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Extension of de Bruijn's identity to dependent non-Gaussian noise channels

Part of: Multivariate analysis Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  21 June 2016

Nayereh Bagheri Khoolenjani  and
Mohammad Hossein Alamatsaz
Nayereh Bagheri Khoolenjani*
Affiliation:
University of Isfahan
Mohammad Hossein Alamatsaz*
Affiliation:
University of Isfahan
*
* Postal address: Department of Statistics, University of Isfahan, Isfahan, 81746-73441, Iran.
* Postal address: Department of Statistics, University of Isfahan, Isfahan, 81746-73441, Iran.
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Abstract

De Bruijn's identity relates two important concepts in information theory: Fisher information and differential entropy. Unlike the common practice in the literature, in this paper we consider general additive non-Gaussian noise channels where more realistically, the input signal and additive noise are not independently distributed. It is shown that, for general dependent signal and noise, the first derivative of the differential entropy is directly related to the conditional mean estimate of the input. Then, by using Gaussian and Farlie–Gumbel–Morgenstern copulas, special versions of the result are given in the respective case of additive normally distributed noise. The previous result on independent Gaussian noise channels is included as a special case. Illustrative examples are also provided.

Keywords

Differential entropyFisher informationGaussian copulaFarlie–Gumbel–Morgenstern copula

MSC classification

Primary: 54C70: Entropy 62H20: Measures of association (correlation, canonical correlation, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 2 , June 2016 , pp. 360 - 368
Copyright
Copyright © Applied Probability Trust 2016 

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