Collaborative algebraic decoding of interleaved Reed–Solomon codes

Abstract

ABSTRACTWe derive and analyse an algorithm for collaborative decoding of heterogeneous interleaved Reed–Solomon (IRS) codes. They are generated by interleaving several codewords from different Reed–Solomon codes with the same length over the same Galois field. The basis of the decoding algorithm is similar to the Guruswami–Sudan (GS) decoding method. However, here multivariate interpolation is used to decode all the codewords of the interleaved scheme simultaneously. In the presence of burst errors, we show that the error‐correction capability of this algorithm is larger than that of independent decoding of each codeword using the standard GS method. In the latter case, the error‐correction capability is equal to the decoding radius of the GS algorithm for the Reed–Solomon code with the largest dimension. Also, concatenated codes using IRS codes as their outer codes and binary linear block codes as their inner codes are considered. Assuming maximum likelihood decoding of the inner code, we derive upper and lower bounds for the word error probability of concatenated codes over additive white Gaussian noise channel with binary phase‐shift keying modulation for both cases of independent and collaborative decoding of the outer IRS codes. We show that collaborative decoding provides considerable coding gain compared with independent decoding. Copyright © 2011 John Wiley & Sons, Ltd.