Smoothing Brascamp-Lieb inequalities and strong converses for common randomness generation

Jingbo Liu; Thomas A. Courtade; Paul Cuff; Sergio Verdu

doi:10.1109/ISIT.2016.7541458

Smoothing Brascamp-Lieb inequalities and strong converses for common randomness generation

Jingbo Liu, Thomas A. Courtade, Paul Cuff, Sergio Verdu

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

14 Scopus citations

Abstract

We study the infimum of the best constant in a functional inequality, the Brascamp-Lieb-like inequality, over auxiliary measures within a neighborhood of a product distribution. In the finite alphabet and the Gaussian cases, such an infimum converges to the best constant in a mutual information inequality. Implications for strong converse properties of two common randomness (CR) generation problems are discussed. In particular, we prove the strong converse property of the rate region for the omniscient helper CR generation problem in the discrete and the Gaussian cases. The latter case is a rare instance of a strong converse for a continuous source when the rate region involves auxiliary random variables.

Original language	English (US)
Title of host publication	Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1043-1047
Number of pages	5
ISBN (Electronic)	9781509018062
DOIs	https://doi.org/10.1109/ISIT.2016.7541458
State	Published - Aug 10 2016
Event	2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain Duration: Jul 10 2016 → Jul 15 2016

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2016-August
ISSN (Print)	2157-8095

Other

Other	2016 IEEE International Symposium on Information Theory, ISIT 2016
Country/Territory	Spain
City	Barcelona
Period	7/10/16 → 7/15/16

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ISIT.2016.7541458

Cite this

Liu, J., Courtade, T. A., Cuff, P., & Verdu, S. (2016). Smoothing Brascamp-Lieb inequalities and strong converses for common randomness generation. In Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory (pp. 1043-1047). Article 7541458 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2016.7541458

Liu, Jingbo ; Courtade, Thomas A. ; Cuff, Paul et al. / Smoothing Brascamp-Lieb inequalities and strong converses for common randomness generation. Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 1043-1047 (IEEE International Symposium on Information Theory - Proceedings).

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abstract = "We study the infimum of the best constant in a functional inequality, the Brascamp-Lieb-like inequality, over auxiliary measures within a neighborhood of a product distribution. In the finite alphabet and the Gaussian cases, such an infimum converges to the best constant in a mutual information inequality. Implications for strong converse properties of two common randomness (CR) generation problems are discussed. In particular, we prove the strong converse property of the rate region for the omniscient helper CR generation problem in the discrete and the Gaussian cases. The latter case is a rare instance of a strong converse for a continuous source when the rate region involves auxiliary random variables.",

author = "Jingbo Liu and Courtade, {Thomas A.} and Paul Cuff and Sergio Verdu",

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Liu, J, Courtade, TA, Cuff, P & Verdu, S 2016, Smoothing Brascamp-Lieb inequalities and strong converses for common randomness generation. in Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory., 7541458, IEEE International Symposium on Information Theory - Proceedings, vol. 2016-August, Institute of Electrical and Electronics Engineers Inc., pp. 1043-1047, 2016 IEEE International Symposium on Information Theory, ISIT 2016, Barcelona, Spain, 7/10/16. https://doi.org/10.1109/ISIT.2016.7541458

Smoothing Brascamp-Lieb inequalities and strong converses for common randomness generation. / Liu, Jingbo; Courtade, Thomas A.; Cuff, Paul et al.
Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc., 2016. p. 1043-1047 7541458 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August).

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

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N2 - We study the infimum of the best constant in a functional inequality, the Brascamp-Lieb-like inequality, over auxiliary measures within a neighborhood of a product distribution. In the finite alphabet and the Gaussian cases, such an infimum converges to the best constant in a mutual information inequality. Implications for strong converse properties of two common randomness (CR) generation problems are discussed. In particular, we prove the strong converse property of the rate region for the omniscient helper CR generation problem in the discrete and the Gaussian cases. The latter case is a rare instance of a strong converse for a continuous source when the rate region involves auxiliary random variables.

AB - We study the infimum of the best constant in a functional inequality, the Brascamp-Lieb-like inequality, over auxiliary measures within a neighborhood of a product distribution. In the finite alphabet and the Gaussian cases, such an infimum converges to the best constant in a mutual information inequality. Implications for strong converse properties of two common randomness (CR) generation problems are discussed. In particular, we prove the strong converse property of the rate region for the omniscient helper CR generation problem in the discrete and the Gaussian cases. The latter case is a rare instance of a strong converse for a continuous source when the rate region involves auxiliary random variables.

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Liu J, Courtade TA, Cuff P, Verdu S. Smoothing Brascamp-Lieb inequalities and strong converses for common randomness generation. In Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc. 2016. p. 1043-1047. 7541458. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT.2016.7541458

Smoothing Brascamp-Lieb inequalities and strong converses for common randomness generation

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