Research On ADMM Decoding For LDPC Codes

Low-Density Parity-Check(LDPC) codes was firstly discovered by Gallager in 1962, and received attention by researchers in 1990 s. Due to its Shannon limit approaching performance and low complexity of the decoding method, LDPC codes has attracted the focus of many researchers and become one of the most promising coding techniques for error correcting in communications system and digital storage system. Alternating Direction Method of Multipliers(ADMM) decoding is a novel decoding method for LDPC codes. It combines advantages of both Belief Propagation(BP) decoding and Linear Programming(LP) decoding,showing a promising prospect.This thesis studies ADMM decoding for LDCP codes from two aspects: accelerating the decoding speed and improving the frame error rate. The main works of the thesis are summarized as follows:1. The basic knowledge of coding theory is introduced. The decoding methods of LDPC codes are presented, including BP decoding and LP decoding. The principle and detail of ADMM decoding of LDPC codes are described and the performance of ADMM decoding is given.2. The most complex operation in ADMM decoding, an Euclidean projection, is analyzed. An accelerated ADMM decoding is proposed by trying to reduce the number of the Euclidean projections. Simulation results show that accelerated ADMM decoding can reduce more than 70% Euclidean projections in high SNR region and use about half of the time when compared with standard ADMM decoding.3. The performance of penalized ADMM decoding method is analyzed. A re-weighted penalized ADMM decoding method is proposed with re-weighted coefficients optimized by difference evolution. Simulation results show that re-weighted penalized ADMM decoding for irregular LDPC codes has more than 1 d B gain when compared with penalized ADMM decoding.