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On monotonicity and superadditivity properties of the entropy function

Published online by Cambridge University Press:  17 February 2009

S. S. Dragomir  and
C. J. Goh
S. S. Dragomir
Affiliation:
School of Communications and Informatics,Victoria University of Technology, PO Box 14428, Melbourne City MC, VIC 8001, Australia.
C. J. Goh
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, WA 6907, Australia.
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Abstract

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We apply superadditivity and monotonicity properties associated with the Jensen discrete inequality to derive relationships between the entropy function of a probability vector and a renormalized arbitrary sub-vector. The results are extended to cover other entropy measures such as joint entropy, conditional entropy and mutual information.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 4 , April 2001 , pp. 515 - 531
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Dragomir, S. S. and Goh, C. J., “A counterpart of Jensen's discrete inequality for dififerentiable convex mappings and applications in information theory” Math. Comp. Modeling 24 (1996) 1–11.Google Scholar
[2]Dragomir, S. S., Pečarić, J. and Persson, L. E., “Properties of some functionals related to Jensen's inequality “Acta Math. Hung.” 70 (1996) 129–143.Google Scholar
[3]McEliece, R. J., The theory of information and coding (Addison Wesley, Reading, 1977).Google Scholar