A construction of high rate quasi-cyclic regular LDPC codes from cyclic difference families with girth 8
In this paper we propose a method of constructing quasicyclic regular LDPC codes from a cyclic difference family, which is a kind of combinatorial design. The resulting codes have no 4-cycle, i.e. cycles of length four and are defined by a small set of generators of codes with high rate and large code length. In particular, for LDPC codes with column weight three, we clarify the conditions on which they have no 6-cycle and their minimum distances are improved. Finally, we show the performance of the proposed codes with high rates and moderate lengths.
ldpc code cyclic difference family girth minimum distance quasi-cyclic code