Linear time encodable and list decodable codes

  • Authors:

  • Venkatesan Guruswami;Piotr Indyk

  • Affiliations:

  • University of Washington, Seattle, WA;Massachusetts Institute of Technology, Cambridge, MA

  • Venue:
  • Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
  • Year:
  • 2003

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Abstract

We present the first construction of error-correcting codes which can be (list) decoded from a noise fraction arbitrarily close to 1 in linear time. Specifically, we present an explicit construction of codes which can be encoded in linear time as well as list decoded in linear time from a fraction (1-ε) of errors for arbitrary ε 0. The rate and alphabet size of the construction are constants that depend only on ε. Our construction involves devising a new combinatorial approach to list decoding, in contrast to all previous approaches which relied on the power of decoding algorithms for algebraic codes like Reed-Solomon codes.Our result implies that it is possible to have, and in fact explicitly specifies, a coding scheme for arbitrarily large noise thresholds with only constant redundancy in the encoding and constant amount of work (at both the sending and receiving ends) for each bit of information to be communicated. Such a result was known for certain probabilistic error models, and here we show that this is possible under the stronger adversarial noise model as well.