Information Inequalities via Ideas from Additive Combinatorics

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. Secondly, we provide stand-alone entropic proofs for some previously known entropic inequalities established via Ruzsa's equivalence theorem. 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.