Construction of LDPC codes based on resolvable group divisible designs

In this paper, we present a method for constructing LDPC codes from resolvable group divisible designs (RGDDs). According to the incidence matrices (or their submatrices) of RGDDs, a class of regular LDPC codes can be constructed. Since the parity-check matrix of the resulting code satisfies the row-column constraint, the girth of the proposed codes is at least six. Furthermore, based on a resolvable group divisible design, we can obtain a sequence of LDPC codes with various lengths and rates, which perform well over the AWGN channel with iterative decoding and have low error floors.