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

Author

Guruswami, Venkatesan ; Vardy, Alexander

Author_Institution

Dept. of Comput. Sci. & Eng., Univ. of Washington, Seattle, WA, USA

Volume

51

Issue

7

fYear

2005

fDate

7/1/2005 12:00:00 AM

Firstpage

2249

Lastpage

2256

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.

Keywords

Reed-Solomon codes; linear codes; maximum likelihood decoding; optimisation; NP-hard problems; Reed-Solomon codes; central algorithmic problem; linear codes; maximum-likelihood decoding; nontrivial algebraic structure; Computer science; Engineering profession; Galois fields; Linear code; Mathematics; Maximum likelihood decoding; NP-complete problem; Vectors; Linear codes; NP- hard problems; Reed–Solomon codes; maximum-likelihood decoding;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2005.850102

Filename

1459041