IRA-LDPC Codes Construction Based On Finite Cyclic Group

Irregular repeat accumulate(IRA) codes are a special class of low-density parity-check codes(LDPC),which have the advantages both of Turbo codes and LDPC codes.IRA codes can be encoded and decoded in linear time.In addition,it has been proved that IRA codes are the only class of codes achiving Shannon limit on the binary erasure channel.Besides,IRA codes can also approve the Shannon limit on the AWGN channel.Therefore,IRA codes have great theoretical and applied research value.Since the invention of IRA codes in mid-1990 s, mainly two different methods of designing IRA codes have been developed.One kind is based on the Turbo codes and another kind is based on the parity-check matrix,the corresponding codes are called IRA-LDPC codes.This paper presents a kind of structured framework of designing IRA-LDPC codes using the parity-check matrix,which can transform the parity-check matrix with larger size into the base extraction matrix with smaller size.On the basis of the structured framework,a specific method of designing IRA-LDPC codes using finite cyclic group is presentd.Besides,the expansion process from matrix D to matrix dH is described.The girth problem of the IRA-LDPC codes base on finite cyclic group is discussed and the analysis model is built.In addition,the necessary and sufficient conditions of exsiting 4-cylce are given and proved.According to the conclusion of girth analysis,the searching algorithm of IRA-LDPC codes of girth-6 is given.At last,the designed IRA-LDPC codes are simulated and compared with the exsiting standards.Simulations under different conditions of girth and iteration numbers are also made.The bit error rate performance of designed codes is better than the LDPC scheme of IEEE802.16 e and DVB-S2 standards.Besides,compared with QC-LDPC codes,the designed codes' length and code rates are more flexible.Thus,it can be applied to a variety of different scenarios.