GLDPC Codes with Reed-Muller Component Codes Suitable for Optical Communications

Abstract

In this paper, we consider the GLDPC codes with Reed-Muller (RM) and Bose-Chaudhuri-Hocquenghem (BCH) codes as component codes. GLDPC codes with RM codes as component codes is an attractive option for high-speed optical transmission because they provide excellent coding gains, while the RM codes can be decoded using low-complexity maximum a posteriori probability (MAP) decoding based on fast Walsh- Hadamard transform. Several classes of GLDPC codes (with component RM or BCH codes) outperforming the turbo product codes in terms of decoding complexity and coding gain are presented. We also identify several turbo product codes suitable for use in optical communications.