Linear Programming Decoding Algorithm For LDPC Codes Over ISI Channels Based On ADMM

The Low-Density Parity-Check(LDPC)codes have a good error-correcting performance,which can approach the channel capacity.Therefore,researchers have focused on the study of LDPC codes in recent years.In communications,LDPC codes have been chosen as the standard codes for 5G enhanced mobile broadband(eMBB)data channel in 3GPP meeting 2016.On the other hand,LDPC code can significantly improve the reliability of SSD compared to BCH code.Inter Symbol Interference(ISI)is one of the most common memory channels in storage system and communication system.Due to the ISI channel model,this thesis focuses on the decoding algorithm of Alternating Direction Method of Multipliers(ADMM).The works of ADMM decoding research are as follows:1.The communication system and channels are summarized.The LDPC decoding model under the memoryless channel AWGN is analyzed in detail with four typical decoding algorithms,which are Sum-Product Algorithm(SPA),Min-Sum Algorithm(MSA),Linear Programming(LP)decoding and ADMM decoding.By comparing the performance under these four algorithms,the conclusion that the ADMM decoding algorithm achieves better performance at high signal-noise-ratio(SNR)is obtained.2.The existing decoding methods on ISI channels are mainly based on the BCJR detection algorithm,which calculates the state transition probability of-the ISI channels and makes soft decision decoding bit by bit.Based on the research of ISI channel communication model,this paper establishes a LP decoding model under ISI channel and solves it by simplex method.By simulating and analyzing LDPC codes with different lengths and code rates,the performance of this algorithm is better than the existing sum-product algorithm based on BCJR detection at high SNR period,but the decoding speed is slower in long codes.3.For the problem of the low decoding speed in LP decoding,this thesis proposes a decoding algorithm for LDPC codes over ISI channels based on ADMM penalized decoding.Compared with flooding scheduling,the performance of two layered scheduling for ADMM decoding is greatly improved.By simulating and analyzing LDPC codes with different lengths and code rates,the proposed ADMM penalized decoding algorithm with vertical layered scheduling has a better performance at all SNR period,compared with the existing SP algorithm based on BCJR detection.