Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-06T02:23:57.853Z Has data issue: false hasContentIssue false
  • English
  • Français

On a generalized entropy and a coding theorem

Published online by Cambridge University Press:  14 July 2016

Pushpa N. Rathie
Pushpa N. Rathie*
Affiliation:
Queen's University, Kingston, Ontario
Get access Rights & Permissions [Opens in a new window]

Extract

Let P= {p1,···, PN} be a finite discrete probability distribution. Then the entropy of the distribution P, introduced by Shannon [12], is defined as Throughout this paper ∑ will stand for and logarithms will be taken to the base D (D > 1).

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 1 , April 1970 , pp. 124 - 133
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Acéel, J. (1968) On different characterizations of entropies. Symp. on Probability and Information Theory. Hamilton.Google Scholar
[2] Acéel, J. (1964) Ein Eindeutigkeitssatz in der Theorie der Funktionalgleichungen und einige ihrer Anwendungen. Acta Math. Acad. Sci. Hung. 15, 355–362.Google Scholar
[3] Acéel, J. (1966) Lectures on Functional Equations and their Applications. Academic Press.Google Scholar
[4] Acéel, J. and DaróCzy, Z. (1963) Über verallgemeinerte quasilineare Mittelwerte, die mit Gewichtsfunktionen gebildet sind. Publ. Math. Debrecen. 10, 171–190.Google Scholar
[5] Beckenbach, E. F. and Bellman, R. (1965) Inequalities. Springer-Verlag.Google Scholar
[6] Campbell, L. L. (1965) A coding theorem and Rényi's entropy. Information and Control 8, 423–429.Google Scholar
[7] Campbell, L. L. (1966) Definition of entropy by means of a coding problem, Z. Wahrscheinlichkeitsth. 6, 113–118.Google Scholar
[8] DaróCzy, Z. (1963) Über die gemeinsame Charakterisierung der zu den nicht vollständigen Verteilungen gehörigen Entropien von Shannon und Rényi. Z. Wahrscheinlichkeitsth. 1, 381–388.Google Scholar
[9] Kapur, J. N. (1967) Generalized entropy of order a and type ß. Math. Seminar, Delhi, 4, 78–94.Google Scholar
[10] Rathie, P. N. (1968) Generalized entropies in coding theory. To appear in Metrika. Google Scholar
[11] Renyi, A. (1961) On measures of entropy and information. Proc. Fourth Berkeley Symp. Math. Stat. and Prob. 1, 547–561.Google Scholar
[12] Shannon, C. E. (1948) A mathematical theory of communication. Bell Syst. Tech. J. 27, 378–423 & 623–656.Google Scholar
[13] Varma, R. S. (1966) Generalizations of Rényi's entropy of order a. J. Math. Sci. Delhi 1, 34–38.Google Scholar