Additive Combinatorics, Abelian Groups, and Entropic Inequalities.

Abstract: uzsa’s equivalence theorem provided a framework for converting certain families of inequalities in additive combinatorics to entropic inequalities (which sometimes did not possess stand-alone entropic proofs). In this talk, we first establish formal equivalences between some families (different from Ruzsa) of inequalities in additive combinatorics and entropic ones. Secondly, we provide stand-alone entropic proofs for previously known entropic inequalities that we established via Ruzsa’s equivalence theorem. As a first step to further these equivalences, we establish an information-theoretic characterization of the magnification ratio of independent interest.

This talk is based on the following paper: Information Inequalities via Ideas from Additive Combinatorics (conference version ISIT 2023: C. W. Ken Lau and C. Nair, "Information Inequalities via Ideas from Additive Combinatorics," 2023 IEEE International Symposium on Information Theory (ISIT), Taipei, Taiwan, 2023, pp. 2452-2457, doi: 10.1109/ISIT54713.2023.10206561.

Computer scienceMathematics

Audience: researchers in the discipline

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Seminar on Algorithmic Aspects of Information Theory

Series comments: This online seminar is a follow up of the Dagstuhl Seminar 22301, www.dagstuhl.de/en/program/calendar/semhp/?semnr=22301.

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