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

共 50 条

[21] Successive Cancellation Decoding of Reed-Solomon Codes
Trifonov, P. V.
PROBLEMS OF INFORMATION TRANSMISSION, 2014, 50 (04) : 303 - 312
[22] Decoding Method of Reed-Solomon Erasure Codes
Tang D.
Cai H.
Geng W.
Jisuanji Yanjiu yu Fazhan/Computer Research and Development, 2022, 59 (03): : 582 - 596
[23] Decoding of rational functioned reed-solomon codes
Hu, Ta-Hsiang, 1600, Chung Cheng Institute of Technology (43):
[24] Unique Decoding of Certain Reed-Solomon Codes
Shen, Lin-Zhi
Fu, Fang-Wei
Guang, Xuan
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2015, E98A (12): : 2728 - 2732
[25] Stochastic Chase Decoding of Reed-Solomon Codes
Leroux, Camille
Hemati, Saied
Mannor, Shie
Gross, Warren J.
IEEE COMMUNICATIONS LETTERS, 2010, 14 (09) : 863 - 865
[26] A new algorithm for decoding Reed-Solomon codes
Gao, SH
COMMUNICATIONS, INFORMATION AND NETWORK SECURITY, 2003, 712 : 55 - 68
[27] Algorithm of recurrent decoding in Reed-Solomon codes
Mazurkov, MI
Mits, SV
Chechelnitskii, VY
IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII RADIOELEKTRONIKA, 2003, 46 (5-6): : A34 - A38
[28] Limits to list decoding Reed-Solomon codes
Guruswami, Venkatesan
Rudra, Atri
IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (08) : 3642 - 3649
[29] FAST TRANSFORMS FOR DECODING REED-SOLOMON CODES
REED, IS
TRUONG, TK
MILLER, RL
HUANG, JP
IEE PROCEEDINGS-F RADAR AND SIGNAL PROCESSING, 1981, 128 (01) : 9 - 14
[30] Successive cancellation decoding of Reed-Solomon codes
P. V. Trifonov
Problems of Information Transmission, 2014, 50 : 303 - 312

← 1 2 3 4 5 →