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A proof of de Bruijn identity based on generalized Price’s theorem

Author
Riba, J.; De Cabrera, F.
Type of activity
Presentation of work at congresses
Name of edition
2019 IEEE International Symposium on Information Theory
Date of publication
2019
Presentation's date
2019-07-12
Book of congress proceedings
2019 IEEE International Symposium on Information Theory: proceedings: July 7-12, 2019: La Maison de La Mutualité: Paris, France
First page
2509
Last page
2513
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
DOI
10.1109/ISIT.2019.8849368
Project funding
Grup de processament del senyal i comunicacions
Wrestling with Interference in Communications and Information Processing (TEC2016-76409-C2-1-R)
Repository
http://hdl.handle.net/2117/171742 Open in new window
URL
https://ieeexplore.ieee.org/document/8849368 Open in new window
Abstract
This paper shows that de Bruijn identity, which relates entropy with Fisher information, can be obtained as a particular case of an immediate generalization of Price’s theorem, which is a tool used in the analysis of nonlinear memoryless systems with Gaussian inputs. It is shown that, while the general Price’s theorem follows since the density of the perturbation satisfies the heat equation, the particular case of de Bruijn identity follows since the score function is zero-mean, which is the...
Citation
Riba, J.; De Cabrera, F. A proof of de Bruijn identity based on generalized Price’s theorem. A: IEEE International Symposium on Information Theory. "2019 IEEE International Symposium on Information Theory: proceedings: July 7-12, 2019: La Maison de La Mutualité: Paris, France". Institute of Electrical and Electronics Engineers (IEEE), 2019, p. 2509-2513.
Keywords
De Bruijn identity, Differential entropy, Fisher information, Kernel methods, Nonlinear signal processing, Price’s theorem, Tsallis entropy
Group of research
SPCOM - Signal Processing and Communications Group

Participants