Maximum-likelihood decoding of Reed-Solomon Codes is NP-hard

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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.
16 pages, no figures

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Computational Complexity, Discrete Mathematics, Information Theory, E.4; F.1.3; F.2.1

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http://salesiana.dossiersoluciones.com/handle/123456789/134176

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cs/0405005
 http://arxiv.org/abs/cs/0405005

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arXiv