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
收藏
页码：2249 / 2256
页数：8
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