  While most useful information theoretic inequalities can be deduced from the
basic properties of entropy or mutual information, Shannon's entropy power
inequality (EPI) seems to be an exception: available information theoretic
proofs of the EPI hinge on integral representations of differential entropy
using either Fisher's information (FI) or minimum mean-square error (MMSE). In
this paper, we first present a unified view of proofs via FI and MMSE, showing
that they are essentially dual versions of the same proof, and then fill the
gap by providing a new, simple proof of the EPI, which is solely based on the
properties of mutual information and sidesteps both FI or MMSE representations.
