Abstract
We study the power-versus-distortion trade-off for the transmission of a
memoryless bivariate Gaussian source over a two-to-one Gaussian multiple-access
channel with perfect causal feedback. In this problem, each of two separate
transmitters observes a different component of a memoryless bivariate Gaussian
source as well as the feedback from the channel output of the previous
time-instants. Based on the observed source sequence and the feedback, each
transmitter then describes its source component to the common receiver via an
average-power constrained Gaussian multiple-access channel. From the resulting
channel output, the receiver wishes to reconstruct both source components with
the least possible expected squared-error distortion. We study the set of
distortion pairs that can be achieved by the receiver on the two source
components.
We present sufficient conditions and necessary conditions for the
achievability of a distortion pair. These conditions are expressed in terms of
the source correlation and of the signal-to-noise ratio (SNR) of the channel.
In several cases the necessary conditions and sufficient conditions coincide.
This allows us to show that if the channel SNR is below a certain threshold,
then an uncoded transmission scheme that ignores the feedback is optimal. Thus,
below this SNR-threshold feedback is useless. We also derive the precise
high-SNR asymptotics of optimal schemes.
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