CN113556135B - Polarization code belief propagation bit overturn decoding method based on frozen overturn list - Google Patents

Polarization code belief propagation bit overturn decoding method based on frozen overturn list Download PDF

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CN113556135B
CN113556135B CN202110849031.4A CN202110849031A CN113556135B CN 113556135 B CN113556135 B CN 113556135B CN 202110849031 A CN202110849031 A CN 202110849031A CN 113556135 B CN113556135 B CN 113556135B
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ffl
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polarization code
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CN113556135A (en
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潘志文
李甲
尹超
刘楠
尤肖虎
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Southeast University
Network Communication and Security Zijinshan Laboratory
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Network Communication and Security Zijinshan Laboratory
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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
    • H03M13/03—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
    • 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 polarization code belief propagation bit inversion decoding method based on a frozen inversion list, wherein the used code words are cascade codes formed by Cyclic Redundancy Check (CRC) codes and polarization codes. Under the condition that the traditional BP decoding result does not pass CRC check, the method in the invention constructs a Frozen Flip List (FFL) by analyzing the decoding result in the BP decoding method, and inverts information bits with polarization codes in the FFL (the bit inversion in the invention is realized by inverting the sign of the log likelihood ratio of the inverted bits at the receiving end, and the absolute value of the log likelihood ratio is unchanged), so that errors in part of BP decoders can be corrected, and further, the block error rate performance of the BPF decoding method is improved.

Description

Polarization code belief propagation bit overturn decoding method based on frozen overturn list
Technical Field
The invention belongs to the field of channel coding in wireless communication, and particularly relates to a polarization code belief propagation bit overturn decoding method based on a frozen overturn list.
Background
The polarization code technology is used as a novel channel coding technology, and when the code length is towards infinity, the transmission rate can reach the channel capacity of a binary input memory-free symmetrical channel. At present, two types of coding modes of polarization codes are mainstream, one type of coding method based on serial offset (Successive Cancellation, SC) comprises a serial offset list (Successive Cancellation List, SCL) coding method based on SC coding, the coding method based on SC belongs to sequential coding, and decoded information bits influence the estimation of subsequent information bits, so that the information bits in code words must be estimated one by one, and larger coding delay is generated. Another type of mainstream decoding method of the polar code is based on a belief propagation (Belief Propagation, BP) decoding method, including a belief propagation bit Flip (Belief Propagation bit-Flip, BPF) decoding method, and the BP-based decoding method is significantly lower in decoding delay than the SC-based decoding method and insensitive to codeword length due to the parallel iterative computation property thereof, so that the BP decoding method is suitable for application scenarios with higher delay requirements. The traditional BP decoding method has poor Block Error Rate (BLER) performance, and the BPF decoding method brings about improvement of the BLER performance, but has higher average iteration times, higher calculation complexity and still has room for improvement of the BLER performance. The polarization code belief propagation bit inversion decoding method based on the frozen inversion list improves the BLER performance of the BPF decoding method and reduces the computational complexity.
Disclosure of Invention
The invention aims to provide a polarization code belief propagation bit overturn decoding method based on a frozen overturn list, which aims to solve the technical problems of high technical complexity and poor block error rate performance.
In order to solve the technical problems, the specific technical scheme of the invention is as follows:
a polarization code belief propagation bit inversion decoding method based on a frozen inversion list comprises the following steps:
step 1, BP decoding with CRC is carried out;
step 2, constructing a frozen flip list FFL;
and step 3, performing polarization code belief propagation bit inversion decoding based on the frozen inversion list.
Further, the step 1 specifically includes the following steps:
step 1.1, marking the information sequence with the length of K and without filling frozen bits after CRC coding as an original information bit sequence, marking the information sequence with the length of N obtained by filling frozen bits from the original information bit sequence with the length of K as an information bit sequence, marking the information bit sequence with the length of N after polarization code coding to generate a bit sequence with the length of N called a code word bit sequence, marking the log likelihood ratio of a received signal as for the polarization code with the length of N and the length of K of the original information bit sequence asFor->Performing polarization code BP decoding, wherein llr i I is more than or equal to 1 and less than or equal to N refers to the log likelihood ratio of the received signal>Is the i-th element of (a);
step 1.2, recordAn output result of the BP decoder being a polarization code, wherein +.>Refers to the information bit u i Is determined by the estimation of (a); if->If the cyclic redundancy check is satisfied, the BP decoder decodes successfully, the whole decoding flow is finished, and the subsequent steps are not executed any more; if->If the cyclic redundancy check is not satisfied, the BP decoder fails to decode and needs to perform heuristic bit-flipping decoding.
Further, the step 2 specifically includes the following steps:
step 2.1, freezing set A according to polarization code c Constructing unordered freeze flip list FFL unsorted Wherein: FFL (FFL) unsorted ＝{k 1 ,k 2 ,…,k m |k j ∈A c M is the polarization code frozen set A c N- (K+r), where r is the length of the CRC, K j J.ltoreq.m is the set FFL unsorted The j-th element of (a);
and 2.2, obtaining a frozen flip list FFL.
Further, step 2.2 specifically includes the following steps:
in the polarization code, each information bit u i Are all corresponding to oneProbability of error p e (u i ) Aggregate FFL unsorted The corresponding set of error probabilities is noted asWherein->Representing information bits->Error probability of>Calculated by means of the Gaussian approximation method according to the error probability +.>High to low pair FFL unsorted The middle elements are ordered to obtain a frozen flip list FFL= { w 1 ,w 2 ,…,w m -w is j 1.ltoreq.j.ltoreq.m is the j-th element in the set FFL.
Further, the step 3 specifically includes the following steps:
step 3.1, initializing t=1, and counting the times of bit flip decoding by using t;
step 3.2, if T is more than T, wherein T is the maximum try overturn times of the preset BPF decoder, and T is less than or equal to m, the BPF decoding method based on the frozen overturn list fails to decode, and the whole decoding flow is ended; if T is less than or equal to T, turning to step 3.3;
step 3.3, initializing a BP decoder; BP decoder in BPF decoding method indexes w in code word bit sequence t Bit flipping of bits of (2), where w t Is the t-th element in the FFL set; the BP decoder corresponds to a matrix L, L being a matrix of size Nx (1+log 2 N), where N is the length of the polar code, the last column of L is used to store the log-likelihood ratio of the codeword bits;
step 3.4, performing BP decoding by using the matrix L assigned according to the step 3.3, and recordingAn output result of the BP decoder being a polarization code, wherein +.>Refers to the information bit u i Is determined by the estimation of (a); if->If the cyclic redundancy check is satisfied, the BP decoder decodes successfully, the whole BPF decoding flow is ended, and the subsequent steps are not executed any more; if->If the cyclic redundancy check is not satisfied, the BP decoder fails to decode, and the BPF fails to decode, so that t=t+1, and the process goes to step 3.2.
Further, the rule of bit flipping described in step 3.3 is: if the BP decoder receives a signal in step 1, which is the codeword bit sequenceW of (w) t The log-likelihood ratio of the individual bits is +.>W of L matrix corresponding to BP decoder t The last column element of the row is assigned +.>Namely:
the polarization code belief propagation bit inversion decoding method based on the frozen inversion list has the following advantages:
1. according to the polarization code belief propagation bit overturn decoding method based on the freezing overturn list, under the condition that the polarization code BP decoding method fails to decode, the freezing overturn list for identifying unreliable code word bit sequences can be constructed by applying the freezing bit set thought, the log likelihood ratio of the overturn unreliable code word bits is opposite in sign and the absolute value is the same, decoding errors in the BP decoding method are corrected in a heuristic decoding mode, the BLER performance of the polarization code under the BPF decoding method is improved, and the calculation complexity is reduced compared with other BPF decoding algorithms.
2. In the middle-low signal-to-noise ratio interval (1-2 dB), compared with the BP decoding method, the method can have a gain of 0.8dB, and compared with a CRC-assisted serial cancellation list decoder (with a list length of 8), the method has a gain of 0.5 dB. In the middle-high signal-to-noise ratio range, the method has the advantage of calculating complexity. Compared with a BP decoder, the method can acquire the gain of the block error rate performance at the cost of smaller decoding delay.
Drawings
Fig. 1 is a flow chart of a polarization code belief propagation bit flipping decoding method based on a frozen flip list.
Detailed Description
For better understanding of the purpose, structure and function of the present invention, a polarization code belief propagation bit-flipping decoding method based on the frozen-flipped list of the present invention is described in further detail below with reference to the accompanying drawings.
The polarization code belief propagation bit inversion decoding method based on the frozen inversion list in the invention uses the code length N=256, the original information bit sequence length K=120 (cyclic redundancy check code length r=24, and the construction polynomial is g (x) =x) 24 +x 23 +x 6 +x 5 The polarization code of +x+1 is illustrated by way of example, where g (x) is a CRC check code, i.e., a construction polynomial of a cyclic redundancy check code. The method of constructing the polarization code in this embodiment is gaussian approximation, and the signal-to-noise ratio of the codeword construction is 2.5 db. The maximum number of iterations of the BP decoder is 100, and the maximum number of inversions T of the bpf decoder is set to 100.
As shown in fig. 1, the method comprises the following steps:
and step 1, performing BP decoding with CRC. The method comprises the following steps:
and 1.1, initializing. For a polarization code with a code length of n=256 and an original information bit sequence length of k=120 (in the present technical solution, an information sequence with a length of k=120 after CRC encoding and without padding with frozen bits is denoted as an original information bit sequence, an information sequence with a length of n=256 obtained by padding an original information bit sequence with a length of k=120 with frozen bits is denoted as an information bit sequence, a bit sequence with a length of n=256 after encoding an information bit sequence with a polarization code is denoted as a codeword bit sequence), and a log likelihood ratio of a received signal is denoted asFor->Performing polarization code BP decoding, wherein llr i I is more than or equal to 1 and less than or equal to N refers to the log likelihood ratio of the received signal>Is the i-th element of (c).
Step 1.2, recordAn output result of the BP decoder being a polarization code, wherein +.>Refers to the information bit u i Is a function of the estimate of (2). If->The cyclic redundancy check is satisfied, and the satisfaction condition is: g (x) can be satisfied by corresponding to a check matrix H, u×h=0, which is well known, so that in the decoding method, no redundant description is needed, the BP decoder decodes successfully, the whole decoding process ends, and no subsequent steps are executed; if->If the cyclic redundancy check is not satisfied, the BP decoder fails to decode, and a tentative bit-flipping decoding is required to be performed, and the process proceeds to step 2.
And 2, constructing a frozen flip list FFL. The method comprises the following steps:
step 2.1, freezing set A according to polarization code c Constructing unordered freeze flip list FFL unsorted Wherein: FFL (FFL) unsorted ＝{k 1 ,k 2 ,…,k m |k j ∈A c M=112 is the polarization code frozen set a c Length, k of j J.ltoreq.m is the set FFL unsorted The j-th element of (a).
And 2.2, obtaining a frozen flip list FFL. In the polarization code, each information bit u i All correspond to an error probability p e (u i ) Aggregate FFL unsorted The corresponding set of error probabilities is noted asWherein the method comprises the steps ofRepresenting information bits->Error probability of>May be calculated by gaussian approximation. According to error probability->High to low pair FFL unsorted The middle elements are ordered to obtain a frozen flip list FFL= { w 1 ,w 2 ,…,w m -w is j 1.ltoreq.j.ltoreq.m is the j-th element in the set FFL.
And step 3, performing polarization code belief propagation bit inversion decoding based on the frozen inversion list. The method comprises the following steps:
step 3.1, initializing t=1, counting the times of bit flip decoding by t, and turning to step 3.2.
Step 3.2, if T > T (at this time, T is the maximum number of times of trial flipping of the preset BPF decoder, T is less than or equal to m, in this example, T is 100), the BPF decoding method based on the frozen flip list fails to decode, and the whole decoding process ends; if T is less than or equal to T, the step 3.3 is carried out.
And 3.3, initializing the BP decoder. BP decoder in BPF method indexes w in code word bit sequence t (w t The t-th element in the FFL set). The BP decoder corresponds to a matrix L, L being a matrix of size Nx (1+log 2 N) (in this embodiment, the matrix size is 256×9), where N is the length of the polarization code. The last column of L is used to store the log-likelihood ratio of the codeword bits. The rule of bit flipping is: if the BP decoder in step 1 code word bit sequence (i.e. received signal) W of (w) t The log-likelihood ratio of the individual bits is +.>W of L matrix corresponding to BP decoder t The last column element of the row is assigned +.>Namely:
in the present embodiment, if the codeword bit log likelihood ratio corresponding to the 3 rd element in FFLLet L (w) 3 ,9)＝-0.052。
The values of the remaining elements in L are still assigned according to the conventional BP decoding method. Go to step 3.4.
And 3.4, performing BP decoding by using the matrix L assigned according to the step 3.3. Recording deviceAn output result of the BP decoder being a polarization code, wherein +.>Refers to the information bit u i Is a function of the estimate of (2). If->If the cyclic redundancy check is satisfied, the BP decoder decodes successfully, the whole BPF decoding flow is ended, and the subsequent steps are not executed any more; if->If the cyclic redundancy check is not satisfied, the BP decoder fails to decode, and the BPF fails to decode, so that t=t+1, and the process goes to step 3.2.
It will be understood that the invention has been described in terms of several embodiments, and that various changes and equivalents may be made to these features and embodiments by those skilled in the art without departing from the spirit and scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims (2)

1. The polarization code belief propagation bit inversion decoding method based on the frozen inversion list is characterized by comprising the following steps of:
step 1, BP decoding with CRC is carried out;
step 2, constructing a frozen flip list FFL;
step 3, performing polarization code belief propagation bit overturn decoding based on the frozen overturn list;
the step 1 specifically comprises the following steps:
step 1.1, marking the information sequence with the length of K and without filling frozen bits after CRC coding as an original information bit sequence, marking the information sequence with the length of N obtained by filling frozen bits from the original information bit sequence with the length of K as an information bit sequence, marking the information bit sequence with the length of N after polarization code coding to generate a bit sequence with the length of N called a code word bit sequence, marking the log likelihood ratio of a received signal as for the polarization code with the length of N and the length of K of the original information bit sequence asFor->Performing polarization code BP decoding, wherein llr i I is more than or equal to 1 and less than or equal to N refers to the log likelihood ratio of the received signal>Is the i-th element of (a);
step 1.2, recordAn output result of the BP decoder being a polarization code, wherein +.>Refers to the information bit u i Is determined by the estimation of (a); if->If the cyclic redundancy check is satisfied, the BP decoder decodes successfully, the whole decoding flow is finished, and the subsequent steps are not executed any more; if->If the cyclic redundancy check is not satisfied, the BP decoder fails to decode and needs to perform heuristic bit flip decoding;
the step 2 specifically comprises the following steps:
step 2.1, freezing set A according to polarization code c Constructing unordered freeze flip list FFL unsorted Wherein: FFL (FFL) unsorted ＝{k 1 ,k 2 ,…,k m |k j ∈A c M is the polarization code frozen set A c N- (K+r), where r is the length of the CRC, K j J.ltoreq.m is the set FFL unsorted The j-th element of (a);
step 2.2, obtaining a frozen flip list FFL;
the step 2.2 specifically comprises the following steps:
in the polarization code, each information bit u i All correspond to an error probability p e (u i ) Aggregate FFL unsorted The corresponding set of error probabilities is noted asWherein->Representing information bits->Is used for the error probability of (1),calculated by means of the Gaussian approximation method according to the error probability +.>High to low pair FFL unsorted The middle elements are ordered to obtain a frozen flip list FFL= { w 1 ,w 2 ,…,w m -w is j 1.ltoreq.j.ltoreq.m is the jth element in the collection FFL;
further, the step 3 specifically includes the following steps:
step 3.1, initializing t=1, and counting the times of bit flip decoding by using t;
step 3.2, if T is more than T, wherein T is the maximum try overturn times of the preset BPF decoder, and T is less than or equal to m, the BPF decoding method based on the frozen overturn list fails to decode, and the whole decoding flow is ended; if T is less than or equal to T, turning to step 3.3;
step 3.3, initializing a BP decoder; BP decoder in BPF decoding method indexes w in code word bit sequence t Bit flipping of bits of (2), where w t Is the t-th element in the FFL set; the BP decoder corresponds to a matrix L, L being a matrix of size Nx (1+log 2 N), where N is the length of the polar code, the last column of L is used to store the log-likelihood ratio of the codeword bits;
step 3.4, performing BP decoding by using the matrix L assigned according to the step 3.3, and recordingAn output result of the BP decoder being a polarization code, wherein +.>Refers to the information bit u i Is determined by the estimation of (a); if->If the cyclic redundancy check is satisfied, the BP decoder decodes successfully, the whole BPF decoding flow is ended, and the subsequent steps are not executed any more; if->If the cyclic redundancy check is not satisfied, the BP decoder fails to decode, and the BPF fails to decode, so that t=t+1, and the process goes to step 3.2.
2. The polarization code belief propagation bit-flipping decoding method based on the frozen flip list according to claim 1, wherein the rule of bit-flipping in step 3.3 is: if the BP decoder receives a signal in step 1, which is the codeword bit sequenceW of (w) t The log-likelihood ratio of the individual bits is +.>W of L matrix corresponding to BP decoder t The last column element of the row is assigned +.>Namely:
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