Regular low-density parity-check codes from combinatorial designs

Analytically constructed LDPC codes comprise only a very small subset of possible codes and as a result LDPC codes are still, for the most part, constructed randomly. This paper extends the class of LDPC codes that can be systematically generated by presenting a construction method for regular LDPC codes based on combinatorial designs known as Kirkman triple systems. We construct (3, ρ)-regular codes whose Tanner graph is free of 4-cycles for any integer ρ, and examine girth and minimum distance properties of several classes of LDPC codes obtained from combinatorial designs.