CN107528597B - LDPC code post-processing decoding method based on CRC code - Google Patents

Abstract

The invention discloses an LDPC code post-processing decoding method based on CRC check codes, which is characterized by comprising the following steps: 1) performing an LBP coding method; 2) CRC checking: 3) sorting LLR values; 4) selecting a target node; 5) turning over the nodes; 6) and CRC checking again: and in the post-processing stage, performing CRC (cyclic redundancy check) on the decoding judgment result again, judging that the decoding is successful and stopping the decoding if the CRC is successful, and otherwise, skipping to the step 5) to continue to turn over. The method can sequentially turn over error bits in the subsequent processing stage of the error frame, destroy potential trapping sets, and improve the error floor while ensuring lower decoding complexity.

Description

LDPC code post-processing decoding method based on CRC code

Technical Field

The invention relates to the technical field of communication, in particular to a Low Density Parity Check (Low Density Parity Check-Check, LDPC) code post-processing decoding method based on CRC (Cyclic Redundancy Check) codes.

Background

The LDPC code is a linear block code first proposed by Gallager in 1962, and is widely applied to multiple communication standards such as DVB-S2, WiMax and deep space communication due to its excellent characteristics close to shannon limit and low decoding complexity, however, an error floor caused by a trapping set makes the LDPC code unable to obtain a very low error rate in a high signal-to-noise ratio region, and the application of the LDPC code to data storage and optical communication systems requiring high reliability data transmission is severely restricted. To address this problem, researchers at home and abroad have begun to try to adopt different approaches to reduce the error floor, and have achieved some research results.

From the perspective of constructing the LDPC code, Tao X and the like analyze the relationship between the eight loops and the small trapping sets in the tanner graph, and find that the small trapping sets can be completely eliminated by avoiding a specific eight loop, and then the LDPC code of a low error floor is constructed, but the design complexity of the code is increased. Starting from an improved decoding algorithm, t.r.halford et al propose a decoding algorithm based on trapping set elimination, and achieve the purpose of eliminating trapping sets and improving error floor by adding a small number of odd check nodes, however, trying to search out all trapping sets is an NP complete problem, and at the same time, it also causes a loss of code rate. Ryan et al designs three decoder structures of bit pattern, bit stuffing and general LDPC to reduce the error floor, but designing the decoder requires to know the trapping set internal information in advance, and is only suitable for specific types of codewords. To solve the problem, Kang J et al propose a Backtracking decoding (Backtracking decoding) strategy, which does not need to know the information related to the trapping set, but only predicts the information bits that may cause decoding failure in the previous iteration in advance, and reverses the initial Log-Likelihood Ratio (LLR) value of the variable node and decodes the variable node again, but may cause decoding failure if the reliable node is mistakenly reversed. Beomkyu et al propose a post-processing scheme that does not require data retransmission and re-reading, destroys the trap set structure by deciding the change of the symbol and LLR amplitude in the codeword, and effectively reduces the error floor. But the overall decoding complexity of the algorithm increases when the maximum number of iterations is reached. Zhang X et al re-decode unsuccessfully decoded codewords in the first decoding step based on a Two-Stage decoding method to reduce the error floor. Likhobabin et al propose a method for deleting variable nodes, directly delete variable nodes with symbols changing in two iterations before and after, to reduce the error floor, but the algorithm has a certain loss in performance in a low signal-to-noise ratio region, the error floor under a high signal-to-noise ratio is still not ideal, and the error rate is to be further reduced.

The invention content is as follows:

the invention aims to provide an LDPC code post-processing decoding method based on CRC codes aiming at the defects of the prior art. The method can sequentially turn over error bits in the subsequent processing stage of the error frame, destroy potential trapping sets, and improve the error floor while ensuring lower decoding complexity.

The technical scheme for realizing the purpose of the invention is as follows:

an LDPC code post-processing decoding method based on CRC codes comprises the following steps:

1) executing an LBP (Layered Belief Propagation, abbreviated as LBP) decoding method;

2) CRC checking: when the LBP decoding method is finished in the step 1), performing CRC check on the decoding judgment result, performing CRC check judgment, judging that the decoding is successful and stopping decoding if the check is successful, and otherwise, performing the next step;

3) LLR (Log-Likelihood Ratio, LLR for short) value sorting: sorting the posterior LLR values of the variable nodes in the error frame in ascending order to obtain an ordered node sequence;

4) selecting a target node: selecting a plurality of target Nodes from the ordered node sequence to form a BN (Bad Nodes, BN for short) set;

5) node overturning: sequentially turning over initial LLR values of information nodes in the BN set;

6) and CRC checking again: and in the post-processing stage, performing CRC (cyclic redundancy check) on the decoding judgment result again, judging that the decoding is successful and stopping the decoding if the CRC is successful, and otherwise, skipping to the step 5) to continue to turn over.

The LBP decoding method in the step 1) comprises the following steps:

(1) initialization: hypothesis matrix H_M×NIs a check matrix of LDPC code, M is the number of check nodes, N is the number of variable nodes, after encodingCode word c ═ c₁,c₂,...,c_n) Mapping the BPSK modulated signal into a transmission code word x ═ (x)₁,x₂,...,x_n) Wherein x is_n＝1-2c_nN is 1, 2., N, and the signal y after noise addition over AWGN channel is (y is) N₁,y₂,...,y_n) Wherein y is_n＝x_n+n_n，n_nGaussian noise, y, representing the superposition of the nth symbol_nIs the mean value x and the variance σ²Gaussian noise of (2); h _mn1 indicates that a check node m is connected with a variable node n by a side, and m (n) represent adjacent nodes of the variable node n and all adjacent nodes of the variable node n except the check node m respectively; let N (m) and N (m) \\ n denote the neighboring nodes of the check node m and all the neighboring nodes of the check node except the variable node n, respectively, and the initial message of the signaling channel is L (P)_n) If the initial message transmitted by the variable node to the check node is L⁽⁰⁾(q_mn)＝L(P_n)＝2y_n/σ²Initializing check node messages of all layers to be 0;

(2) and (3) message updating: for all check nodes m and the check nodes n belonging to the check nodes m and adjacent to the check nodes m, the message transmitted from the variable node to the check node in the ith iteration is as follows:

for all variable nodes n and the check nodes m adjacent to the variable nodes n, belonging to M (n), in the ith iteration, the messages transmitted from the check nodes to the variable nodes are as follows: l is^(l)(q_mn)＝L^(l-1)(q_n)-L^(l-1)(r_mn)，

Hard decision messages are computed for all variable nodes: l is^(l)(q_n)＝L^(l-1)(q_n)-L^(l-1)(r_mn)+L^(l)(r_mn)；

(3) And (3) decoding judgment: mixing L with^(l)(q_n) Is compared with zero if L^(l)(q_n) If less than 0, then

Otherwise, the value is 0;

(4) syndrome judgment: if the syndrome H_MxNc^TIf the iteration number is 0 or the maximum iteration number is reached, ending the decoding, otherwise, returning to the step (2) to continue the iteration.

Compared with the prior art, the technical scheme combines a CRC check post-processing decoding method in the LDPC decoding process, firstly, CRC check is carried out on the judgment result of LBP decoding, if the check fails, the posterior LLR values of variable nodes in an error frame are arranged in an ascending order, then a plurality of previous target nodes are selected from the ordered node sequence to form a bad node set, the initial LLR value of the information node in the BN set is turned over and decoding is continued until the CRC check succeeds, so that a potential trap set is broken, and the node reliability is improved.

The method can sequentially turn over error bits in the subsequent processing stage of the error frame, destroy potential trapping sets, and improve the error floor while ensuring lower decoding complexity.

Description of the drawings:

FIG. 1 is a schematic flow chart of an exemplary method;

FIG. 2 shows trapping sets of example (3, 1);

FIG. 3 is an embodiment of a CRC encoding scheme;

FIG. 4 is a comparison of error performance curves of the CRC-LBP decoding method under different P values in the embodiment;

FIG. 5 is a comparison of error rates of the PEG-LDPC code in the embodiment under five different decoding algorithms;

FIG. 6 is a comparison of bit error rates of QC-LDPC codes in three different decoding algorithms according to an embodiment;

fig. 7 is a bit error rate comparison of the Mackay code under three different decoding algorithms in the embodiment.

The specific implementation mode is as follows:

the invention will be further illustrated, but not limited, by the following description of the embodiments with reference to the accompanying drawings.

Example (b):

referring to fig. 1, a method for decoding an LDPC code post-processing based on a CRC check code includes the steps of:

1) performing an LBP coding method;

2) CRC checking: when the LBP decoding method is finished in the step 1), performing CRC check on the decoding judgment result, performing CRC check judgment, judging that the decoding is successful and stopping decoding if the check is successful, and otherwise, performing the next step;

3) LLR value sorting: sorting the posterior LLR values of the variable nodes in the error frame in ascending order to obtain an ordered node sequence;

4) selecting a target node: selecting a plurality of first target nodes from the ordered node sequence to form a BN set;

5) node overturning: sequentially turning over initial LLR values of information nodes in the BN set;

6) and CRC checking again: and in the post-processing stage, performing CRC (cyclic redundancy check) on the decoding judgment result again, judging that the decoding is successful and stopping the decoding if the CRC is successful, and otherwise, skipping to the step 5) to continue to turn over.

The LBP decoding method in the step 1) comprises the following steps:

(1) initialization: hypothesis matrix H_M×NThe code is a check matrix of the LDPC code, wherein M is the number of check nodes, N is the number of variable nodes, and the coded code word c is equal to (c)₁,c₂,...,c_n) Mapping the BPSK modulated signal into a transmission code word x ═ (x)₁,x₂,...,x_n) Wherein x is_n＝1-2c_nN is 1, 2., N, and the signal y after noise addition over AWGN channel is (y is) N₁,y₂,...,y_n) Wherein y is_n＝x_n+n_n，n_nGaussian noise, y, representing the superposition of the nth symbol_nIs the mean value x and the variance σ²Gaussian noise of (2); h _mn1 indicates that a check node m is connected with a variable node n by a side, and m (n) represent adjacent nodes of the variable node n and all adjacent nodes of the variable node n except the check node m respectively; let N (m) and N (m) \\ n denote the neighboring nodes of the check node m and all the neighboring nodes of the check node except the variable node n, respectively, and the initial message of the signaling channel is L (P)_n) Then the variable node is transferred to the first of the check nodesThe initial message is L⁽⁰⁾(q_mn)＝L(P_n)＝2y_n/σ²Initializing check node messages of all layers to be 0;

(2) and (3) message updating: for all check nodes m and the check nodes n belonging to the check nodes m and adjacent to the check nodes m, the message transmitted from the variable node to the check node in the ith iteration is as follows:

for all variable nodes n and the check nodes m adjacent to the variable nodes n, belonging to M (n), in the ith iteration, the messages transmitted from the check nodes to the variable nodes are as follows: l is^(l)(q_mn)＝L^(l-1)(q_n)-L^(l-1)(r_mn)，

Hard decision messages are computed for all variable nodes: l is^(l)(q_n)＝L^(l-1)(q_n)-L^(l-1)(r_mn)+L^(l)(r_mn)；

(3) And (3) decoding judgment: mixing L with^(l)(q_n) Is compared with zero if L^(l)(q_n) If less than 0, then

Otherwise, the value is 0;

(4) syndrome judgment: if the syndrome H_MxNc^TIf the iteration number is 0 or the maximum iteration number is reached, ending the decoding, otherwise, returning to the step (2) to continue the iteration.

Specifically, the method comprises the following steps: fig. 3 shows an example of a CRC encoding scheme, in which an LDPC code is divided into data bits, CRC bits, and parity bits, and effective data bits are CRC-encoded and then LDPC-encoded.

CRC coding uses the principles of division and remainder to achieve accurate detection of erroneous frames occurring during decoding. In practical application, a CRC value is calculated at a message sending end according to an original code word sequence, the CRC value and a transmitted updating message are sent to a decoding receiving end at the same time, the CRC value is recalculated for a decoding result by the receiving end and is compared with the received CRC value, and if the two CRC values are different, an error occurs in decoding;

as shown in fig. 2, one (3,1) trapping set in the embodiment:

defining: (w, v) trapping set is a set composed of w variable nodes, the subgraph induced by the set comprises v odd-degree check nodes and any even-degree check node,

in particular, in a decoding algorithm based on message updating, a small trapping set is a key cause of a wrong leveling phenomenon, because w and v values of the decoding algorithm are relatively small, the probability that w nodes make mistakes simultaneously is high, w wrong nodes cannot obtain enough reliable messages from v odd-degree check nodes to correct LLR values of the check nodes, and a decoder is always in a 'trapping' state until the maximum iteration number is reached.

In a high signal-to-noise ratio region, due to the existence of the trapping set, although most bit nodes can achieve correct decoding, partial error nodes still exist, and the nodes cannot be corrected even if the iteration number is increased. The phenomenon of false floor leveling caused by trapping mainly has two characteristics: 1) node oscillation, namely the phenomenon that LLR values of partial nodes greatly oscillate in two iterations; 2) the error converges, and the decoding converges to a certain error state and does not change any more in subsequent iterations. Usually, the sign of the error node frequently changes and the LLR amplitude is small, and is easily affected by information transmitted from neighboring nodes, so that the nodes are selected for re-decoding, and the trapping set is damaged. It should be noted that the selected target node is not necessarily a variable node in the trapping set, and the external node may also cause decoding failure to generate an error bit.

As shown in figure 3 for the CRC coding scheme,

the cyclic redundancy check code adopted in this embodiment is the most commonly used error check code in the field of data communication, polynomial operation is performed on a transmission codeword, an obtained redundancy code is attached to a data bit, and the same polynomial operation is performed after decoding is completed to ensure the correctness and integrity of codeword transmission. The selected version of the international CRC standard in this embodiment is CRC-16 ═ CRCX¹⁶+X¹⁵+X²+1, the corresponding check binary sequence is 11000000000000101, the information bit is divided into two segments, data bit and CRC, the CRC coding is performed on the valid data bit first, and then the LDPC coding is performed. In this embodiment, CRC check is selected to replace the conventional syndrome decision rule, and mainly because the number of error nodes is not reduced with the increase of the iteration number after the decoding reaches a certain iteration number, but the error nodes are in an oscillation state, so that it is very likely that the number of error nodes is oscillated to the highest when the maximum iteration number is reached, and if the syndrome decision is adopted at this time, the state is the final decoding output, which not only brings additional decoding iteration and increases the decoding complexity, but also seriously affects the decoding performance.

Fig. 4 shows error performance curves of the CRC-LBP algorithm at different P values.

Setting the number of the selected target nodes as P, determining the optimal value by computer simulation, and turning over the P target nodes in the BN set one by one in the subsequent decoding treatment, thereby generating 2^P1 flip vector (except for all-zero vector), when the value of P is too small, the initial information of partial error bit is not flipped, and the improvement of error level is not obvious; when the P value is too large to exceed a certain threshold, the decoding performance is improved in a high signal-to-noise ratio region to a limited extent, and a large amount of hardware resources are consumed, so that the selection of the P value needs to compromise the error code performance and the decoding complexity.

Under the conditions of BPSK modulation and AWGN channel, an IEEE 802.16e (576,288) LDPC code is selected, and P values are respectively taken as [8,11,12 and 14 ].

As can be seen from fig. 4, as the P value increases, the performance of the method of this embodiment is gradually improved, but when P >11, the error performance falls into a bottleneck, and at this time, if the P value continues to increase, a small number of correct nodes are selected into the BN set, which not only does not greatly improve the error performance, but also brings an exponential rise of complexity, and in sum, the P value is preferably selected to be 11.

As shown in FIGS. 5, 6 and 7, when simulation verification is performed by using the PEG-LDPC code, the QC-LDPC code and the Mackay code, the CRC-LBP decoding method of the invention can obtain a lower error rate in a high signal-to-noise ratio region.

Claims (2)

1. An LDPC code post-processing decoding method based on CRC codes is characterized by comprising the following steps:

1) performing an LBP coding method;

2) CRC checking: in step 1), when the LBP decoding method is finished, performing CRC check on a decoding judgment result, performing CRC check judgment, and if the check is successful, judging that the decoding is successful and stopping the decoding; otherwise, executing the next step;

3) LLR value sorting: sorting the posterior LLR values of the variable nodes in the error frame in ascending order to obtain an ordered node sequence;

4) selecting a target node: selecting a plurality of first target nodes from the ordered node sequence to form a BN set;

5) node overturning: sequentially turning over initial LLR values of information nodes in the BN set;

6) and CRC checking again: and in the post-processing stage, performing CRC (cyclic redundancy check) on the decoding judgment result again, judging that the decoding is successful and stopping the decoding if the CRC is successful, and otherwise, skipping to the step 5) to continue to turn over.

2. The LDPC code postprocessing decoding method based on the CRC check code according to claim 1, wherein the LBP decoding method in step 1) includes the steps of:

(1) initialization: hypothesis matrix H_M×NThe code is a check matrix of the LDPC code, wherein M is the number of check nodes, N is the number of variable nodes, and the coded code word c is equal to (c)₁,c₂,...,c_n) Mapping the BPSK modulated signal into a transmission code word x ═ (x)₁,x₂,...x,_n) Wherein x is_n＝1-2c_nN is 1, 2., N, and the signal y after noise addition over AWGN channel is (y is) N₁,y₂,...,y_n) Wherein y is_n＝x_n+n_n，n_nGaussian noise, y, representing the superposition of the nth symbol_nIs the mean value x and the variance σ²Gaussian noise of (2); h_mn1 indicates that a check node m is connected with a variable node n by an edge, and M (n) each indicate a variable noden and all the adjacent nodes of the variable node n except the check node m; let N (m) and N (m) \\ n denote the neighboring nodes of the check node m and all the neighboring nodes of the check node except the variable node n, respectively, and the initial message of the signaling channel is L (P)_n) If the initial message transmitted by the variable node to the check node is L⁽⁰⁾(q_mn)＝L(P_n)＝2y_n/σ²Initializing check node messages of all layers to be 0;

(2) and (3) message updating: for all check nodes m and the check nodes n belonging to the check nodes m and adjacent to the check nodes m, the message transmitted from the variable node to the check node in the ith iteration is as follows:

for all variable nodes n and the check nodes m adjacent to the variable nodes n, belonging to M (n), in the ith iteration, the messages transmitted from the check nodes to the variable nodes are as follows: l is^(l)(q_mn)＝L^(l-1)(q_n)-L^(l-1)(r_mn)，

Hard decision messages are computed for all variable nodes: l is^(l)(q_n)＝L^(l-1)(q_n)-L^(l-1)(r_mn)+L^(l)(r_mn)；

(3) And (3) decoding judgment: mixing L with^(l)(q_n) Is compared with zero if L^(l)(q_n) If less than 0, then

Otherwise, the value is 0;

(4) syndrome judgment: if the syndrome H_MxNc^TIf the iteration number is 0 or the maximum iteration number is reached, ending the decoding, otherwise, returning to the step (2) to continue the iteration.

Images