Low Complexity Estimation Method of Rényi Entropy for Ergodic Sources†
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.
Received: 11 July 2018 / Revised: 28 August 2018 / Accepted: 30 August 2018 / Published: 31 August 2018
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
. Since the Rényi entropy of order
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
. After deriving a general representation of parameters of the proposed estimator, we discuss on the particular orders of Rényi entropy such as
. 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.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Kim, Y.-S. Low Complexity Estimation Method of Rényi Entropy for Ergodic Sources. Entropy 2018, 20, 657.
Kim Y-S. Low Complexity Estimation Method of Rényi Entropy for Ergodic Sources. Entropy. 2018; 20(9):657.
Kim, Young-Sik. 2018. "Low Complexity Estimation Method of Rényi Entropy for Ergodic Sources." Entropy 20, no. 9: 657.
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