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

Makkuva, Ashok Vardhan

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Description

Title

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

Author(s)

Makkuva, Ashok Vardhan

Issue Date

2017-04-26

Director of Research (if dissertation) or Advisor (if thesis)

• Viswanath, Pramod
• Wu, Yihong

Department of Study

Electrical & Computer Eng

Discipline

Electrical & Computer Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.S.

Degree Level

Thesis

Keyword(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.

Graduation Semester

2017-05

Type of Resource

text

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

Copyright and License Information

Copyright 2017 Ashok Makkuva

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