Title :
On Divergence-Power Inequalities
Author_Institution :
New Elective Eng. Services Ltd, Haifa
fDate :
3/1/2007 12:00:00 AM
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;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2006.890715
