Multi-Trial Guruswami--Sudan Decoding for Generalised Reed--Solomon Codes
Johan Sebastian Rosenkilde Nielsen (Technical University of Denmark),, Alexander Zeh (INT - University of Ulm., INRIA Saclay - Ile de France)
TL;DR
This paper introduces an iterated refinement method for Guruswami--Sudan list decoding of Generalised Reed--Solomon codes, enhancing efficiency and flexibility in decoding algorithms.
Contribution
It presents a parametrisable refinement procedure based on Alekhnovich's module minimisation, enabling improved average-case complexity for list decoding.
Findings
Enhanced average-case decoding complexity
Retains worst-case complexity guarantees
Flexible decoding radius options
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 \emph{closest} codewords within an intermediate radius can be performed with improved average-case complexity while retaining the worst-case complexity.
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Taxonomy
TopicsCoding theory and cryptography · Cellular Automata and Applications · Cryptographic Implementations and Security