English

Information Inequalities via Ideas from Additive Combinatorics

Information Theory 2025-02-06 v3 Combinatorics math.IT Number Theory

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

R2 v1 2026-06-28T13:54:22.131Z