research-article

Linear-time decoding of regular expander codes

Author:

Michael VidermanAuthors Info & Claims

ACM Transactions on Computation Theory (TOCT), Volume 5, Issue 3

Article No.: 10, Pages 1 - 25

https://doi.org/10.1145/2493252.2493255

Published: 22 August 2013 Publication History

Abstract

Sipser and Spielman (IEEE IT, [1996]) showed that any c,d)-regular expander code with expansion parameter >¾ is decodable in linear time from a constant fraction of errors. Feldman et al. (IEEE IT, [2007]) proved that expansion parameter >⅔ + 1/3c is sufficient to correct a constant fraction of errors in polynomial time using LP decoding.

In this work, we give a simple combinatorial algorithm that achieves even better parameters. In particular, our algorithm runs in linear time and works for any expansion parameter >⅔ − 1/6c. We also prove that our decoding algorithm can be executed in logarithmic time on a linear number of parallel processors.

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Cited By

Chen XCheng KLi XOuyang M(2023)Improved Decoding of Expander CodesIEEE Transactions on Information Theory10.1109/TIT.2023.323916369:6(3574-3589)Online publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1109/TIT.2023.3239163
Dowling MGao S(2018)Fast Decoding of Expander CodesIEEE Transactions on Information Theory10.1109/TIT.2017.272606464:2(972-978)Online publication date: 1-Feb-2018
https://dl.acm.org/doi/10.1109/TIT.2017.2726064

Index Terms

Linear-time decoding of regular expander codes
1. Software and its engineering
  1. Software creation and management
    1. Software development techniques
      1. Error handling and recovery

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cover image ACM Transactions on Computation Theory

ACM Transactions on Computation Theory Volume 5, Issue 3

Special issue on innovations in theoretical computer science 2012

August 2013

94 pages

ISSN:1942-3454

EISSN:1942-3462

DOI:10.1145/2493252

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Copyright © 2013 ACM.

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Publication History

Published: 22 August 2013

Accepted: 01 March 2013

Received: 01 May 2012

Published in TOCT Volume 5, Issue 3

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Cited By

Chen XCheng KLi XOuyang M(2023)Improved Decoding of Expander CodesIEEE Transactions on Information Theory10.1109/TIT.2023.323916369:6(3574-3589)Online publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1109/TIT.2023.3239163
Dowling MGao S(2018)Fast Decoding of Expander CodesIEEE Transactions on Information Theory10.1109/TIT.2017.272606464:2(972-978)Online publication date: 1-Feb-2018
https://dl.acm.org/doi/10.1109/TIT.2017.2726064

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