McEliece, Robert J. and Yu, Zhong (1995) An Inequality On Entropy. In: Proceedings 1995 IEEE International Symposium on Information Theory. IEEE , Piscataway, N.J., p. 329. ISBN 0-7803-2453-6 http://resolver.caltech.edu/CaltechAUTHORS:20120223-100956421
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Abstract
The entropy H(X) of a discrete random variable X of alphabet size m is always non-negative and upper-bounded by log m. In this paper, we present a theorem which gives a non-trivial lower bound for H(X). We show that for any discrete random variable X with range R={x_0,…,x_(m-1)}, if p_i=Pr{X=x_i} and p_0⩾p_1⩾…pm_(-1), then H(X)⩾(2logm)/(m-1)Σ_(i=0)^(m-1)ip_i, with equality iff (i) X is uniformly distributed, i.e., p_i=1/m for all i, or trivially (ii) p_0=1, and p i=0 for 1⩽i⩽m-1.
| Item Type: | Book Section | ||||
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| Additional Information: | © 1995 IEEE. Date of Current Version: 06 August 2002. This work was support by a Grant from Pacific Bell. | ||||
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| Record Number: | CaltechAUTHORS:20120223-100956421 | ||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20120223-100956421 | ||||
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| Official Citation: | McEliece, R.J.; Zhong Yu; , "An inequality on entropy," Information Theory, 1995. Proceedings., 1995 IEEE International Symposium on , vol., no., pp.329, 17-22 Sep 1995 doi: 10.1109/ISIT.1995.550316 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=550316&isnumber=11520 | ||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||
| ID Code: | 29436 | ||||
| Collection: | CaltechAUTHORS | ||||
| Deposited By: | Ruth Sustaita | ||||
| Deposited On: | 23 Feb 2012 18:49 | ||||
| Last Modified: | 23 Feb 2012 18:49 |
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