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Gaussian bounds for discrete entropies

Abstract : It is well known that the Gaussian distribution has the largest differential entropy amongst all distributions of equal variance. In this paper, we derive similar (generalized) Gaussian upper bounds for discrete (Rényi) entropies of integer-valued variables. Using a mixed discrete-continuous bounding technique and the Poisson summation formula from Fourier analysis, it is proved that in many cases, such Gaussian bounds hold with an additive term that vanishes exponentially as the variance increases.
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https://hal.telecom-paris.fr/hal-03718693
Contributor : Olivier Rioul Connect in order to contact the contributor
Submitted on : Saturday, July 9, 2022 - 7:20:38 AM
Last modification on : Saturday, August 13, 2022 - 3:10:09 AM

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  • HAL Id : hal-03718693, version 1

Citation

Olivier Rioul. Gaussian bounds for discrete entropies. IEEE Information Theory and Applications Workshop (ITA 2022), May 2022, San Diego, United States. ⟨hal-03718693⟩

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