Large deviations of probability rank

Date
2000
Advisor
Instructor
Source Title
Proceedings of the International Symposium on Information Theory, IEEE 2000
Print ISSN
2157-8095
Electronic ISSN
Publisher
IEEE
Volume
Issue
Pages
27
Language
English
Type
Conference Paper
Journal Title
Journal ISSN
Volume Title
Abstract

Consider a pair of random variables (X,Y) with distribution P. The probability rank function is defined so that G(x|y) = 1 for the most probable outcome x conditional on Y = y, G(x|y) = 2 for the second most probable outcome, and so on, resolving ties between elements with equal probabilities arbitrarily. The function G was considered in [1] in the context of finding the unknown outcome of a random experience by asking question of the form 'Is the outcome equal to x?' sequentially until the actual outcome is determined. The primary focus in [1], and the subsequent works [2], [3], was to find tight bounds on the moments E[G(X|Y)θ]. The present work is closely related to these works but focuses more directly on the large deviations properties of the probability rank function.

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Book Title
Keywords
Channel coding, Large deviations, Probability rank function, Source coding, Boundary conditions, Convergence of numerical methods, Decoding, Function evaluation, Probability density function, Probability distributions, Signal encoding, Vectors, Communication channels (information theory)
Citation
Published Version (Please cite this version)