Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 56, Issue 4, Pages 1852-1864Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2010.2040870
Keywords
Achievable distortion; combined source-channel coding; correlated sources; feedback; Gaussian multiple-access channel with feedback; Gaussian source; mean squared-error distortion; multiple-access channel with feedback; uncoded transmission
Funding
- Swiss National Science Foundation [200021-111863/1]
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We study the power-versus-distortion tradeoff 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 each source component 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 are shown to agree. In particular, we 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 optimal high-SNR asymptotics.
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