On the NP-hardness of bounded distance decoding of Reed-Solomon codes

Venkata Gandikota, Badih Ghazi, Elena Grigorescu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

Guruswami and Vardy (IEEE Trans. Inf. Theory, 2005) show that given a Reed-Solomon code over a finite field F, of length n and dimension k, and given a target vector v ϵ Fn, it is NP-hard to decide if there is a codeword that disagrees with v on at most n - k - 1 coordinates. Understanding the complexity of this Bounded Distance Decoding problem as the amount of error in the target decreases is an important open problem in the study of Reed-Solomon codes. In this work, we extend the result of Guruswami and Vardy by proving that it is NP-hard to decide the existence of a codeword that disagrees with v on n - k - 2, and on n - k - 3 coordinates. No other NP-hardness results were known before for an amount of error < n - k - 1. The core of our proofs is showing the NP-hardness of a parameterized generalization of the Subset-Sum problem to higher degrees (called Moments Subset-Sum) that may be of independent interest.

Original languageEnglish (US)
Title of host publicationProceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2904-2908
Number of pages5
ISBN (Electronic)9781467377041
DOIs
StatePublished - Sep 28 2015
Externally publishedYes
EventIEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong
Duration: Jun 14 2015Jun 19 2015

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2015-June
ISSN (Print)2157-8095

Other

OtherIEEE International Symposium on Information Theory, ISIT 2015
Country/TerritoryHong Kong
CityHong Kong
Period6/14/156/19/15

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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