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Decoding of NB-LDPC Codes based on Multi-Layer Perceptual Neural Networks

Tianwei Han, Meiling Zhang, Yuyan Wang, Guijun Hu

Published Jul 21, 2022• 0 citations
Publisher

Abstract

Abstract Low Density Parity Check (LDPC) codes have been extraordinarily important in the field of communications because its error-correction approximates to Shannon limit. Binary LDPC codes have been applied in many fields, and relatively Non-Binary (NB) LDPC codes have recently attracted considerable attention on account of their better error performance. Common NB-LDPC codes decoding algorithm involves Belief Propagation (BP) algorithm, Fast Hadamard Transform-BP (FHT-BP) algorithm, etc. The decoding performance of each algorithm has a certain upper limit. In this paper, the code word structure of NB-LDPC codes is considered, and the decoding of LDPC codes under Galois Field(4) (GF(4)) is mainly indicated. On the basis of the FHT-BP algorithm, Multi-Layer Perceptron (MLP) neural networks and bit flipping (BF) method are introduced for joint decoding. This method can improve the error performance of LDPC codes and achieve better decoding results.

DOI
10.21203/rs.3.rs-1818360/v1

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Abstract Low Density Parity Check (LDPC) codes have been extraordinarily important in the field of communications because its error-correction approximates to Shannon limit. Binary LDPC codes have been applied in many fields, and relatively Non-Binary (NB) LDPC codes have recently attracted considerable attention on account of their better error performance. Common NB-LDPC codes decoding algorithm involves Belief Propagation (BP) algorithm, Fast Hadamard Transform-BP (FHT-BP) algorithm, etc. The decoding performance of each algorithm has a certain upper limit. In this paper, the code word structure of NB-LDPC codes is considered, and the decoding of LDPC codes under Galois Field(4) (GF(4)) is mainly indicated. On the basis of the FHT-BP algorithm, Multi-Layer Perceptron (MLP) neural networks and bit flipping (BF) method are introduced for joint decoding. This method can improve the error performance of LDPC codes and achieve better decoding results.
A very important and near optimum group of the block codes that have been developed in direction of Shannon's theory concept, is low density parity check (LDPC) code. There have been presented different algorithms for decoding of this class of code such as maximum likelihood (ML), bit flipping (BF), a posteriori probability (APP) and sum product (SP) algorithms that the first two of them decode by hard criterion and two others decode by soft criterion. In this article, considering LDPC codes structure and taking advantage of LDPC codes demonstrated by Tanner graph, we have presented a quite new method based on multi layer perceptron (MLP) neural networks that decodes LDPC codes by soft decision manner. This method opens another new way for LDPC and even other block codes decoding. Simulation results display good performance of this method compared to other known algorithms.
Low density parity check (LDPC) code is a kind of linear block code with excellent performance which is proposed by Dr. Gallager. It overcomes the shortcomings of other error correcting codes and it is the nearest channel code from Shannon limit at the present discover. The decoding algorithms of L DPC code can reduce the decoding delay by the parallel decoding structure, so this has caused great concern in many fields. In recent years more and more scholars begin to study LDPC code, this makes the coding and decoding algorithms of LDPC code improved continuously. LDPC code has been widely used in many fields such as optical fiber communication, digital watermarking, underwater communication and deep space communication because of its excellent performance. Non-binary LDPC code has better performance compared with binary LDPC code. In this paper, FFT-BP decoding algorithm of non-binary LDPC code is studied, and on this basis, we proposed an improved FFT-BP algorithm. The improved decoding algorithm can effectively reduce the average iteration number. Finally, we achieved encode and decode algorithm of non-binary LDPC code with FPGA.
In this paper, a new method for decoding Low Density Parity Check (LDPC) codes, based on Multi-Layer Perceptron (MLP) neural networks is proposed. Due to the fact that in neural networks all procedures are processed in parallel, this method can be considered as a viable alternative to Message Passing Algorithm (MPA), with high computational complexity. Our proposed algorithm runs with soft criterion and concurrently does not use probabilistic quantities to decide what the estimated codeword is. Although the neural decoder performance is close to the error performance of Sum Product Algorithm (SPA), it is comparatively less complex. Therefore, the proposed decoder emerges as a new infrastructure for decoding LDPC codes.
The Layered Belief Propagation L-BP algorithm is is a modified Belief Propagation BP algorithm, where the check nodes are divided in subgroups called layers and each iteration is broken into multiple sub-iterations. In this paper, we consider layered belief propagation decoding and propose an efficient variable node layering for decoding LDPC codes that performs well. We compare the performance of the first introduced LDPC decoding algorithm BP and Layered BP using check node layering with Layered BP using variable node layering in terms of bit error rate (BER). We show that the convergence for decoding LDPC codes is increasing by using a simple and efficient layering strategy.
When the code length is moderate, non-binary low-density parity-check (NB-LDPC) codes can achieve better error correcting performance than their binary counterparts at the expense of higher decoding complexity. The check node processing is a major bottleneck of NB-LDPC decoding. In this paper, Min-max decoding algorithm is proposed based on a new forward backward processing method of check nodes, select only a part of the most reliable information to the forward-backward calculation process, and change the variable nodes to check nodes (v-to-c) generation of information. Using this algorithm, a kind of code (768,1152) defined on GF(4) is simulated and compared with belief propagation in log domain (LOG-BP) decoding algorithm. Simulation results show Min-max decoding algorithm reduce information storage requirements and the computational complexity, conducive to engineering implementation.
A Hybrid Bit Flip(HBF) decoding algorithm for Low-Density Parity-Check (LDPC) codes is proposed in this paper. The algorithm makes full use of the soft output of belief-propagation (BP) (decoding) algorithm for LDPC codes, and greatly improves the bit error rate (BER) of the classical bit-flip (BF) algorithm. The simulation results in AWGN channel show that the HBF algorithm outperforms the BP algorithm under almost the same computational complexity. Furthermore, the former can achieve much lower error floor than the latter can do.