NDLI: A note on Fanos inequality

Content Provider	IEEE Xplore Digital Library
Author	Xue-Bin Liang
Copyright Year	2011
Description	Author affiliation: Louisiana State University, Department of Electrical and Computer Engineering, Baton Rouge, 70803 USA (Xue-Bin Liang)
Abstract	Fanos inequality is a sharp upper bound on conditional entropy in terms of the probability of error. It plays a fundamental role in the proof of converse part in coding theorems of information theory. A standard proof of Fanos inequality as seen in textbooks is based on properties of Shannons information measures with a trick of introducing an auxiliary random variable. In this brief, it is observed that the generic ℒ1 bound on entropy can straightforwardly provide an upper bound on conditional entropy in terms of the probability of error. This generic ℒ1 bound on conditional entropy is still equally effective as the Fano bound for applications in the converse proof. Compared with the generic ℒ1 bound, Fanos inequality can be regarded as a specific bound on conditional entropy by employing the structural property of the two joint probability distributions. This viewpoint motivates us to find an identity to connect the conditional entropy and the probability of error. As a corollary, a necessary and sufficient condition for tightness of the Fano bound is also obtained.
Starting Page	1
Ending Page	3
File Size	180169
Page Count	3
File Format	PDF
ISBN	9781424498468
e-ISBN	9781424498482
e-ISBN	9781424498475
DOI	10.1109/CISS.2011.5766186
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-03-23
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	ℒ1 bound on entropy conditional entropy Calculus Fanos inequality
Content Type	Text
Resource Type	Article

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