On Divergence-Power Inequalities

Details On Divergence-Power Inequalities On Divergence-Power Inequalities

2006-09-08

arxiv.org/abs/cs/0609042v1

Computer Science

Information Theory

Submitted to IEEE Transactions on Information Theory

Scientific paper

Expressions for (EPI Shannon type) Divergence-Power Inequalities (DPI) in two cases (time-discrete and band-limited 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 entropy-power inequality 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.

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