Re-encoding reformulation and application to Welch-Berlekamp algorithm

TL;DR

This paper generalizes the re-encoding technique to reduce decoding complexity in Reed-Solomon codes, specifically applying it to the Welch-Berlekamp algorithm, expanding its practical efficiency.

Contribution

It introduces a reformulation of the re-encoding method that can be applied to any interpolation algorithm, specifically enabling its use with the Welch-Berlekamp algorithm.

Findings

Re-encoding reduces the practical decoding time for Welch-Berlekamp.

The reformulation extends re-encoding applicability beyond Koetter's algorithm.

Potential for improved decoding efficiency in Reed-Solomon codes.

Abstract

The main decoding algorithms for Reed-Solomon codes are based on a bivariate interpolation step, which is expensive in time complexity. Lot of interpolation methods were proposed in order to decrease the complexity of this procedure, but they stay still expensive. Then Koetter, Ma and Vardy proposed in 2010 a technique, called re-encoding, which allows to reduce the practical running time. However, this trick is only devoted for the Koetter interpolation algorithm. We propose a reformulation of the re-encoding for any interpolation methods. The assumption for this reformulation permits only to apply it to the Welch-Berlekamp algorithm.