Upper Bound on List-Decoding Radius of Binary Codes
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1409.7765.pdf
Description
Submitted version
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232.53 KB
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Adobe PDF
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1cb72a0c7ce81f785b72eee3259f4bb4
Author(s)
Polyanskiy, Yury
Date Issued
March 2016
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Polyanskiy, Yury. "Upper bound on list-decoding radius of binary codes." IEEE Transactions on Information Theory 62, no. 3 (September 2014).
Version
Original manuscript
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 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 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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/tit.2016.2516560
