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arXiv · 0710.5376

Broadcasting Correlated Gaussians

Shraga Bross·Amos Lapidoth·Stephan Tinguely
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Abstract

We consider 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. That is, Receiver~1 wishes to estimate the first source component and Receiver~2 wishes to estimate the second source component. 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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Shraga Bross, Amos Lapidoth, Stephan Tinguely. 2009-03-20. Broadcasting Correlated Gaussians. https://arxiv.org/abs/0710.5376

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