4.5 Article

Entropy Bounds for Discrete Random Variables via Maximal Coupling

Journal

IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 59, Issue 11, Pages 7118-7131

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2013.2274515

Keywords

Coupling; entropy; local distance; Stein's method; total variation distance

Funding

  1. Israel Science Foundation [12/12]

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This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal coupling, and they apply to discrete random variables which are defined over finite or countably infinite alphabets. Loosened versions of these bounds are demonstrated to reproduce some previously reported results. The use of the new bounds is exemplified for the Poisson approximation, where bounds on the local and total variation distances follow from Stein's method.

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