NDLI: Mutual information and minimum mean-square error in Gaussian channels

Content Provider	IEEE Xplore Digital Library
Author	Guo, D. Shamai, S. Verdu, S.
Copyright Year	1963
Abstract	This paper deals with arbitrarily distributed finite-power input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the input-output mutual information and the minimum mean-square error (MMSE) achievable by optimal estimation of the input given the output. That is, the derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input statistics. This relationship holds for both scalar and vector signals, as well as for discrete-time and continuous-time noncausal MMSE estimation. This fundamental information-theoretic result has an unexpected consequence in continuous-time nonlinear estimation: For any input signal with finite power, the causal filtering MMSE achieved at SNR is equal to the average value of the noncausal smoothing MMSE achieved with a channel whose SNR is chosen uniformly distributed between 0 and SNR.
Sponsorship	IEEE Information Theory Society
Starting Page	1261
Ending Page	1282
Page Count	22
File Size	609162
File Format	PDF
ISSN	00189448
Volume Number	51
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-04-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Mutual information Gaussian channels Signal to noise ratio Additive noise Gaussian noise Network address translation Statistics Power filters Filtering Smoothing methods Wiener process Gaussian channel minimum mean-square error (MMSE) mutual information nonlinear filtering optimal estimation smoothing
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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