Low Density Parity Check Codes And Application

The low-density parity-check codes are one kind of sparse parity-check matrix based linear block error-correcting codes which could highly approach the Shannon limit with iterative decoding.The recent research result tells us that,with the decoding algorithm of belief propagation(BP Algorithm),the optimized LDPC codes have performances surpassing Turbo codes,which could be within only 0.0045 dB of the Shannon limit.So far,LDPC codes are considered to be with the best performance,and now the research about LDPC is one of the most amazing highlights in the area of channel coding.And meanwhile,the application of LDPC codes has also been raised in practice and lists as essential technology of the fourth generation mobile communication system(4G).With the profound understanding and grasping of the elementary theory of LDPC codes as basis,this thesis conducts thorough research on decoding algorithms of LDPC codes and proposes some improvements,then discusses in detail the performance of LDPC codes in HARQ system.(1)The appearance,present situation and developing prospect of LDPC codes are systematically summarized and discussed.Concisely introduces and discusses the encoding-decoding principles of inear block codes and LDPC codes,and involves some important relative concepts such as parity-check matrix,factor graph,circle, iterative decoding,and probability of error and so on.In the world scope recognizing the LDPC codes again started later and in our country the research on LDPC codes is comparatively more limited,so it requires urgently that researchers should profoundly understand and grasp the elementary theory of LDPC codes to prepare for the deep level research.(2)Mainly pay attention to the comprehensive study and discussion about the decoding algorithms of LDPC codes.Systematically study and compare the main decoding algorithms of belief propagation(probability-domain BP & LLR-domain BP)and obtain the corresponding decoding performance results.In order to reduce the complexity of decoding and enhance the decoding performance,based on the current LLR-domain BP algorithm,propose some improvements and simplifications to the LDPC codes' decoding algorithms.The theoretical analysis and computer simulation results prove the superiority of improved decoding algorithms comparing with standard LLR-BP algorithm.With the improved algorithms,not only the decoding performance can be improved,but also the complexity of decoding operations can be reduced and the decoding process can be simplified.This makes it easy for hardware realization.(3)Traditional ARQ and hybrid ARQ conducted a comprehensive technical presentations and discussions were on Stop-and-Wait ARQ,Go-back-N ARQ and the Selective-Repeat ARQ,three heavy-ARQ technology,then the three types of hybrid ARQ:hybrid typeⅠARQ,hybrid TypeⅡARQ and hybrid typeⅢARQ were done a detailed description.LDPC codes in the final application of hybrid typeⅡARQ system was simulated,and HARQ LDPC codes in the system of performance is analyzed.(4)The main work of this thesis is concluded and meanwhile the questions and research directions which should be concentrated on in the next steps are proposed.