Design Of Low-Rate LDPC Codes

Due to the interference and fading in the wireless channel,the wireless signal is very prone to errors during transmission.Therefore,error correcting techniques must be applied to enhance the ability of the data of resisting various interference during channel transmission,so as to improve the reliability of the system.Compared to conventional channel coding,low-density parity-check?LDPC?codes have been proved to have the closest performance to the shannon limit,but the performance is worse than that of Turbo codes at lower code rates.In order to make up for the shortage of LDPC codes at low code rates,construction methods of low rate LDPC codes is studied in this thesis.LDPC codes with excellent performance,flexible structure,and low complexity of coding and decoding are designed.In this thesis,based on channel coding theory and shannon limit,the research background and research status of LDPC codes are introduced,the check matrix construction methods,coding algorithms and decoding algorithms of LDPC codes are explained,especially the protograph LDPC codes are discussed.On this basis,the following series of studies have been carried out on low-rate LDPC codes.Firstly,rate-compatible LDPC codes for the time-varying of wireless channels and the limited resources of channels are studied in this thesis.A design method of low-rate LDPC codes based on progressive edge-growth?PEG?extension is proposed to construct low-rate LDPC codes in hybrid automatic repeat request?HARQ?systems.In this method the improved PEG algorithm is used to optimize the position of non-zero elements in the extended part to obtain a better code structure,the transmission performance is further improved.Secondly,two kinds of protograph performance analysis tools are studied.A low-rate protograph design method based on check node splitting is proposed,and the optimization design criteria and method of protograph are given.In this method the check node splitting technology is used to reduce the search dimension,simplify the optimization design,and reduce the complexity of the matrix search.This design method is used to design a series of protographs with rate from 1/2 to 1/6,and their good performance are proved through theory and simulation analysis.there is about0.2dB improvement compared to RC-AR4JA code with the same code rate when the bits error rate is 10^-5.As the code rate decreases,the gap between the LDPC code that has been optimized and the Shannon limit is gradually increased.In this regard,an encoding scheme for LDPC-Hadamard codes based on the photographs is proposed in this thesis.The extrinsic information transfer?EXIT?curves of variable nodes and check nodes in LDPC-Hadamard codes cannot be optimized and matched to each other,and a large amount of computation in the LDPC-Hadamard code-degree distribution optimization process.Therefore,a design method for the protograph LDPC-Hadamard codes is proposed.This method eliminates the process of degree distribution optimization and greatly reduces the amount of computation.In addition,the puncturing method is used to puncture the class II variable nodes that are less associated with the check nodes,a rate compatible LDPC-Hadamard code with good performance and code rate below 1/2is obtained.