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Browse Journals & Magazines > Information Theory, IEEE Tran ...> Volume:51 Issue:7 Help

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.

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

Date of Publication: July 2005

Page(s):
2249 - 2256
ISSN :
0018-9448
INSPEC Accession Number:
8491305
Digital Object Identifier :
10.1109/TIT.2005.850102
Date of Current Version :
27 June 2005
Issue Date :
July 2005
Sponsored by :
IEEE Information Theory Society

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