Generalized LDPC Codes and Turbo-Product Codes with Reed-Muller Component Codes

A forward error correction (FEC) scheme based on generalized low-density parity-check (GLDPC) codes can improve overall characteristics of LDPC codes by decreasing the decoding complexity. We consider the GLDPC codes with Reed- Muller (RM) and Bose-Chaudhuri-Hocquenghem (BCH) component codes. GLDPC codes with RM codes as component codes is an attractive option for high-speed applications, such as optical communications, because they provide excellent coding gains, while the RM codes can be decoded using low-complexity maximum a posteriori probability (MAP) decoding algorithm due to Ashikhmin and Lytsin, based on Walsh-Hadamard transform. Several classes of GLDPC codes (with component RM or BCH codes) outperforming the turbo product codes are presented. Several turbo product codes suitable for use in highspeed transmission are identified as well.