ETH Series in Information Theory and its Applications, Vol. 4
edited by Amos Lapidoth

Stéphane Tinguely

Transmitting Correlated Sources

over Wireless Networks

1^st edition 2009. XVIII, 214 pages, € 64,00.
ISBN 978-3-86628-248-3

Abstract

This dissertation addresses the problem of transmitting correlated sources over wireless networks. More precisely, it studies the Shannon-theoretic limits in the power-versus-distortion trade-off for two elementary Gaussian scenarios: a multiple-access scenario and a broadcast scenario.

The two considered models can be described as follows. In the multiple-access case, a memoryless bivariate Gaussian source is to be transmitted over an average-power constrained Gaussian two-to-one multiple-access channel. The source is observed distributedly by the two transmitters; Transmitter 1 observes the first source component and Transmitter 2 observes the second source component. Each transmitter then describes its source component to the central receiver which wishes to reconstruct each source component subject to expected squared-error distortion. In the broadcast case, a memoryless bivariate Gaussian source is to be transmitted over an average-power constrained Gaussian one-to-two broadcast channel. The source is observed by the central transmitter and is to be reconstructed distributedly by the two receivers which both observe the same transmitted signal corrupted by different additive white Gaussian noise. From its observation, Receiver 1 wishes to estimate the first source component and Receiver 2 wishes to estimate the second source component. For both scenarios we seek to characterize the pairs of expected squared-error distortions that are simultaneously achievable on the two source components. In the multiple-access scenario the problem is additionally studied for the case with perfect feedback from the channel output to the two receivers.

The main results of this dissertation are sufficient conditions and necessary conditions for the achievability of a distortion pair expressed as a function of the channel SNR and of the source correlation. In several cases these necessary conditions and sufficient conditions are shown to agree. In particular, for each considered scenario (multiple-access, multiple-access with feedback, and broadcast) we show that if the channel SNR is below a certain threshold, then the minimal distortion pairs are achieved by an uncoded transmission scheme. In each case, the SNR-threshold is expressed as a function of the source correlation. Moreover, for the multiple-access scenarios, with feedback and without feedback, we additionally evaluate the precise high-SNR asymptotics of the optimal distortion pairs.

Keywords: wireless networks, correlated sources, joint source-channel coding, power-versus-distortion trade-off, Gaussian networks, multiple-access, broadcast, feedback, bivariate Gaussian, squared-error distortion, uncoded, high-SNR asymptotics.

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