoding sequence is larger than the code length of the polarization code, if so, executing the step (3) after taking the current decoding sequence as a serial elimination SC decoding sequence, otherwise, executing the step (2a) after adding 1 to the serial number of the current decoding sequence;
(3) judging whether the serial elimination SC decoding sequence passes through cyclic redundancy CRC (cyclic redundancy check), if so, executing the step (9), otherwise, executing the step (4):
(4) initializing the list width and the bit flipping times of the serial elimination list algorithm by using values of 2 to the power of an integer;
(5) selecting a position set with a wrong judgment:
according to a sorting method from small to large, sequentially selecting the positions with decoding judgment errors corresponding to the information bit set from a serial elimination SC decoding sequence which does not pass through cyclic redundancy CRC (cyclic redundancy check), and forming the positions with errors into a position set with serial elimination SC decoding judgment errors;
(6) elements are selected from a position set for serially eliminating SC decoding judgment errors in sequence;
(7) decoding by using a bit flipping serial elimination list algorithm:
(7a) judging whether the sequence number of the current decoding sequence is equal to the value of the selected error position set element, if so, executing the step (7b), otherwise, executing the step (7 c);
(7b) calculating the metric value of each expansion paths at the position where each decoding sequence numbers in the decoding tree are equal to the element value in the position set with the decoding judgment error by using a penalty factor according to the following formula so as to indirectly realize bit flipping;
Figure FDA0002265545580000011
wherein,
Figure FDA0002265545580000021
indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to ith bitiThe values of the metrics of the constructed extension paths,
Figure FDA0002265545580000022
indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to i-1 biti-1Metric values of the formed extension paths, ueIndicating the bit value corresponding to the e-th bit in the serial elimination SC decoding sequence, e indicating the value of an element selected from the set of serial elimination SC decoding decision error positions, LiRepresenting the absolute value of the log-likelihood ratio of the ith polarization channel in the decision layer of the decoding structure, and α representing a penalty factor, wherein the value range of the penalty factor is more than or equal to 100 and less than or equal to α and less than or equal to 2000;
(7c) calculating the metric value of each expansion paths at the sequence number of each decoding sequences in the decoding tree according to the following formula;
wherein,
Figure FDA0002265545580000024
indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to ith bitiThe values of the metrics of the constructed extension paths,
Figure FDA0002265545580000025
indicating the bit u decoded by bit 1 in the decoding tree1Decoding bit u to i-1 biti-1The metric value of the formed extended path belongs to operation, wherein the epsilon represents the selected information bit set during coding, the lambda represents the correct frozen bit value, the value of which is 0, and the value of LiRepresenting the absolute value of the log-likelihood ratio of the ith bit polarization channel in the decision layer;
(7d) judging whether the metric value of the extended path is less than or equal to the list width value of the serial elimination list algorithm, if so, executing the step (7e), otherwise, executing the step (7 f);
(7e) reserving all the extension paths;
(7f) sorting the metric values of the extended paths from large to small, and taking the first Q extended paths in the sorting as candidate paths, wherein the value of Q is equal to the list width value of a serial elimination list algorithm;
(7g) judging whether the serial number of the current decoding sequence is larger than the code length of the polarization code, if so, executing the step (7h), otherwise, adding 1 to the serial number of the current decoding sequence and executing the step (7 a);
(7h) judging whether the candidate paths have paths passing the cyclic redundancy check, if so, selecting paths with the maximum path metric from the candidate paths passing the cyclic redundancy check as a decoding sequence, and then executing the step (9), otherwise, executing the step (8);
(8) judging whether all elements in the position set with errors in serial elimination SC decoding judgment are selected, if so, executing the step (10), otherwise, executing the step (6);
(9) decoding is successful, and a successfully decoded sequence is output;
(10) if the decoding fails, the serial cancellation SC decoding sequence is output.
2. The method for decoding polar codes based on the bit flipping senium elimination list algorithm according to claim 1, wherein the calculating the log-likelihood ratio of the polarized channel in step (2a) is to calculate the log-likelihood ratio of the polarized channel in the decision layer of the decoding structure according to the parity of the serial number of the polarized channel:
A. calculating the log-likelihood ratio of each polarized channel with odd serial number in the decision layer of the decoding structure according to the following formula;
wherein,
Figure FDA0002265545580000032
the input of the polarization channel of the kth odd-numbered sequence number in the decoding structure decision layer which represents the length of the polarization code word is N is
Figure FDA0002265545580000033
K represents the serial number of the polarized channel in the decision layer of the decoding structure, the value of the serial number is 2j-1, j is more than or equal to 1 and less than or equal to N/2, N represents the code word length after the code coding of the polarized code,representing the input of the polarized channel, y represents the sequence received by the communication terminal,
Figure FDA0002265545580000035
represents the decoded first k-1 bit code word sequence, sign (h) represents code words1And L2When the product of (A) is positive, the function value is 1, and when L is positive1And L2When the product of (a) is negative, the function value is a function of-1, L1Representing the log-likelihood ratio, L, of the polarized channel of the upper branch in the adjacent layers of the decoding structure2Represents the log-likelihood ratio of the polarized channel of the lower branch in the adjacent layer of the decoding structure, min (-) represents the function of solving the minimum value of two real numbers, | - | represents the operation of solving the absolute value:
B. calculating the log-likelihood ratio of each polarized channel with even serial number in the decision layer of the decoding structure according to the following formula;
Figure FDA0002265545580000036
wherein,the input of the polarization channel of the mth even serial number in the decoding structure decision layer which represents the length of the polarization code word as N is
Figure FDA0002265545580000038
M represents the serial number of the polarized channel in the decision layer of the decoding structure, the value of the serial number is 2j, j is more than or equal to 1 and less than or equal to N/2, N represents the code word length after the polarized code is coded,
Figure FDA0002265545580000041
representing the input of the polarized channel, y represents the sequence received by the communication terminal,
Figure FDA0002265545580000042
representing the first m-1 bit codeword sequence that has been decoded,
Figure FDA0002265545580000043
indicating the m-1 th bit of the codeword, L, that has been decoded1Representing the log-likelihood ratio, L, of the polarized channel of the upper branch in the adjacent layers of the decoding structure2Representing the log-likelihood ratio of the polarized channel of the lower branch in the layer adjacent to the decoding structure.
3. The polar code decoding method based on the bit flipping serial elimination list algorithm according to claim 1, wherein the sorting method from small to large in step (5) specifically comprises sorting log likelihood ratio absolute values of polar channels corresponding to information bits in a decision layer from small to large, sequentially selecting polar channel index positions corresponding to absolute values of log likelihood ratios of first T polar channels to form a decision error position set, wherein T is values equal to the number of bit flipping times.
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