Information Inequalities via Ideas from Additive Combinatorics

Chin Wa Lau; Chandra Nair

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arXiv · 2312.11017

Information Inequalities via Ideas from Additive Combinatorics

Chin Wa Lau·Chandra Nair

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Abstract

Ruzsa'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 work, we first establish formal equivalences between some families (different from Ruzsa) of inequalities in additive combinatorics and entropic ones. As a first step to further these equivalences, we establish an information-theoretic characterization of the magnification ratio that could also be of independent interest.

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Chin Wa Lau, Chandra Nair. 2023-12-18. Information Inequalities via Ideas from Additive Combinatorics. https://arxiv.org/abs/2312.11017

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