Non-binary LDPC codes vs. Reed-solomon codes

This paper investigates the potential of non-binary LDPC codes to replace widely used Reed-Solomon (RS) codes for applications in communication and storage systems for combating mixed types of noise and interferences. The investigation begins with presentation of four algebraic constructions of RS-based non-binary quasi-cyclic (QC)-LDPC codes. Then, the performances of some codes constructed based on the proposed methods with iterative decoding are compared with those of RS codes of the same lengths and rates decoded with the harddecision Berlekamp-Massey (BM)-algorithm and the algebraic soft-decision Kotter-Vardy (KV)-algorithm over both the AWGN ¨ and a Rayleigh fading channels. Comparison shows that the constructed non-binary QC-LDPC codes significantly outperform their corresponding RS codes decoded with either the BMalgorithm or the KV-algorithm.