We consider a problem of broadcast communication in sensor networks,
in which samples of a random field are collected at each node, and the
goal is for all nodes to obtain an estimate of the entire field within
a prescribed distortion value. The main idea we explore in this paper
is that of jointly compressing the data generated by different nodes
as this information travels over multiple hops, to eliminate correlations
in the representation of the sampled field. Our main contributions
are: (a) we obtain, using simple network flow concepts, conditions on
the rate/distortion function of the random field, so as to guarantee
that any node can obtain the measurements collected at every other node
in the network, quantized to within any prescribed distortion value;
and (b), we construct a large class of physically-motivated stochastic
models for sensor data, for which we are able to prove that the joint
rate/distortion function of all the data generated by the whole network
grows slower than the bounds found in (a). A truly novel aspect of our
work is the tight coupling between routing and source coding, explicitly
formulated in a simple and analytically tractable model---to the best
of our knowledge, this connection had not been studied before.