Information Inequalities via Ideas from Additive Combinatorics
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.
Keywords
Cite
@article{arxiv.2312.11017,
title = {Information Inequalities via Ideas from Additive Combinatorics},
author = {Chin Wa Lau and Chandra Nair},
journal= {arXiv preprint arXiv:2312.11017},
year = {2025}
}
Comments
21 pages, update appendices; the authors were made aware that some of the results had been obtained earlier. The revised version acknowledges and references this work. A conference version of this was published in the proceeding of IEEE ISIT 2023