Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-28T10:44:52.815Z Has data issue: false hasContentIssue false
  • English
  • Français

Some refinements of Shannon's inequalities

Published online by Cambridge University Press:  17 February 2009

M. Matić ,
C. E. M. Pearce  and
J. Pečarić
M. Matić
Affiliation:
FESB, Mathematics Department, University of Split, R. Boškovića bb, 21000 Split, Croatia.
C. E. M. Pearce
Affiliation:
Applied Mathematics Department, University of Adelaide, Adelaide SA 5005, Australia.
J. Pečarić
Affiliation:
Applied Mathematics Department, University of Adelaide, Adelaide SA 5005, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We refine Shannon's inequality, in its discrete and integral forms, by presenting upper estimates of the difference between its two sides.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 4 , April 2002 , pp. 493 - 511
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Alencar, M. S. and Assis, F. M., “Inequalities involving the incomplete Renyi entropy, divergence and variational distance”, in Proceedings Globecom '98, Sydney (1998).Google Scholar
[2]Dragomir, S. S., “Grüss inequality in inner product spaces”, RGMIA Research Report Collection 1 (1998) 67–71.Google Scholar
[3]Dragomir, S. S. and Goh, C. J., “A counterpart of Jensen's discrete inequality for differentiable convex mappings and applications in information theory”, Math. Comput. Modelling 24 (1996) 1–11.CrossRefGoogle Scholar
[4]Matić, M., Pearce, C. E. M. and Pečarić, J., “Improvements of some bounds on entropy measures in information theory”, Math. Ineq. Appl. 1 (1998) 295–304.Google Scholar
[5]Matić, M., Pearce, C. E. M. and Pečarić, J., “On an inequality for the entropy of a probability distribution”, Acta Math. Hungarica 85 (1999) 345–349.Google Scholar
[6]Matić, M., Pearce, C. E. M. and Pečarić, J., “Refinements of some bounds in information theory”, ANZIAM J. 42 (2001) 387–399.CrossRefGoogle Scholar
[7]McEliece, R. J., The theory of information and coding (Addison-Wesley, Reading, Mass., 1977).Google Scholar
[8]Mitrinovć, D. S., Pečarić, J. E. and Fink, A. M., Classical and new inequalities in analysis (Kluwer, Dordrecht, 1993).Google Scholar
[9]Pauše, Z., Uvod u teoriju informacije (Školska Knjiga, Zagreb, 1989).Google Scholar
[10]Pečarić, J. E., Proschan, F. and Tong, Y. L., Convex functions, partial orderings, and statistical applications (Academic Press, New York, 1992).Google Scholar
[11]Rudin, W., Real and complex analysis (McGraw-Hill, London, 1970).Google Scholar