Multi-Trial Guruswami-Sudan Decoding for Generalised Reed--Solomon Codes
Abstract
An iterated refinement procedure for the Guruswami-Sudan list decoding algorithm for Generalised Reed-Solomon codes based on Alekhnovich's module minimisation is proposed. The method is parametrisable and allows variants of the usual list decoding approach. In particular, finding the list of closest codewords within an intermediate radius can be performed with improved average-case complexity while retaining the worst-case complexity. We provide a detailed description of the module minimisation, reanalysing the Mulders-Storjohann algorithm and drawing new connections to both Alekhnovich's algorithm and Lee-O'Sullivan's. Furthermore, we show how to incorporate the re-encoding technique of K\"otter and Vardy into our iterative algorithm.
Keywords
Cite
@article{arxiv.1404.3022,
title = {Multi-Trial Guruswami-Sudan Decoding for Generalised Reed--Solomon Codes},
author = {Johan Sebastian Rosenkilde Nielsen and Alexander Zeh},
journal= {arXiv preprint arXiv:1404.3022},
year = {2014}
}
Comments
Design Codes and Cryptography (2014)