Optimal error correction for computationally bounded noise

  • Authors:

  • Silvio Micali;Chris Peikert;Madhu Sudan;David A. Wilson

  • Affiliations:

  • Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA;School of Computing, Georgia Institute of Technology, Atlanta, GA;Department of Electrical Engineering and Computer Science, MIT, Cambridge, MA and Microsoft Research New England, Cambridge, MA;Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2010

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Abstract

For adversarial but computationally bounded models of error, we construct appealingly simple and efficient cryptographic encoding and unique decoding schemes whose error-correction capability is much greater than classically possible. In particular: 1) For binary alphabets, we construct positive-rate coding schemes that are uniquely decodable under a 1/2 - γ error rate for any constant γ 0. 2) For large alphabets, we construct coding schemes that are uniquely decodable under a 1 - R error rate for any information rate R 0. Our results for large alphabets are actually optimal, since the "computationally bounded but adversarial channel" can simulate the behavior of the q-ary symmetric channel, where q denotes the size of the alphabet, the capacity of which is known to be upper-bounded by 1- R. Our results hold under minimal assumptions on the communication infrastructure, namely: 1) we allowthe channel to be more powerful than the receiver and 2) we only assume that some information about the sender--a public key--is known. (In particular, we do not require any shared secret key or joint local state between sender and receivers).