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.

The Renyi entropy coprises a group of data estimates that sums up the well-known Shannon entropy, acquiring considerable lot its properties. It appears as unqualified and restrictive relative or common data, has found numerous applications in information theory. Renyi's argument, area law black hole plays significant role. However, total can be modified by some quantum effects, motivated random...

We investigate the Rényi entropy of sums independent integer-valued random variables through Fourier theoretic means, and give sharp comparisons between variance for Bernoulli variables. As applications, we prove that a discrete “min-entropy power” is superadditive with respect to convolution modulo universal constant, new bounds on an entropic generalization Littlewood-Offord problem are in “P...