A generalization of the entropy power inequality with applications

The authors prove the following generalization of the entropy power inequality: h(ax_)⩾h(Ax_) where h(·) denotes (joint-) differential-entropy x_=x₁...x_n , is a random vector with independent components, x˜_=x˜...x˜_n, is a Gaussian vector with independent components such that h(x¯_i)=h(x_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