A Unifying Variational Perspective on Some Fundamental Information Theoretic Inequalities
Sangwoo Park, Erchin Serpedin, Khalid Qaraqe

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsWireless Communication Security Techniques · Statistical Mechanics and Entropy · Sparse and Compressive Sensing Techniques
