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On Relations Between the Relative Entropy and χ2-Divergence, Generalizations and Applications
Tomohiro Nishiyama1, Igal Sason2
1Independent Researcher, Tokyo 206-0003, Japan.
Abstract:
The relative entropy and the chi-squared divergence are fundamental divergence measures in information theory and statistics. This paper is focused on a study of integral relations between the two divergences, the implications of these relations, their information-theoretic applications, and some generalizations pertaining to the rich class of f-divergences. Applications that are studied in this paper refer to lossless compression, the method of types and large deviations, strong data-processing inequalities, bounds on contraction coefficients and maximal correlation, and the convergence rate to stationarity of a type of discrete-time Markov chains.
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