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 b...

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Bibliographic Details
Published inProceedings / IEEE International Symposium on Information Theory pp. 2231 - 2235
Main Author Polyanskiy, Yury
Format Conference Proceeding Journal Article
LanguageEnglish
Published IEEE 01.06.2015
Subjects
Asymptotic properties
Binary codes
Combinatorial coding theory
converse bounds
Decoding
Estimates
Information theory
Joints
list-decoding
Polynomials
Programming
Slopes
Thresholds
Tin
Upper bound
Upper bounds
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ISSN2157-8095
2157-8117
DOI10.1109/ISIT.2015.7282852

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Summary: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 linear- programming 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.
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ISSN:2157-8095
2157-8117
DOI:10.1109/ISIT.2015.7282852