Noiseless Coding Theorems on New Generalized Useful Information Measure of order α and β type

Authors

  • Ashiq Hussain Bhat
  • Mirza Abdul Khalique Baig University of Kashmir

Keywords:

Shannon’s entropy, codeword length, useful information measure, Kraft inequality, Holder’s inequality, Huffman codes, Shannon-Fano codes, Noiseless coding theorem

Abstract

In this paper we define new generalized useful average code-word length  of order and type and its relationship with new generalized useful information measure of order and type has been discussed. The lower and upper bound of, in terms of are derived for a discrete noiseless channel. The measures defined in this communication are not only new but some well known measures are the particular cases of our proposed measures that already exist in the literature of useful information and coding theory. The noiseless coding theorems for discrete channel proved in this paper are verified by considering Huffman and Shannon-Fano coding schemes on taking empirical data. The important properties of  have also been studied.

References

Belis M, Guiasu S. A quantitative-qualitative Measure of Information in cybernetic System. IEEE Transaction on information theory, 1968; 14:593-594

Bhaker U.S, Hooda D.S. Mean value characterization of ‘useful’ information measure. Tamkang Journal of Mathematics, 1993; 24:283-294

Bhat A.H, Baig M.A.K. Some coding theorems on generalized Reyni’s entropy of order and type International Journal of Applied Mathematics and Information Sciences Letters, 2016; 5:1-5

Campbell L.L. A coding theorem and Renyi’s entropy. Information and control, 1965; 8:423-429

Guiasu S, Picard C.F. Borne inferieure de la longueur de certain codes. C.R Academic Sciences, Paris, 1971; 273:248-251

Gurdial, Pessoa F. On ‘useful’ Information of order Journal of Combinatorics Information and System Sciences, 1977; 2:158–162

Hartley R.V.L. Transmission of information. Bell System Technical Journal, 1928; 7: 535-563

Hooda D.S, Bhaker U.S. A generalized ‘useful’ information measure and coding theorems. Soochow Journal of Mathematics, 1997; 23:53–62

Jain P, Tuteja R.K. On coding theorem connected with ‘useful’ entropy of order International Journal of Mathematics and Mathematical Sciences, 1989; 12:193-198

Khan A.B, Bhat B.A, Pirzada S. Some results on a generalized ‘useful’ information measure. Journal of Inequalities in Pure and Applied Mathematics, 2005; 6:117

Kraft L.G. A device for quantizing grouping and coding amplitude modulates pulses. M.S Thesis, Department of Electrical Engineering, MIT, Cambridge, 1949

Longo G. A noiseless coding theorem for source having utilities. SIAM Journal of Applied Mathematics, 1976; 30:739-748

Mitter J, Mathur Y.D. Comparison of entropies of power distributions. ZAMM, 1972; 52:239-240

Nyquist H. Certain factors affecting telegraph speed. Bell System Technical Journal, 1924; 3:324-346

Nyquist H. Certain topics in telegraphy transmission theory. Journal of the American Institute of Electrical Engineers, 1928; 47:617

Renyi A. On measure of entropy and information. In: Proceeding Fourth Berkely Symposium on Mathematical Statistics and probability, University of California Press, 1961; 1:547-561

Shannon C.E. A mathematical theory of communication. Bell System Technical Journal, 1948; 27:379-423,623-659

Sharma B.D, Man Mohan, Mitter J. On measure of ‘useful’ information. Information and Control, 1978; 39:323-33.

Taneja H.C, Hooda D.S, Tuteja R.K. Coding theorems on a generalized ‘useful’ information. Soochow Journal of Mathematics, 1985; 11:123-131

Downloads

Additional Files

Published

2017-01-02

How to Cite

Bhat, A. H., & Baig, M. A. K. (2017). Noiseless Coding Theorems on New Generalized Useful Information Measure of order α and β type. Asian Journal of Fuzzy and Applied Mathematics, 4(6). Retrieved from https://www.ajouronline.com/index.php/AJFAM/article/view/4017

Issue

Vol. 4 No. 6 (2016): December 2016

Section

Articles

License

  • Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
  • It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
  • The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
  • The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
  • The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.