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 <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula>. For odd &l...

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Vydáno v:IEEE transactions on information theory Ročník 62; číslo 3; s. 1119 - 1128
Hlavní autor: Polyanskiy, Yury
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.03.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Asymptotic methods
Asymptotic properties
Binary codes
Combinatorial coding theory
converse bounds
Decoding
Estimates
Indexes
Information theory
Linear programming
list-decoding
Programming
Slopes
Thresholds
Upper bound
Upper bounds
Combinatorial coding theory
list-decoding
converse bounds
ISSN:0018-9448, 1557-9654
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Shrnutí: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 <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula>. For odd <inline-formula> <tex-math notation="LaTeX">L\ge 3 </tex-math></inline-formula>, an asymptotic upper bound on the rate of any such packing is proved. 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 previously used to improve the estimates of Blinovsky for <inline-formula> <tex-math notation="LaTeX">L=2 </tex-math></inline-formula>) and a Ramsey-theoretic technique of Blinovsky. As an application, it is shown that for all odd <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula>, the slope of the rate-radius tradeoff is zero at zero rate.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2016.2516560