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

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. The work of Venkatesan Guruswami was supported by an NSF Career Award. The work of Alexander Vardy was supported in part by the David and Lucile Packard Foundation and by the National Science Foundation. 

• Type: Journal
• Year: 2004
• Where: CORR
• Authors: Venkatesan Guruswami, Alexander Vardy
• Keywords: Central Algorithmic Problems, CORR 2004, Education, Maximum-likelihood, Reed-Solomon Codes