An Explicit Method to Generate Some QC LDPC Codes with Girth 8

Recently, the incidence matrices of some block designs have been considered as the mother matrices of some quasi-cyclic (QC) low-density parity-check (LDPC) codes with maximum girth 20. In fact, the authors have introduced a deterministic algorithm which randomly, by a computer search, generates the slope vectors corresponding to the codes with desired girth, not greater than 20. In this paper, by rearranging the blocks of each block design, some slope vectors are proposed with an explicit method such that their corresponding QC LDPC codes have girth 8. Then, for each slope vector S, the lower bound Q(S) is found such that the QC LDPC codes with slope vector S and block size N, N ≥ Q, have girth at least 8.