**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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