Abstract:

The best codes of short or intermediate blocklength that have so far been discovered are usually defined in ways that do not immediately suggest a sparse parity check matrix representation. For this reason, large classes of classical textbook codes, which would give excellent performance under optimal decoding, have been mostly ignored as candidates for the belief propagation (BP) decoding algorithm. A notable exception are the one-step majority logic decodable codes, which have been shown to have excellent error-correcting performance when decoded using BP. We report here on a method for generating sparse generalized parity check (GPC) matrix representations of other classical codes.