Bit-Level Soft-Decision Decoding of Double and Triple-Parity Reed-Solomon Codes Through Binary Hamming Code Constraints

This paper discusses bit-level soft-decision decoding of double and triple-parity Reed-Solomon (RS) codes through binary Hamming code constraints. The new expressions of parity-check equations which possess a certain inherent structure in GF(2) are derived. This structure enables representation of a non-binary parity-check equation as that of a compound binary Hamming code. Such technique makes it possible to decode [n, n-2, 3] and [n, n-3, 4] RS codes by Belief-Propagation (BP) algorithm. Simulation results show that the performance comparable to the existing RS decoding techniques is achievable with the presented methodology.