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

被引：41

作者：

Guruswami, V ^{[1
]}

Vardy, A

机构：

[1] Univ Washington, Dept Comp Sci & Engn, Seattle, WA 98195 USA

[2] Univ Calif San Diego, Dept Elect & Comp Engn, La Jolla, CA 92093 USA

[3] Univ Calif San Diego, Dept Comp Sci, La Jolla, CA 92093 USA

[4] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2005年 / 51卷 / 07期

基金：

美国国家科学基金会;

关键词：

linear codes; maximum-likelihood decoding; NP-hard problems; Reed-Solomon codes;

D O I：

10.1109/TIT.2005.850102

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：2249 / 2256

页数：8

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