Large deviations of probability rank
Author(s)
Date
2000Source Title
Proceedings of the International Symposium on Information Theory, IEEE 2000
Print ISSN
2157-8095
Publisher
IEEE
Pages
27
Language
English
Type
Conference PaperItem Usage Stats
174
views
views
113
downloads
downloads
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.
Keywords
Channel codingLarge 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)