  We are interested in how to best communicate a (usually real valued) source
to a number of destinations (sinks) over a network with capacity constraints in
a collective fidelity metric over all the sinks, a problem which we call joint
network-source coding. Unlike the lossless network coding problem, lossy
reconstruction of the source at the sinks is permitted. We make a first attempt
to characterize the set of all distortions achievable by a set of sinks in a
given network. While the entire region of all achievable distortions remains
largely an open problem, we find a large, non-trivial subset of it using ideas
in multiple description coding. The achievable region is derived over all
balanced multiple-description codes and over all network flows, while the
network nodes are allowed to forward and duplicate data packets.
