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Viswanath, Pramod Wu, Yihong Makkuva, Ashok Vardhan 2017-08-10T19:15:57Z 2017-08-10T19:15:57Z 2017-04-26 2017-05 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-08-10 without embargo terms The student, Ashok Makkuva, accepted the attached license on 2017-04-24 at 13:15. The student, Ashok Makkuva, submitted this Thesis for approval on 2017-04-24 at 13:16. This Thesis was approved for publication on 2017-04-26 at 17:46. DSpace SAF Submission Ingestion Package generated from Vireo submission #10999 on 2017-08-10 at 13:45:33 Made available in DSpace on 2017-08-10T19:15:57Z (GMT). No. of bitstreams: 2 MAKKUVA-THESIS-2017.pdf: 599339 bytes, checksum: c2c6cb2ce9513dae120140237f937bf7 (MD5) LICENSE.txt: 4210 bytes, checksum: 0820f5de79755d3e01231f3919d544ec (MD5) Previous issue date: 2017-04-26 application/pdf http://hdl.handle.net/2142/97446 en Copyright 2017 Ashok Makkuva Shannon entropy Differential entropy Information theory Additive combinatorics Entropy inequalities On equivalence of additive-combinatorial inequalities for Shannon entropy and differential entropy text text Electrical & Computer Eng Electrical & Computer Engr University of Illinois at Urbana-Champaign Thesis M.S.