Derivative of mutual information at zero SNR: The gaussian-noise case

Yihong Wu; Dongning Guo; Sergio Verdú

doi:10.1109/TIT.2011.2161752

Derivative of mutual information at zero SNR: The gaussian-noise case

Yihong Wu^*, Dongning Guo, Sergio Verdú

^*Corresponding author for this work

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Assuming additive Gaussian noise, a general sufficient condition on the input distribution is established to guarantee that the ratio of mutual information to signal-to-noise ratio (SNR) goes to one half nat as SNR vanishes. The result allows SNR-dependent input distribution and side information.

Original language	English (US)
Article number	5953516
Pages (from-to)	7307-7312
Number of pages	6
Journal	IEEE Transactions on Information Theory
Volume	57
Issue number	11
DOIs	https://doi.org/10.1109/TIT.2011.2161752
State	Published - Nov 2011

Funding

Manuscript received December 19, 2010; revised April 22, 2011; accepted June 06, 2011. Date of current version November 11, 2011. This work was supported in part by the NSF under grants CCF-0644344 and CCF-0635154. Y. Wu and S. Verdú are with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA. D. Guo is with the Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208 USA. Communicated by D. Palomar, Associate Editor for Detection and Estimation. Digital Object Identifier 10.1109/TIT.2011.2161752 1A finer Taylor series expansion is found in [5]. 2Throughout the paper, natural logarithms are adopted and information units are nats.

Keywords

Gaussian noise
low-power regime
minimum mean-square error (MMSE)
mutual information
signal-to-noise ratio (SNR)

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2011.2161752

Cite this

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title = "Derivative of mutual information at zero SNR: The gaussian-noise case",

abstract = "Assuming additive Gaussian noise, a general sufficient condition on the input distribution is established to guarantee that the ratio of mutual information to signal-to-noise ratio (SNR) goes to one half nat as SNR vanishes. The result allows SNR-dependent input distribution and side information.",

keywords = "Gaussian noise, low-power regime, minimum mean-square error (MMSE), mutual information, signal-to-noise ratio (SNR)",

author = "Yihong Wu and Dongning Guo and Sergio Verd{\'u}",

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T2 - The gaussian-noise case

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AU - Guo, Dongning

AU - Verdú, Sergio

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AB - Assuming additive Gaussian noise, a general sufficient condition on the input distribution is established to guarantee that the ratio of mutual information to signal-to-noise ratio (SNR) goes to one half nat as SNR vanishes. The result allows SNR-dependent input distribution and side information.

KW - Gaussian noise

KW - low-power regime

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KW - mutual information

KW - signal-to-noise ratio (SNR)

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Derivative of mutual information at zero SNR: The gaussian-noise case

Abstract

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Keywords

ASJC Scopus subject areas

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