Upper Bound on List-Decoding Radius of Binary Codes
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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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
IEEE Transactions on Information Theory
Institute of Electrical and Electronics Engineers (IEEE)
Polyanskiy, Yury. "Upper bound on list-decoding radius of binary codes." IEEE Transactions on Information Theory 62, no. 3 (September 2014).