Combinatorial Construction of Low-Density Parity-Check Codes for Short Block Length and High Rate Applications

This paper presents a method to construct regular low-density parity-check (LDPC) codes of short block length and high rate based on a special type of combinatoric designs, i.e., balanced incomplete block designs (BIBDs) with lambda = 2 whose construction are based on cyclic difference families. Although the Tanner graph of the codes constructed contains some cycles of length 4, simulation results show that they perform well under belief propagation (BP) decoding. Further, these codes are quasi-cyclic (QC) codes and hence can be encoded efficiently