Linear-time decoding of regular expander codes

  • Authors:
  • Michael Viderman

  • Affiliations:
  • Technion — Israel Institute of Technology Andmicrosoft Research, New England

  • Venue:
  • ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
  • Year:
  • 2013

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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.