Error Bounds on a Mixed Entropy Inequality

James Melbourne; Saurav Talukdar; Shreyas Bhaban; Murti V. Salapaka

doi:10.1109/ISIT.2018.8437601

Error Bounds on a Mixed Entropy Inequality

James Melbourne, Saurav Talukdar, Shreyas Bhaban, Murti V. Salapaka

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Scopus citations

Abstract

Motivated by the entropy computations relevant to the evaluation of decrease in entropy in bit reset operations, the authors investigate the deficit in an entropic inequality involving two independent random variables, one continuous and the other discrete. In the case where the continuous random variable is Gaussian, we derive strong quantitative bounds on the deficit in the inequality. More explicitly it is shown that the decay of the deficit is sub-Gaussian with respect to the reciprocal of the standard deviation of the Gaussian variable. What is more, up to rational terms these results are shown to be sharp.

Original language	English (US)
Title of host publication	2018 IEEE International Symposium on Information Theory, ISIT 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1973-1977
Number of pages	5
ISBN (Print)	9781538647806
DOIs	https://doi.org/10.1109/ISIT.2018.8437601
State	Published - Aug 15 2018
Event	2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States Duration: Jun 17 2018 → Jun 22 2018

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2018-June
ISSN (Print)	2157-8095

Other

Other	2018 IEEE International Symposium on Information Theory, ISIT 2018
Country/Territory	United States
City	Vail
Period	6/17/18 → 6/22/18

Bibliographical note

Funding Information:
We would like to thank Prof. Mokshay Madiman, University of Delaware and Prof. Arnab Sen, University of Minnesota for initial discussion about the problem. The authors acknowledge the support of the National Science Foundation for funding the research under Grant No. CMMI-1462862, CNS 1544721 and the first author acknowledges support from NSF Grant No. 1248100

Funding Information:
We would like to thank Prof. Mokshay Madiman, University of Delaware and Prof. Arnab Sen, University of Minnesota for initial discussion about the problem. The authors acknowledge the support of the National Science Foundation for funding the research under Grant No. CMMI-1462862, CNS 1544721 and the first author acknowledges support from NSF Grant No. 1248100. Portions of this article and related results were announced at the March Meeting of the American Physical Society [11], [18].

Publisher Copyright:
© 2018 IEEE.

Publisher link

10.1109/ISIT.2018.8437601

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Melbourne, J., Talukdar, S., Bhaban, S., & Salapaka, M. V. (2018). Error Bounds on a Mixed Entropy Inequality. In 2018 IEEE International Symposium on Information Theory, ISIT 2018 (pp. 1973-1977). [8437601] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2018.8437601

Error Bounds on a Mixed Entropy Inequality. / Melbourne, James; Talukdar, Saurav; Bhaban, Shreyas et al.

2018 IEEE International Symposium on Information Theory, ISIT 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 1973-1977 8437601 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2018-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Melbourne, J, Talukdar, S, Bhaban, S & Salapaka, MV 2018, Error Bounds on a Mixed Entropy Inequality. in 2018 IEEE International Symposium on Information Theory, ISIT 2018., 8437601, IEEE International Symposium on Information Theory - Proceedings, vol. 2018-June, Institute of Electrical and Electronics Engineers Inc., pp. 1973-1977, 2018 IEEE International Symposium on Information Theory, ISIT 2018, Vail, United States, 6/17/18. https://doi.org/10.1109/ISIT.2018.8437601

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AB - Motivated by the entropy computations relevant to the evaluation of decrease in entropy in bit reset operations, the authors investigate the deficit in an entropic inequality involving two independent random variables, one continuous and the other discrete. In the case where the continuous random variable is Gaussian, we derive strong quantitative bounds on the deficit in the inequality. More explicitly it is shown that the decay of the deficit is sub-Gaussian with respect to the reciprocal of the standard deviation of the Gaussian variable. What is more, up to rational terms these results are shown to be sharp.

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Error Bounds on a Mixed Entropy Inequality

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