This paper introduces a new class of fractal dimension measures which we call relative multifractal measures. The relative multifractal measures developed are formed through a melding of the Rényi dimension spectrum, which is based on the Rényi generalized entropy, and relative entropy as given with the Kullback-Leibler distance. This new class of multifractal measures is then used to find the ...

In this paper, the two parameter ADK entropy, as a generalized of Re'nyi entropy, is considered and some properties of it, are investigated. We will see that the ADK entropy for continuous random variables is invariant under a location and is not invariant under a scale transformation of the random variable. Furthermore, the joint ADK entropy, conditional ADK entropy, and chain rule of this ent...

The Shannon entropy is a widely used summary statistic, for example, network traffic measurement, anomaly detection, neural computations, spike trains, etc. This study focuses on estimating Shannon entropy of data streams. It is known that Shannon entropy can be approximated by Rényi entropy or Tsallis entropy, which are both functions of the αth frequency moments and approach Shannon entropy a...

We consider optimal scalar quantization with rth power distortion and constrained Rényi entropy of order α. For sources with absolutely continuous distributions the high rate asymptotics of the quantizer distortion has long been known for α = 0 (fixed-rate quantization) and α = 1 (entropyconstrained quantization). These results have recently been extended to quantization with Rényi entropy cons...

In this paper, we explore the issue of network infrastructure and architecture in Deep Space Communication Networks (DSCNs). Firstly, we present a typical structural sample infrastructure of our vision of DSCNs by separating the whole network into three major parts. We then use hypergraph theory and Rényi entropy paradigm to formulate Relaying Networks for Deep Space Communications (RNDSC) as a...

We derive a new upper bound for Eve’s information in secret key generation from a common random number without communication. This bound improves on Bennett[7]’s bound based on the Rényi entropy of order 2 because the bound obtained here uses the Rényi entropy of order 1+s for s ∈ [0, 1]. This bound is applied to a wire-tap channel. Then, we derive an exponential upper bound for Eve’s informati...

Second order lower bounds for the entropy function expressed in terms of the index of coincidence are derived. Equivalently, these bounds involve entropy and Rényi entropy of order 2. The constants found either explicitly or implicitly are best possible in a natural sense. The inequalities developed originated with certain problems in universal prediction and coding which are briefly discussed.

The definition of weighted entropy allows for easy calculation of the entropy of the mixture of measures. In this paper we investigate the problem of equivalent definition of the general entropy function in weighted form. We show that under reasonable condition, which is satisfied by the well-known Shannon, Rényi and Tsallis entropies, every entropy function can be defined equivalently in the w...