Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Decoding Reed–Solomon Codes

1999; Guruswami, Sudan
  • Venkatesan Guruswami
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_101

Keywords and Synonyms

Decoding ;  Error correction        

Problem Definition

In order to ensure the integrity of data in the presence of errors, an error-correcting code is used to encode data into a redundant form (called a codeword). It is natural to view both the original data (or message) as well as the associated codeword as strings over a finite alphabet. Therefore, an error-correcting code C is defined by an injective encoding map \( { E: \Sigma^k \rightarrow \Sigma^n } \)

Keywords

Block Length Weighted Degree Solomon Code Decode Problem List Decode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Recommended Reading

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    Guruswami, V.: Algorithmic Results in List Decoding. In: Foundations and Trends in Theoretical Computer Science, vol. 2, issue 2, NOW publishers, Hanover (2007)Google Scholar
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    Guruswami, V.: List Decoding of Error-Correcting Codes. Lecture Notes in Computer Science, vol. 3282. Springer, Berlin (2004)Google Scholar
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    Guruswami, V., Rudra, A.: Explicit codes achieving list decoding capacity: Error-correction with optimal redundancy. IEEE Trans. Inform. Theor. 54(1), 135–150 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
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    Guruswami, V., Rudra, A.: Limits to list decoding Reed–Solomon codes. IEEE Trans. Inf. Theory. 52(8), 3642–3649 (2006)MathSciNetCrossRefGoogle Scholar
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    Guruswami, V., Sudan, M.: Improved decoding of Reed–Solomon and algebraic-geometric codes. IEEE Trans. Inf. Theory. 45(6), 1757–1767 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
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    Guruswami, V., Vardy A.: Maximum Likelihood Decoding of Reed–Solomon codes is NP-hard. IEEE Trans. Inf. Theory. 51(7), 2249–2256 (2005)MathSciNetCrossRefGoogle Scholar
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    Koetter, R., Vardy, A.: Algebraic soft-decision decoding of Reed–Solomon codes. IEEE Trans. Inf. Theory. 49(11), 2809–2825 (2003)MathSciNetCrossRefGoogle Scholar
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    Peterson, W.W.: Encoding and error-correction procedures for Bose-Chaudhuri codes. IEEE Trans. Inf. Theory. 6, 459–470 (1960)CrossRefGoogle Scholar
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    Sudan, M.: Decoding of Reed–Solomon codes beyond the error-correction bound. J. Complex. 13(1), 180–193 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Sudan, M.: List decoding: Algorithms and applications. SIGACT News. 31(1), 16–27 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Venkatesan Guruswami
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of WashingtonSeattleUSA