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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Published in:Proceedings / IEEE International Symposium on Information Theory pp. 2231 - 2235
Main Author: Polyanskiy, Yury
Format: Conference Proceeding Journal Article
Language:English
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
ISSN:2157-8095, 2157-8117
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Abstract 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.
AbstractList 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 greater than or equal to 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.
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.
Author Polyanskiy, Yury
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Snippet 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...
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StartPage 2231
SubjectTerms 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
Title Upper bound on list-decoding radius of binary codes
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