Broadcasting correlated gaussians

Shraga I. Bross; Amos Lapidoth; Stephan Tinguely

doi:10.1109/TIT.2010.2048453

Broadcasting correlated gaussians

Shraga I. Bross, Amos Lapidoth, Stephan Tinguely

Communication Engineering

Swiss Federal Institute of Technology Zurich

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

30 Scopus citations

Abstract

We study the transmission of a memoryless bivariate Gaussian source over an average-power-constrained one-to-two Gaussian broadcast channel. The transmitter observes the source and describes it to the two receivers by means of an average-power-constrained signal. Each receiver observes the transmitted signal corrupted by a different additive white Gaussian noise and wishes to estimate the source component intended for it: Receiver 1 wishes to estimate the first source component and Receiver 2 wishes to estimate the second. Our interest is in the pairs of expected squared-error distortions that are simultaneously achievable at the two receivers. We prove that an uncoded transmission scheme that sends a linear combination of the source components achieves the optimal power-versus-distortion trade-off whenever the signal-to-noise ratio is below a certain threshold. The threshold is a function of the source correlation and the distortion at the receiver with the weaker noise.

Original language	English
Article number	5484980
Pages (from-to)	3057-3068
Number of pages	12
Journal	IEEE Transactions on Information Theory
Volume	56
Issue number	7
DOIs	https://doi.org/10.1109/TIT.2010.2048453
State	Published - Jul 2010

Bibliographical note

Funding Information:
Manuscript received March 20, 2009; revised February 19, 2010. Current version published June 16, 2010. S. Tinguely was supported in part by the Swiss National Science Foundation under Grant 200021-111863/1. The material in this paper was presented in part at the 2008 IEEE International Symposium on Information Theory, Toronto, ON, CA. S. Bross is with the School of Engineering, Bar-Ilan University, Ramat Gan 52900, Israel. A. Lapidoth is with the Department of Information Technology and Electrical Engineering, ETH Zurich, 8092 Zurich, Switzerland. S. Tinguely was with the Department of Information Technology and Electrical Engineering, ETH Zurich, 8092 Zurich, Switzerland. Communicated by I. Kontoyiannis, Associate Editor for Shannon Theory. Digital Object Identifier 10.1109/TIT.2010.2048453

Funding

Manuscript received March 20, 2009; revised February 19, 2010. Current version published June 16, 2010. S. Tinguely was supported in part by the Swiss National Science Foundation under Grant 200021-111863/1. The material in this paper was presented in part at the 2008 IEEE International Symposium on Information Theory, Toronto, ON, CA. S. Bross is with the School of Engineering, Bar-Ilan University, Ramat Gan 52900, Israel. A. Lapidoth is with the Department of Information Technology and Electrical Engineering, ETH Zurich, 8092 Zurich, Switzerland. S. Tinguely was with the Department of Information Technology and Electrical Engineering, ETH Zurich, 8092 Zurich, Switzerland. Communicated by I. Kontoyiannis, Associate Editor for Shannon Theory. Digital Object Identifier 10.1109/TIT.2010.2048453

Funders	Funder number
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung	200021-111863/1

Keywords

Broadcast channel
Combined source-channel coding
Correlated sources
Gaussian broadcast channel
Gaussian sources
Lossy compression
Mean squared-error distortion
Uncoded transmission

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10.1109/TIT.2010.2048453

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title = "Broadcasting correlated gaussians",

abstract = "We study the transmission of a memoryless bivariate Gaussian source over an average-power-constrained one-to-two Gaussian broadcast channel. The transmitter observes the source and describes it to the two receivers by means of an average-power-constrained signal. Each receiver observes the transmitted signal corrupted by a different additive white Gaussian noise and wishes to estimate the source component intended for it: Receiver 1 wishes to estimate the first source component and Receiver 2 wishes to estimate the second. Our interest is in the pairs of expected squared-error distortions that are simultaneously achievable at the two receivers. We prove that an uncoded transmission scheme that sends a linear combination of the source components achieves the optimal power-versus-distortion trade-off whenever the signal-to-noise ratio is below a certain threshold. The threshold is a function of the source correlation and the distortion at the receiver with the weaker noise.",

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Broadcasting correlated gaussians

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Keywords

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