Construction Of Hybrid LDPC Codes With Linear Block Codes As Component Codes

Due to elegant performance of Shannon-limit-approaching and low decoding complexity,low density parity check(LDPC)codes have become a kind of important channel encodings,where the construction method is one of the research focus in this field.For the construction of LDPC codes,the hybrid construction method is effective to generate long codes.Base matrix and component code are two main factors in this method.The base matrix is obtained by the general method,such as the progressive edge growth(PEG)algorithm.Then the base matrix is expanded with the aid of component code,where the component code is crucial for the hybrid construction.Allowing for the low decoding complexity,we discover two special codes from the numerous block codes,namely,(14,8)extended Hamming code(EHC)and(7,7,3,3,1)balanced incomplete block designs(BIBD)code.On one hand,neither of the two codes have 4-cycles.On the other hand,the decoding performance of the two codes with sum-product algorithm(SPA)is almost identical to that with maximum likelihood decoding(MLD).This property can benefit the decoding.Based on the above base matrix and component code,the hybrid codes are constructed with unique mapping rule by combined base matrix with EHC or BIBD code.Firstly,we construct hybrid codes with two kinds of code length.Simulation results over AWGN channel show that,hybrid code with column weight 2 is 2 dB away from the Shannon limit and 1.5 dB away for code with column weight 3,which have code length of 3,920.The decoding performance of hybrid code with column 3 is better than that with column 2,which indicates that column weight is a factor in the decoding performance.Simulation results over flat Rayleigh fading channel shows that hybrid codes with code length 2,000 have comparable performance,compared to PEG codes with similar code parameters.In addition,hybrid codes with base matrices constructed by PEG algorithm have better average iterations than that wih Gallager algorithm.Secondly,four hybrid codes are constructed with BIBD code as component code.The simulation results in AWGN channel shows that hybrid codes with base matrix from PEG algorithm has the best performance,only 1.3 dB away from the Shannon limit.Furthermore,in AWGN and flat Rayleigh fading channel,the simulation results of hybrid codes based on PEG and DS algorithms again indicate the performance advantage of hybrid codes with PEG algorithm in constructing base matrix.Additionally,the hybrid code with base matrix from EG behaves similarly to PEG code with approximate code parameters.Finally,we analyze the impact of degree distribution of hybrid codes on the asymptotic performance over binary erasure channel(BEC)with EXIT chart.Three kinds of degree distributions are considered,and the asymptotic performance changes with the degree distributions.We find the channel compacity loss reaches 0.0066,0.0043 and 0.0133 for the three kinds of degree distributions,respectively.The degree distribution trend of hybrid codes with EHC and BIBD codes as component codes is reasonable.