Efficiently decodable codes meeting Gilbert-Varshamov bound for low rates

Authors:
Venkatesan Guruswami;Piotr Indyk
Affiliations:
University of Washington, Seattle;Laboratory for Computer Science, MIT, Cambridge, MA
Venue:
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2004

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Abstract

We demonstrate a probabilistic construction of binary linear codes meeting the GV bound (with overwhelming probability) for rates up to about 10-4 together with polynomial time algorithms to perform encoding and decoding up to half the distance. The only previous result of this type (for rates up to about 0.02) suffered from sub-exponential time decoding [3].