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International Journal of Mathematics and Mathematical Sciences
Volume 2017, Article ID 2683293, 5 pages
https://doi.org/10.1155/2017/2683293
Research Article

A Joint Representation of Rényi’s and Tsalli’s Entropy with Application in Coding Theory

Department of Mathematics, College of Natural and Computational Science, University of Gondar, Gondar, Ethiopia

Correspondence should be addressed to Satish Kumar; moc.liamffider@47hsitasrd

Received 22 July 2017; Accepted 10 September 2017; Published 15 October 2017

Academic Editor: Hans Engler

Copyright © 2017 Litegebe Wondie and Satish Kumar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce a quantity which is called Rényi’s-Tsalli’s entropy of order and discussed some of its major properties with Shannon and other entropies in the literature. Further, we give its application in coding theory and a coding theorem analogous to the ordinary coding theorem for a noiseless channel is proved. The theorem states that the proposed entropy is the lower bound of mean code word length.