Upper Bound on List-Decoding Radius of Binary Codes

4 years 9 months ago
Upper Bound on List-Decoding Radius of Binary Codes
—Consider the problem of packing Hamming balls of a given relative radius subject to the constraint that they cover any point of the ambient Hamming space with multiplicity at most L. For odd L ≥ 3 an asymptotic upper bound on the rate of any such packing is proven. The resulting bound improves the best known bound (due to Blinovsky’1986) for rates below a certain threshold. The method is a superposition of the linearprogramming idea of Ashikhmin, Barg and Litsyn (that was used previously to improve the estimates of Blinovsky for L = 2) and a Ramsey-theoretic technique of Blinovsky. As an application it is shown that for all odd L the slope of the rate-radius tradeoff is zero at zero rate.
Yury Polyanskiy
Added 11 Apr 2016
Updated 11 Apr 2016
Type Journal
Year 2016
Where TIT
Authors Yury Polyanskiy
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