Conditional Rényi Entropy and the Relationships between Rényi Capacities
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
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Entropy 2020, 22(5), 526; https://doi.org/10.3390/e22050526
Received: 16 November 2019
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Revised: 31 January 2020
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Accepted: 30 April 2020
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Published: 6 May 2020
(This article belongs to the Special Issue Information Measures with Applications)
The analogues of Arimoto’s definition of conditional Rényi entropy and Rényi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to those known in the discrete setting. In addition to laying out some such basic properties and the relations to Rényi divergences, the relationships between the families of mutual informations defined by Sibson, Augustin-Csiszár, and Lapidoth-Pfister, as well as the corresponding capacities, are explored.
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Keywords:
conditional Rényi entropy; Rényi mutual information; Rényi capacity; Sibson mutual information
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MDPI and ACS Style
Aishwarya, G.; Madiman, M. Conditional Rényi Entropy and the Relationships between Rényi Capacities. Entropy 2020, 22, 526. https://doi.org/10.3390/e22050526
AMA Style
Aishwarya G, Madiman M. Conditional Rényi Entropy and the Relationships between Rényi Capacities. Entropy. 2020; 22(5):526. https://doi.org/10.3390/e22050526
Chicago/Turabian StyleAishwarya, Gautam, and Mokshay Madiman. 2020. "Conditional Rényi Entropy and the Relationships between Rényi Capacities" Entropy 22, no. 5: 526. https://doi.org/10.3390/e22050526
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