NDLI: Likelihood Ratios and Inference for Poisson Channels

Content Provider	IEEE Xplore Digital Library
Author	Reveillac, A.
Copyright Year	1963
Abstract	In recent years, infinite-dimensional methods have been introduced for Gaussian channel estimation. The aim of this paper is to study the application of similar methods to Poisson channels. In particular, we compute the noncausal conditional mean estimator of a Poisson channel using the likelihood ratio and the discrete Malliavin gradient. This algorithm is suitable for numerical implementation via the Monte-Carlo scheme. As an application, we provide a new proof of a very deep and remarkable formula in Information Theory obtained recently in the literature and relating the derivatives of the input-output mutual information of a general Poisson channel and the conditional mean estimator of the input regardless the distribution of the latter. The use of the aforementioned stochastic analysis techniques allows us to extend these results to more general channels such as mixed Gaussian-Poisson channels.
Sponsorship	IEEE Information Theory Society
Starting Page	6261
Ending Page	6272
Page Count	12
File Size	3150321
File Format	PDF
ISSN	00189448
Volume Number	59
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Channel estimation Mutual information Stochastic processes Noise Calculus Additives Poisson process Conditional mean estimation extended De Bruijn identities Malliavin calculus mutual information
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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