Near maximum-likelihood decoding of Generalized LDPC and woven graph codes

Relations between Generalized LDPC codes, nonbinary LDPC codes, and woven graph codes are considered. Focus is on rather short codes suitable, for example, for coding control signaling information in mobile communications. In particular, codes of lengths less than 200 bits are studied. Low-complexity near maximum-likelihood (ML) decoding for these classes of codes is introduced and analyzed. Frame error rate (FER) performance of the new decoding procedure is compared with the same performance of ML and belief propagation (BP) decoding. It is shown that unlike BP decoding whose performances are mainly governed by the girth of the Tanner graph the new decoding procedure has performances which significantly depend on the minimum distance and spectrum of the woven code. Short woven graph codes with large minimum distances are tabulated.