We present a new lower bound on the differential entropy rate of stationary
processes whose sequences of probability density functions fulfill certain
regularity conditions. This bound is obtained by showing that the gap between
the differential entropy rate of such a process and the differential entropy
rate of a Gaussian process with the same autocovariance function is bounded.
This result is based on a recent result on bounding the Kullback-Leibler
divergence by the Wasserstein distance given by Polyanskiy and Wu. Moreover, it
is related to the famous hyperplane conjecture, also known as slicing problem,
in convex geometry originally stated by J. Bourgain. Based on an entropic
formulation of the hyperplane conjecture given by Bobkov and Madiman we discuss
the relation of our result to the hyperplane conjecture.Comment: presented at the 2016 IEEE Information Theory Workshop (ITW),
Cambridge, U