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Conditional Rényi Entropy and the Relationships between Rényi Capacities.
Gautam Aishwarya1, Mokshay Madiman1
1Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study explores analogues of conditional Rényi entropy and mutual information for abstract alphabets. Useful properties and relationships to divergences and other mutual information families are detailed.
Area of Science:
- Information Theory
- Mathematical Physics
Background:
- Conditional Rényi entropy and mutual information are key concepts in information theory.
- Existing definitions are primarily for discrete settings.
Purpose of the Study:
- To explore analogues of Arimoto's conditional Rényi entropy and Rényi mutual information for abstract alphabets.
- To investigate their properties and relationships with other information-theoretic quantities.
Main Methods:
- Generalization of Arimoto's definitions to abstract alphabets.
- Analysis of properties related to reference measure dependence.
- Comparison with Sibson, Augustin-Csiszár, and Lapidoth-Pfister mutual information families.
Main Results:
- Analogues exhibit useful properties, mirroring discrete settings despite reference measure dependence.
- Established basic properties and relations to Rényi divergences.
- Explored relationships between different mutual information families and their capacities.
Conclusions:
- The generalized quantities offer a valuable extension of information theory to abstract settings.
- Understanding these relationships deepens insights into information measures and capacities.
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