Upper bound on list-decoding radius of binary codes
Name
Polyanskiy_Upper bound.pdf
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335.52 KB
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Checksum (MD5)
1591a4f6079cc5a6896907daf3fddf70
Author(s)
Polyanskiy, Yury
Date Issued
June 2015
Journal
Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Polyanskiy, Yury. “Upper Bound on List-Decoding Radius of Binary Codes.” 2015 IEEE International Symposium on Information Theory (ISIT) (June 2015).
Version
Author's final 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 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.
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/ISIT.2015.7282852
