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Information Inequalities via Ideas from Additive Combinatorics (2312.11017v3)
Published 18 Dec 2023 in cs.IT, math.CO, math.IT, and math.NT
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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