Modeling Like-Random Frame Structure Of RA-LDPC Code And IRA-LDPC Code

Low-density parity check(LDPC)codes and Turbo codes are practical error correction codes that approximate the Shannon capacity limit and are adopted by the communications industry standard.The repeated accumulate(RA)code and the irregular repeated accumulate(IRA)code are defined and constructed in the form of Turbo-like codes,while having the structural features of the parity check matrix of the LDPC code.Therefore,they have the advantages of Turbo code linear complexity coding and the decoding advantages of LDPC code parallel linear complexity.This topic mainly studies the like-random construction method of RA-LDPC and IRA-LDPC codes with good performance.The main work and innovations of this paper are described as follows:Firstly,establishing a structural framework of the like-random parity check matrix corresponding to the RA-LDPC code information bits.the H~d matrix is divided into columns to obtain the first column extraction matrix H~b;Then,each column of theH~b matrix is segmented into rows to obtain a base matrix B;Finally,the base matrix B is compactly designed to obtain the pairwise array P.The first column extraction matrix H~b,the base matrix B,and the pairwise array P together form a frame of H~d.Secondly,an RA-LDPC code with a maximum column weight of 3 and H~d with girth 6/8/10 is designed.The girth model of the pairwise array P is established.On this basis,the necessary and sufficient conditions for the existence of 2girth in the H~d matrix are proposed.The RA-LDPC code with a maximum column weight of 3 is searched in the frame structure by using the balanced incomplete block design(BIBD)in the combinational mathematics and the constraint of eliminating the girth 6/8/10 in the pairwise array P.Finally,constructing the like-random matrix in the IRA-LDPC code with the girth as large as possible.An improved progressive edge growth(PEG)search algorithm is proposed.Under the frame constraint of the base matrix B,the IRA-LDPC code with the girth as large as possible is searched.Simulation experiments show that the performance of the IRA-LDPC code obtained by this study is better than or close to that of the IRA-LDPC code in the DVB-S2 standard on the AWGN channel under the same code length and code rate.