| Low Density Parity Check(LDPC)code is a high-efficiency and high-performance error correction code proposed by Gallager in 1962.Limited by the hardware and software equipment conditions at that time,this code was not widely used until it was re-proposed by scholars in the 1990 s.Non-binary LDPC codes show stronger error correction capabilities due to their sparse Tanner graph and longer girth.They have been used in the research of wireless communication and optical fiber communication,and have become the focus of the research in the domain of error-correction code in recent years.Symbol Flipping Decoding(SFD)algorithm is a sort of non-binary LDPC code Decoding method by Flipping the wrong Symbol for error correction.Compared with the traditional SFD decoding algorithm that only considers the message before the symbol flip,Symbol Flipping Decoding Based on Prediction(SFDP)mechanism algorithm considers the message before and after the symbol flip,has better code performance.This thesis focuses on the SFDP decoding algorithm for non-binary LDPC codes.In allusion to the problem that the number of iterations of the SFDP decoding algorithm is too high under medium and low signal-to-noise ratios(SNR),a SFDP decoding algorithm(Early Termination SFDP,ET-SFDP)based on the idea of early stopping is proposed,which can speed up the decoding convergence speed;In allusion to the problem that some SFDP decoding algorithms of non-binary LDPC codes have error flat layer in high SNR region,a two-stage SFDP decoding algorithm with random noise is proposed,which can effectively improve the decoding performance in high SNR region.The main research content of the thesis is summarized as follows:1.Introduced the digital communication system and channel model;expounded the finite field related theoretical knowledge and the basic concepts of non-binary LDPC codes;focused on the analysis of generalized symbol flipping decoding algorithm and generalized weighting Symbol reversal decoding algorithm.2.The iterative termination condition of the non-binary LDPC code SFDP decoding algorithm is that all check constraint equations of the code meet or reach the preset maximum number of iterations.In the middle and low SNR region,SFDP decoding algorithm will appear a large number of uncorrectable error frames,and this stop condition cannot avoid unnecessary decoding iteration,resulting in a significant increase in the average number of iterations and decoding delay.Aiming at this problem in the SFDP decoding algorithm,a symbol reversal algorithm ET-SFDP based on the early stopping method is proposed,which can validly refrain from invalid iterations.The experimental results illustrate that in the medium and low SNR region,the suggested apporach can validly reduce the average iteration times of SFDP decoding algorithm and accelerate the convergence rate of SFDP decoding algorithm Under the condition that the bit error rate is basically the same.3.The error performance of the existing two-stage SFDP decoding algorithm is basically the same as the original SFDP decoding algorithm,but the decoding convergence speed is significantly improved.In addition,for some non-binary LDPC codes,the SFDP decoding algorithm has error leveling phenomenon in the area of high SNR.For the sake of improving the error rate level of SFDP decoding algorithm and ensuring the fast convergence of decoding rate,an improved two-stage SFDP decoding algorithm is proposed.With binary LDPC codes have noise Gradient Descent a flip(Nosiy Gradient Descent Bit-Flipping,NGDBF)decoding algorithm,the main idea of the improved algorithm is proposed on the basis of two-phase SFDP decoding algorithm,random noise added to the reverse measure to perturbation weighted coefficient,when in the decoder can jump out of local optimum with greater probability,so as to improve the decoding performance.The experimental results illustrate that the improved two-stage SFDP algorithm has better decoding performance and fewer average iteration times than the original SFDP algorithm. |
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