List decoding of repeated codes
Fernando Hernando, Michael O'Sullivan, Diego Ruano
TL;DR
This paper addresses decoding repeated codes $C^\ell$ formed from Reed–Solomon codes by introducing a hard-decision list-decoding algorithm that leverages a soft-decision RS decoder for the constituent code $C$, using two multiplicity assignment strategies in the interpolation step. The approach achieves near-RS performance at a lower computational cost by operating over a smaller field and performing RS-like interpolation on a single block, rather than the extended longer RS code. The authors provide both theoretical bounds on the correction capability for each multiplicity scheme and extensive simulations that show practical decoding performance matching or exceeding conservative estimates. Overall, the work demonstrates that repeated codes with this interpolation-based decoding can offer substantial practical benefits in terms of efficiency while maintaining strong error-correction capability.
Abstract
Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to their parameters, we show that they have a good performance with this algorithm. We compare, by computer simulations, our algorithm for the repeated code of a Reed-Solomon code against a decoding algorithm of a Reed-Solomon code. Finally, we estimate the decoding capability of the algorithm for Reed-Solomon codes and show that performance is somewhat better than our estimates.