@inproceedings{c357510e8f354021b7f459e3f21edabf,
title = "Convexity/concavity of renyi entropy and α-mutual information",
abstract = "Entropy 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 R{\'e}nyi entropy and the Tsallis entropy. Lower bounds on the difference in the R{\'e}nyi (or Tsallis) entropy are given in terms of a new divergence which is related to the R{\'e}nyi (or Tsallis) divergence. This paper also considers a notion of generalized mutual information, namely α-mutual information, which is defined through the R{\'e}nyi 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 R{\'e}nyi entropy.",
author = "Ho, {Siu Wai} and Sergio Verd{\'u}",
year = "2015",
month = sep,
day = "28",
doi = "10.1109/ISIT.2015.7282554",
language = "English (US)",
series = "IEEE International Symposium on Information Theory - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "745--749",
booktitle = "Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015",
address = "United States",
note = "IEEE International Symposium on Information Theory, ISIT 2015 ; Conference date: 14-06-2015 Through 19-06-2015",
}