Converse bounds for interference channels via coupling and proof of Costa's conjecture

Yury Polyanskiy; Yihong Wu

doi:10.1109/ISIT.2016.7541691

Converse bounds for interference channels via coupling and proof of Costa's conjecture

Yury Polyanskiy, Yihong Wu

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

Abstract

It is shown that under suitable regularity conditions, differential entropy is O(√n)-Lipschitz as a function of probability distributions on ℝⁿ with respect to the quadratic Wasserstein distance. Under similar conditions, (discrete) Shannon entropy is shown to be O(n)-Lipschitz in distributions over the product space with respect to Ornstein's d-distance (Wasserstein distance corresponding to the Hamming distance). These results together with Talagrand's and Marton's transportation-information inequalities allow one to replace the unknown multi-user interference with its i.i.d. approximations. As an application, a new outer bound for the two-user Gaussian interference channel is proved, which, in particular, settles the 'missing corner point' problem of Costa (1985).

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	2209-2213
Number of pages	5
ISBN (Electronic)	9781509018062
DOIs	https://doi.org/10.1109/ISIT.2016.7541691
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

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

Online availability

10.1109/ISIT.2016.7541691

Library availability

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Polyanskiy, Y., & Wu, Y. (2016). Converse bounds for interference channels via coupling and proof of Costa's conjecture. In Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory (pp. 2209-2213). Article 7541691 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2016.7541691

Converse bounds for interference channels via coupling and proof of Costa's conjecture. / Polyanskiy, Yury; Wu, Yihong.
Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc., 2016. p. 2209-2213 7541691 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August).

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

Polyanskiy, Y & Wu, Y 2016, Converse bounds for interference channels via coupling and proof of Costa's conjecture. in Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory., 7541691, IEEE International Symposium on Information Theory - Proceedings, vol. 2016-August, Institute of Electrical and Electronics Engineers Inc., pp. 2209-2213, 2016 IEEE International Symposium on Information Theory, ISIT 2016, Barcelona, Spain, 7/10/16. https://doi.org/10.1109/ISIT.2016.7541691

Polyanskiy Y, Wu Y. Converse bounds for interference channels via coupling and proof of Costa's conjecture. In Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc. 2016. p. 2209-2213. 7541691. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT.2016.7541691

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Converse bounds for interference channels via coupling and proof of Costa's conjecture

Abstract

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