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...

Properties of scalar quantization with rth power distortion and constrained Rényi entropy of order α ∈ (0, 1) are investigated. For an asymptotically (high-rate) optimal sequence of quantizers, the contribution to the Rényi entropy due to source values in a fixed interval is identified in terms of the “entropy density” of the quantizer sequence. This extends results related to the well-known po...

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 ...

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.

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