A class of quasi-cyclic regular LDPC codes from cyclic difference families with girth 8

In this paper, we propose a class of regular LDPC codes from a cyclic difference family, which is a kind of combinatorial design. These LDPC codes have no 4-cycles, i.e., cycles of length 4. We clarify the conditions on which these codes with column weight 3 have no 6-cycles and discuss their minimum distance. Finally, we show the performance of the proposed codes with high rates and moderate lengths