Maximum-likelihood decoding of Reed-Solomon Codes is NP-hard
Computational Complexity
2007-07-16 v1 Discrete Mathematics
Information Theory
math.IT
Abstract
Maximum-likelihood decoding is one of the central algorithmic problems in coding theory. It has been known for over 25 years that maximum-likelihood decoding of general linear codes is NP-hard. Nevertheless, it was so far unknown whether maximum- likelihood decoding remains hard for any specific family of codes with nontrivial algebraic structure. In this paper, we prove that maximum-likelihood decoding is NP-hard for the family of Reed-Solomon codes. We moreover show that maximum-likelihood decoding of Reed-Solomon codes remains hard even with unlimited preprocessing, thereby strengthening a result of Bruck and Naor.
Cite
@article{arxiv.cs/0405005,
title = {Maximum-likelihood decoding of Reed-Solomon Codes is NP-hard},
author = {Venkatesan Guruswami and Alexander Vardy},
journal= {arXiv preprint arXiv:cs/0405005},
year = {2007}
}
Comments
16 pages, no figures