On equivalence of additive-combinatorial inequalities for Shannon entropy and differential entropy

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2017

Author dc:creator

• Makkuva, Ashok Vardhan

Contributors dc:contributor

• Viswanath, Pramod
• Wu, Yihong

• Shannon entropy
• Differential entropy
• Information theory
• Additive combinatorics
• Entropy inequalities

Statement dc:rights

• Copyright 2017 Ashok Makkuva

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/97446

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/97446