We study the power versus distortion trade-off for the distributed transmission of a memoryless bi-variate Gaussian source over a two-to-one average-power limited Gaussian multiple-access channel. In this problem, each of two separate transmitters observes a different component of a memoryless bi-variate Gaussian source. The two transmitters then describe their source component to a common receiver via an average-power constrained Gaussian multiple-access channel. From the output of the multiple-access channel, the receiver wishes to reconstruct each source component with the least possible expected squared-error distortion. Our interest is in characterizing the distortion pairs that are simultaneously achievable on the two source components.We present sufficient conditions and necessary conditions for the achievability of a distortion pair. These conditions are expressed as a function of the channel signal-to-noise ratio (SNR) and of the source correlation. 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 is optimal. We also derive the precise high-SNR asymptotics of an optimal scheme.
We study the power versus distortion trade-off for the distributed transmission of a memoryless bi-variate Gaussian source over a two-to-one average-power limited Gaussian multiple-access channel. In this problem, each of two separate transmitters observes a different component of a memoryless bi-variate Gaussian source. The two transmitters then describe their source component to a common receiver via an average-power constrained Gaussian multiple-access channel. From the output of the multiple-access channel, the receiver wishes to reconstruct each source component with the least possible expected squared-error distortion. Our interest is in characterizing the distortion pairs that are simultaneously achievable on the two source components.We present sufficient conditions and necessary conditions for the achievability of a distortion pair. These conditions are expressed as a function of the channel signal-to-noise ratio (SNR) and of the source correlation. 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 is optimal. We also derive the precise high-SNR asymptotics of an optimal scheme.
We consider a one-to-two Gaussian broadcasting problem where the transmitter observes a memoryless bi-variate Gaussian source and each receiver wishes to estimate one of the source components. The transmitter describes the source pair by means of an average-power-constrained signal and each receiver observes this signal corrupted by a different additive white Gaussian noise. From its respective observation, Receiver 1 wishes to estimate the first source component and Receiver 2 wishes to estimate the second. We seek to characterize the pairs of expected squared-error distortions that are simultaneously achievable at the two receivers.Our result is that below a certain SNR-threshold an "uncoded scheme" that sends a linear combination of the source components is optimal. We present a lower bound on this threshold in terms of the source correlation and the distortion at the receiver with weaker channel noise.
Abstract-We propose to send a Gaussian source over an average-power limited additive white Gaussian noise channel by transmitting a linear combination of the source sequence and the result of its quantization using a high dimensional Gaussian vector quantizer. We show that, irrespective of the rate of the vector quantizer (assumed to be fixed and smaller than the channel's capacity), this transmission scheme is asymptotically optimal (as the quantizer's dimension tends to infinity) under the mean squared-error fidelity criterion. This generalizes the classical result of Goblick about the optimality of scaled uncoded transmission, which corresponds to choosing the rate of the vector quantizer as zero, and the classical source-channel separation approach, which corresponds to choosing the rate of the vector quantizer arbitrarily close to the capacity of the channel.
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