On Divergence-Power Inequalities

Author

Binia, Jacob

Author_Institution

New Elective Eng. Services Ltd, Haifa

Volume

53

Issue

3

fYear

2007

fDate

3/1/2007 12:00:00 AM

Firstpage

1179

Lastpage

1182

Abstract

Expressions for (entropy-power inequality (EPI) Shannon type) divergence-power inequalities (DPIs) in two cases (time-discrete and time-continuous) of stationary random processes are given. The new expressions connect the divergence rate of the sum of independent processes, the individual divergence rate of each process, and their power spectral densities. All divergences are between a process and a Gaussian process with same second-order statistics, and are assumed to be finite. A new proof of the Shannon EPI, based on the relationship between divergence and causal minimum mean-square error (CMMSE) in Gaussian channels with large signal-to-noise ratio, is also shown

Keywords

Gaussian channels; entropy; least mean squares methods; random processes; spectral analysis; CMMSE; Gaussian process; Shannon EPI; causal minimum mean-square error; divergence-power inequality; entropy power inequality; power spectral density; second-order statistics; stationary random process; Distortion measurement; Gaussian processes; H infinity control; Jacobian matrices; Laplace equations; Notice of Violation; Quantization; Random processes; Rate distortion theory; Rate-distortion; Causal minimum mean-square error (CMMSE); divergence rate; divergence-power inequality; entropy-power inequality;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2006.890715

Filename

4106109