Upper Bounds on the Relative Entropy and R\'enyi Divergence as a Function of Total Variation Distance for Finite Alphabets

Igal Sason; Sergio Verdu

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arXiv · 1503.03417

Upper Bounds on the Relative Entropy and R\'enyi Divergence as a Function of Total Variation Distance for Finite Alphabets

Igal Sason·Sergio Verdu

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Abstract

A new upper bound on the relative entropy is derived as a function of the total variation distance for probability measures defined on a common finite alphabet. The bound improves a previously reported bound by Csisz\'ar and Talata. It is further extended to an upper bound on the R\'enyi divergence of an arbitrary non-negative order (including $\infty$) as a function of the total variation distance.

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Igal Sason, Sergio Verdu. 2015-03-11. Upper Bounds on the Relative Entropy and R\'enyi Divergence as a Function of Total Variation Distance for Finite Alphabets. https://arxiv.org/abs/1503.03417

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