A vector generalization of costa entropy-power inequality and applications

Ruoheng Liu; Tie Liu; H. Vincent Poor; Shlomo Shamai

doi:10.1109/ISIT.2009.5205459

A vector generalization of costa entropy-power inequality and applications

Ruoheng Liu, Tie Liu, H. Vincent Poor, Shlomo Shamai

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

2 Scopus citations

Abstract

This paper considers an entropy-power inequality (EPI) of Costa and presents a natural vector generalization with a real positive semidefinite matrix parameter. This new inequality is proved using a perturbation approach via a fundamental relationship between the derivative of mutual information and the minimum mean-square error (MMSE) estimate in linear vector Gaussian channels. As an application, a new extremal entropy inequality is derived from the generalized Costa EPI and then used to establish the secrecy capacity regions of the degraded vector Gaussian broadcast channel with layered confidential messages.

Original language	English (US)
Title of host publication	2009 IEEE International Symposium on Information Theory, ISIT 2009
Pages	299-303
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2009.5205459
State	Published - 2009
Externally published	Yes
Event	2009 IEEE International Symposium on Information Theory, ISIT 2009 - Seoul, Korea, Republic of Duration: Jun 28 2009 → Jul 3 2009

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8102

Other

Other	2009 IEEE International Symposium on Information Theory, ISIT 2009
Country/Territory	Korea, Republic of
City	Seoul
Period	6/28/09 → 7/3/09

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

Access to Document

10.1109/ISIT.2009.5205459

Cite this

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title = "A vector generalization of costa entropy-power inequality and applications",

abstract = "This paper considers an entropy-power inequality (EPI) of Costa and presents a natural vector generalization with a real positive semidefinite matrix parameter. This new inequality is proved using a perturbation approach via a fundamental relationship between the derivative of mutual information and the minimum mean-square error (MMSE) estimate in linear vector Gaussian channels. As an application, a new extremal entropy inequality is derived from the generalized Costa EPI and then used to establish the secrecy capacity regions of the degraded vector Gaussian broadcast channel with layered confidential messages.",

author = "Ruoheng Liu and Tie Liu and Poor, {H. Vincent} and Shlomo Shamai",

year = "2009",

doi = "10.1109/ISIT.2009.5205459",

language = "English (US)",

isbn = "9781424443130",

series = "IEEE International Symposium on Information Theory - Proceedings",

pages = "299--303",

booktitle = "2009 IEEE International Symposium on Information Theory, ISIT 2009",

note = "2009 IEEE International Symposium on Information Theory, ISIT 2009 ; Conference date: 28-06-2009 Through 03-07-2009",

}

Liu, R, Liu, T, Poor, HV & Shamai, S 2009, A vector generalization of costa entropy-power inequality and applications. in 2009 IEEE International Symposium on Information Theory, ISIT 2009., 5205459, IEEE International Symposium on Information Theory - Proceedings, pp. 299-303, 2009 IEEE International Symposium on Information Theory, ISIT 2009, Seoul, Korea, Republic of, 6/28/09. https://doi.org/10.1109/ISIT.2009.5205459

A vector generalization of costa entropy-power inequality and applications. / Liu, Ruoheng; Liu, Tie; Poor, H. Vincent et al.
2009 IEEE International Symposium on Information Theory, ISIT 2009. 2009. p. 299-303 5205459 (IEEE International Symposium on Information Theory - Proceedings).

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

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AU - Shamai, Shlomo

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N2 - This paper considers an entropy-power inequality (EPI) of Costa and presents a natural vector generalization with a real positive semidefinite matrix parameter. This new inequality is proved using a perturbation approach via a fundamental relationship between the derivative of mutual information and the minimum mean-square error (MMSE) estimate in linear vector Gaussian channels. As an application, a new extremal entropy inequality is derived from the generalized Costa EPI and then used to establish the secrecy capacity regions of the degraded vector Gaussian broadcast channel with layered confidential messages.

AB - This paper considers an entropy-power inequality (EPI) of Costa and presents a natural vector generalization with a real positive semidefinite matrix parameter. This new inequality is proved using a perturbation approach via a fundamental relationship between the derivative of mutual information and the minimum mean-square error (MMSE) estimate in linear vector Gaussian channels. As an application, a new extremal entropy inequality is derived from the generalized Costa EPI and then used to establish the secrecy capacity regions of the degraded vector Gaussian broadcast channel with layered confidential messages.

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A vector generalization of costa entropy-power inequality and applications

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