This paper is a follow-up of a recent work by Bobkov and Chistyakov, obtaining some improved Rényi entropy power inequalities (R-EPIs) for sums of independent random vectors. The first improvement relies on the same bounding techniques used in the former work, while the second significant improvement relies on additional interesting properties from matrix theory. The improvements obtained by th...

The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are derived. Notions of additivity, extensivity and homogeneity are clarified. The relation between mean code lengths in coding theory and various expressions for ...

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

We discuss entropy definition for composite systems composed of two Tsallis (or Rényi) systems with different q indices using the bi-composability nature. The most general bi-composable entropy form is given.

In this paper, we propose a novel layering approach to achieve end-to-end exponential security without resorting to presumed physical layer conditions. The only requirement for such an exponentially secure system is existence of a common key source between legitimate users that is partially known by Eve. The novel framework includes a random cipher and key stream generating scheme constituting ...

Transport-entropy inequalities are considered in terms of Rényi informational divergence.