Optimal error correction for computationally bounded noise
Name
Micali_Optimal error.pdf
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Author(s)
Micali, Silvio
Peikert, Chris
Sudan, Madhu
Wilson, David A.
Date Issued
November 2010
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Micali, Silvio et al. “Optimal Error Correction for Computationally Bounded Noise.” IEEE Transactions on Information Theory 56.11 (2010): 5673–5680. © Copyright 2010 IEEE
Version
Final published version
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 allow the 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).
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1109/TIT.2010.2070370
