A Unifying Variational Perspective on Some Fundamental Information Theoretic Inequalities

TL;DR

This paper introduces a unifying variational framework to prove and extend key information theoretic inequalities, offering a new perspective that encompasses several classical results through calculus of variations.

Contribution

It presents a novel variational approach that unifies and generalizes fundamental information inequalities within a single theoretical framework.

Findings

Unified proof of classical inequalities like EPI and EEI

Extension of inequalities using calculus of variations

Potential applications in information theory analysis

Abstract

This paper proposes a unifying variational approach for proving and extending some fundamental information theoretic inequalities. Fundamental information theory results such as maximization of differential entropy, minimization of Fisher information (Cram\'er-Rao inequality), worst additive noise lemma, entropy power inequality (EPI), and extremal entropy inequality (EEI) are interpreted as functional problems and proved within the framework of calculus of variations. Several applications and possible extensions of the proposed results are briefly mentioned.