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Linear-time decoding of regular expander codes

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Published:22 August 2013Publication History
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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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    • Published in

      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
      Issue’s Table of Contents

      Copyright © 2013 ACM

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 22 August 2013
      • Accepted: 1 March 2013
      • Received: 1 May 2012
      Published in toct Volume 5, Issue 3

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