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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.

Linked References

  1. C. E. Shannon, “A mathematical theory of communication,” Bell System Technical Journal, vol. 27, no. 4, pp. 623–656, 1948. View at Publisher · View at Google Scholar · View at Scopus
  2. A. Rényi, “On measures of entropy and information,” in Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, pp. 547–561, University of California Press, 1961. View at Google Scholar · View at MathSciNet
  3. J. Havrda and F. S. Charvát, “Quantification method of classification processes. Concept of structural α-entropy,” Kybernetika, vol. 3, pp. 30–35, 1967. View at Google Scholar · View at MathSciNet
  4. C. Tsallis, “Possible generalization of Boltzmann-Gibbs statistics,” Journal of Statistical Physics, vol. 52, no. 1-2, pp. 479–487, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. N. R. Pal and S. K. Pal, “Object-background segmentation using new definitions of entropy,” IEE Proceedings Part E Computers and Digital Techniques, vol. 136, no. 4, pp. 284–295, 1989. View at Publisher · View at Google Scholar · View at Scopus
  6. N. R. Pal and S. K. Pal, “Entropy: a new definition and its applications,” The Institute of Electrical and Electronics Engineers Systems, Man, and Cybernetics Society, vol. 21, no. 5, pp. 1260–1270, 1991. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. T. O. Kvalseth, “On exponential entropies,” in Proceedings of the IEEE International Conference on Systems, Man And Cybernatics, vol. 4, pp. 2822–2826, 2000.
  8. A. Feinstein, Foundations of Information Theory, McGraw-Hill, New York, NY, USA, 1956. View at MathSciNet
  9. L. L. Campbell, “A coding theorem and Rényi's entropy,” Information and Control, vol. 8, no. 4, pp. 423–429, 1965. View at Publisher · View at Google Scholar · View at Scopus
  10. J. C. Kieffer, “Variable-length source coding with a cost depending only on the code word length,” Information and Control, vol. 41, no. 2, pp. 136–146, 1979. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. F. Jelinek, “Buffer overflow in variable length coding of fixed rate sources,” IEEE Transactions on Information Theory, vol. 14, no. 3, pp. 490–501, 1968. View at Publisher · View at Google Scholar · View at Scopus
  12. E. F. Beckenbach and R. Bellman, Inequalities, Springer, New York, NY, USA, 1961. View at MathSciNet
  13. D. A. Huffman, “A method for the construction of minimum-redundancy codes,” Proceedings of the IRE, vol. 40, no. 9, pp. 1098–1101, 1952. View at Publisher · View at Google Scholar