A class of quasi-cyclic LDPC codes from B2(mod m) sequences

Abstract

A new class of binary low-density parity-check (LDPC) codes is proposed based on B2(mod m) sequences. The parity-check matrix of such a code has a column weight of three and a row weight of an arbitrary integer, and a quasi-cyclic structure. The parity-check matrix also has a girth at least 8, and corresponds to a code with minimal distance at least 12. When m is prime, an 8-cycles reduction method is presented to completely avoid the two types of 8-cycles within the total four types existed in the Tanner graph. Simulation results show that, for a prime integer m, the new LDPC code outperforms the random (quasi-) regular counterpart generated by the PEG algorithm. Finally, a heuristic algorithm based on a strategy called neighboring extension search is presented to search for the B2(mod m) sequences whose lengths approach or meet the upper bound.