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

Authors:
V. Guruswami;A. Vardy
Affiliations:
Dept. of Comput. Sci. & Eng., Univ. of Washington, Seattle, WA, USA;-
Venue:
IEEE Transactions on Information Theory
Year:
2005

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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.