Linear time decoding of regular expander codes

  • Authors:
  • Michael Viderman

  • Affiliations:
  • Technion -- Israel Institute of Technology, Haifa, Israel

  • Venue:
  • Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
  • Year:
  • 2012

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Abstract

Sipser and Spielman (IEEE IT, 1996) showed that any (c, d)-regular expander code with expansion parameter 3/4 is decodable in linear time from a constant fraction of errors. Feldman et al. (IEEE IT, 2007) proved that expansion parameter 2/3 + 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 2/3−1/6c. We also prove that our decoding algorithm can be executed in logarithmic time on a linear number of parallel processors.