On The Girth Of Structured IRA-LDPC Codes

Turbo codes and Low-Density Parity-Check(LDPC)codes are both good codes which approach the Shannon limit very close.Irregular Repeat Accumulate(IRA)codes can be seen as a common subset of Turbo and LDPC codes,which means IRA codes have the low encoding conplexity characteristic of Turbo codes,and the low decoding conplexity characteristic of LDPC codes.It is proved by researchers that IRA codes can achieve the Shannon limit on the binary erasure channel and asymptotically perform within less than 0.1dB of the Shannon limit on the binary-input additive white gaussian noise(AWGN)channel.Therefore,the researches for IRA codes have great theory study significance and brilliant application prospect.IRA codes have received great interest because of some of its special advantages.This paper proceeds with the design of parity-check matrix H,the constructed IRA codes are called IRA-LDPC codes.Devided by the column vector,we turn the design of matrix H with larger size into the design of smaller matrix: base extraction matrix and position matrix.A construction of structured IRA-LDPC codes is presented,so does the girth analysis model which is based on the structured IRA-LDPC codes and position matrix.We construct the position in position matrix through the balanced incomplete block design(BIBD),further more,all possible conditions that may form a cycle of length 4,6,8 is analysesed.On the basis of the girth analysis model,a search algorithm which insures the girth of structured IRA-LDPC codes to be 10 is proposed.The proposal of row distance matrix simplifies the search procedure.To study the influence of girth and column weight,the structured IRA-LDPC codes are simulated.To prove the validity of the search algorithm,that is,to verify the girth of structured IRA-LDPC codes to be 10,an improved algorithm to determine girth is proposed.