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Electronic Colloquium on Computational Complexity

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TR04-040 | 4th May 2004 00:00

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



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.

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