Improvement And Performance Analysis On Belief-Propagation Decoding Algorithm For LDPC Codes

Low density parity check?LDPC?code is a channel error correcting code approximating the Shannon limit.Because the density of the 1 element is very sparse in the constructed H matrix,LDPC codes have a low encoding and decoding complexity.At the same time,it is easy for hardware implementation.So far,LDPC codes have been adopted as standard codes in many communications fields,such as deep space communications,optical fiber communications,GPS systems,Wireless Local Area Networks and even the latest 5G Communications.This paper reviews the development history of error correcting codes,and summarizes the research status of LDPC codes in the direction of construction,encoding and decoding.Besides,we analyze the factors which influence the performance of error correction,such as code length,code rate and iteration number.Based on these preconditions,various decoding algorithms are studied.This paper optimizes and analyzes the belief-propagation?BP?decoding algorithm,and then gives my own innovation.The main research work is as follows.1.Set up a MATLAB simulation environment,under the additive white gauss noise?AWGN?channel,QC-LDPC?961,721?codes constructed in the finite fields modulated by binary phase shift keying?BPSK?,then we draw the performance curve of various decoding algorithms.In the simulation diagram,X axis represents the signal to noise ratio and the Y axis represents the bit error rate.The simulation results show that the error rate of the soft iterative algorithm is the smallest under the same SNR,which shows that its performance is optimal.In contrast,the error rate of hard decision algorithm is the largest under the same SNR,which indicates that its performance is the worst.The mixed decision decoding curve is sandwiched between them,and the performance is also a balance between them.The key of practical application is to select different decoding algorithms according to different needs.2.In view of the possible existence of correlation between the Sum-Product?SP?algorithm variable nodes,the decision information after a certain number of iterations can not convergence correctly and the decoding sequence is error.By changing the channel initialization conditions and check node update processing process,a improved Sum-Product decoding algorithm for LDPC code is proposed.The simulation results show that,when the maximum number of iterations is 16 times,the Bit Error Rate?BER?is 10^-6,the proposed improvement and accumulation method can improve the net coding gain of about 0.4dB compared to the traditional and product decoding algorithm.When the SNR is 5dB,5.5dB,6dB,the average iteration number of the improved and accumulated algorithm is greatly reduced,and the corresponding complexity is reduced.In conclusion,the improved SP decoding algorithm can improve the performance of error correction and reduce the complexity of decoding.3.Aiming at the problem of high complexity caused by the full parallel decoding of LDPC code,the introduction of bit quantization can effectively reduce the decoding complexity and facilitate the implementation of the LDPC code.The Min-Sum?MS?of the multiplicative factor and beta factor is introduced at the same time,and the quantization method of the complement quantization range is quantized,the channel information is corrected,and a LDPC code decoding algorithm based on the quantization technique is proposed.The simulation results show that the improved algorithm proposed in this paper improves the net coding gain of about 0.25dB compared with the original algorithm when the bit error rate is BER=10^-4,and the improved algorithm achieves an effective balance between performance and complexity.