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Title:On equivalence of additive-combinatorial inequalities for Shannon entropy and differential entropy
Author(s):Makkuva, Ashok Vardhan
Advisor(s):Viswanath, Pramod; Wu, Yihong
Department / Program:Electrical & Computer Eng
Discipline:Electrical & Computer Engr
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Shannon entropy
Differential entropy
Information theory
Additive combinatorics
Entropy inequalities
Abstract:Entropy inequalities are very important in information theory and they play a crucial role in various communication-theoretic problems, for example, in the study of the degrees of freedom of interference channels. In this thesis, we are concerned with the additive-combinatorial entropy inequalities which are motivated by their combinatorial counterparts: cardinality inequalities for subsets of abelian groups. As opposed to the existing approaches in the literature in the study of the discrete and continuous entropy inequalities, we consider a general framework of balanced linear entropy inequalities. In particular, we show a fundamental equivalence relationship between these classes of discrete and continuous entropy inequalities. In other words, we show that a balanced Shannon entropy inequality holds if and only if the corresponding differential entropy inequality holds. We also investigate these findings in a more general setting of connected abelian Lie groups and in the study of the sharp constants for entropy inequalities.
Issue Date:2017-04-26
Rights Information:Copyright 2017 Ashok Makkuva
Date Available in IDEALS:2017-08-10
Date Deposited:2017-05

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