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Convexity/concavity of renyi entropy and α-mutual information

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dc.contributor.authorHo, S.W.
dc.contributor.authorVerdú, S.
dc.contributor.conferenceInternational symposium on information theory (14 Jun 2015 - 19 Jun 2015 : Hong Kong)
dc.date.issued2015
dc.description.abstractEntropy is well known to be Schur concave on finite alphabets. Recently, the authors have strengthened the result by showing that for any pair of probability distributions P and Q with Q majorized by P, the entropy of Q is larger than the entropy of P by the amount of relative entropy D(P||Q). This result applies to P and Q defined on countable alphabets. This paper shows the counterpart of this result for the Rényi entropy and the Tsallis entropy. Lower bounds on the difference in the Rényi (or Tsallis) entropy are given in terms of a new divergence which is related to the Rényi (or Tsallis) divergence. This paper also considers a notion of generalized mutual information, namely α-mutual information, which is defined through the Rényi divergence. The convexity/concavity for different ranges of α is shown. A sufficient condition for the Schur concavity is discussed and upper bounds on α-mutual information are given in terms of the Rényi entropy.
dc.identifier.citationIEEE International Symposium on Information Theory - Proceedings, 2015, vol.2015-June, iss.7282554, pp.745-749
dc.identifier.doi10.1109/ISIT.2015.7282554
dc.identifier.isbn9781467377041
dc.identifier.issn2157-8095
dc.identifier.orcidHo, S.W. [0000-0002-8630-494X]
dc.identifier.urihttps://hdl.handle.net/11541.2/116258
dc.language.isoen
dc.publisherIEEE
dc.publisher.placeUS
dc.relation.ispartofseriesIEEE International Symposium on Information Theory
dc.rightsCopyright 2015 IEEE
dc.source.urihttps://doi.org/10.1109/ISIT.2015.7282554
dc.subjectentropy
dc.subjectprobability distribution
dc.subjectmutual information
dc.subjectupper bound
dc.subjectAustralia
dc.subjectelectronic mail
dc.titleConvexity/concavity of renyi entropy and α-mutual information
dc.typeConference paper
pubs.publication-statusPublished
ror.mmsid9915960511601831

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