A generalization of the entropy power inequality with applications

The authors prove the following generalization of the entropy power inequality: h(ax)>or=h(Ax) where h(.) denotes (joint-) differential-entropy x=x/sub 1/...x/sub n/, is a random vector with independent components, x=x...x/sub n/, is a Gaussian vector with independent components such that h(x/sub i/)=h(x/sub i/), i=1...n, and A is any matrix. This generalization of the entropy-power inequality is applied to show that a non-Gaussian vector with independent components becomes "closer" to Gaussianity after a linear transformation, where the distance to Gaussianity is measured by the information divergence. Another application is a lower bound, greater than zero, for the mutual-information between nonoverlapping spectral components of a non-Gaussian white process. They also describe a dual generalization of the Fisher information inequality.<
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