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A correlation measure based on vector-valued Lp norms
, Article 2019 IEEE International Symposium on Information Theory, ISIT 2019, 7 July 2019 through 12 July 2019 ; Volume 2019-July , 2019 , Pages 1132-1136 ; 21578095 (ISSN); 9781538692912 (ISBN) ; Beigi, S ; Gohari, A ; Yassaee, M. H ; Aref, M. R ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2019
Abstract
In this paper, a new measure of correlation is introduced. This measure depends on a parameter α, and is defined in terms of vector-valued Lp norms. The measure is within a constant of the exponential of α-Rényi mutual information, and reduces to the trace norm (total variation distance) for α = 1. We provide some properties and applications of this measure of correlation. In particular, we establish a bound on the secrecy exponent of the wiretap channel (under the total variation metric) in terms of the α-Rényi mutual information according to Csiszár's proposal. © 2019 IEEE