A Vector Generalization of Costa´s Entropy-Power Inequality With Applications

Author

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

Author_Institution

Dept. of Electr. Eng., Princeton Univ., Princeton, NJ, USA

Volume

56

Issue

4

fYear

2010

fDate

4/1/2010 12:00:00 AM

Firstpage

1865

Lastpage

1879

Abstract

This paper considers an entropy-power inequality (EPI) of Costa and presents a natural vector generalization with a real positive semidefinite matrix parameter. The 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.

Keywords

Gaussian channels; broadcast channels; entropy; least mean squares methods; Costa entropy power inequality; Gaussian broadcast channel; MMSE estimate; linear vector Gaussian channels; minimum mean-square error estimate; perturbation approach; semideflnite matrix parameter; vector generalization; Broadcasting; Covariance matrix; Degradation; Entropy; Gaussian channels; Information theory; Linear matrix inequalities; MIMO; Mutual information; Vectors; Entropy-power inequality (EPI); extremal entropy inequality; information-theoretic security; mutual information and minimum mean-square error (MMSE) estimate; vector Gaussian broadcast channel;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2010.2040879

Filename

5437423