Linear-time decoding of regular expander codes

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.