The entropy power inequality (EPI) and the Brascamp-Lieb (BLI) are fundamental inequalities concerning differential entropies of linear transformations random vectors. EPI provides lower bounds for vectors with independent components. BLI, on other hand, upper a vector in terms some its transformations. In this paper, we define family functionals, which show subadditive. We then establish that ...

As was shown recently by the authors, the entropy power inequality can be reversed for independent summands with sufficiently concave densities, when the distributions of the summands are put in a special position. In this note it is proved that reversibility is impossible over the whole class of convex probability distributions. Related phenomena for identically distributed summands are also d...

We present a simple proof of the entropy-power inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse inequality involving a conditional differential entropy which has its own interest. For each inequality, the equality case is easily captured by this method and the proof is formally identical in one and sever...

An extension of the entropy power inequality to the form N r (X +Y ) ≥ N r (X) +N r (Y ) with arbitrary independent summands X and Y in R is obtained for the Rényi entropy and powers α ≥ (r + 1)/2.

Shannon’s entropy power inequality characterizes the minimum differential entropy achievable by the sum of two independent random variables with fixed differential entropies. Since the pioneering work of Shannon, there has been a steady stream of results over the years, trying to understand the structure of Shannon’s entropy power inequality, as well as trying to develop similar entropy power i...

We give a counterexample to the vector generalization of Costa’s entropy power inequality (EPI) due to Liu, Liu, Poor and Shamai. In particular, the claimed inequality can fail if the matix-valued parameter in the convex combination does not commute with the covariance of the additive Gaussian noise. Conversely, the inequality holds if these two matrices commute. For a random vector X with dens...