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

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2 Author(s)
Guruswami, V. ; Dept. of Comput. Sci. & Eng., Univ. of Washington, Seattle, WA, USA ; Vardy, A.

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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Information Theory, IEEE Transactions on  (Volume:51 ,  Issue: 7 )