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Low Complexity Estimation Method of Rényi Entropy for Ergodic Sources

by Young-Sik Kim
Department of Information and Communication Engineering, Chosun University, 309 Pilmoondae-ro Dong-gu, Gwangju 61452, Korea
This paper is an extended version of my paper published in the 2014 International Symposium on Information Theory and Its Applications, Melbourne, VIC, Australia, 26–29 October 2014.
Entropy 2018, 20(9), 657; https://doi.org/10.3390/e20090657
Received: 11 July 2018 / Revised: 28 August 2018 / Accepted: 30 August 2018 / Published: 31 August 2018
(This article belongs to the Section Information Theory, Probability and Statistics)
Since the entropy is a popular randomness measure, there are many studies for the estimation of entropies for given random samples. In this paper, we propose an estimation method of the Rényi entropy of order α . Since the Rényi entropy of order α is a generalized entropy measure including the Shannon entropy as a special case, the proposed estimation method for Rényi entropy can detect any significant deviation of an ergodic stationary random source’s output. It is shown that the expected test value of the proposed scheme is equivalent to the Rényi entropy of order α . After deriving a general representation of parameters of the proposed estimator, we discuss on the particular orders of Rényi entropy such as α 1 , α = 1 / 2 , and α = 2 . Because the Rényi entropy of order 2 is the most popular one, we present an iterative estimation method for the application with stringent resource restrictions. View Full-Text
Keywords: entropy estimation; Shannon entropy; Rényi entropy; quadratic entropy; random number generation; nearest neighbor distance; security entropy estimation; Shannon entropy; Rényi entropy; quadratic entropy; random number generation; nearest neighbor distance; security
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Kim, Y.-S. Low Complexity Estimation Method of Rényi Entropy for Ergodic Sources. Entropy 2018, 20, 657.

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