  This paper deals with the problem of multicasting a set of discrete
memoryless correlated sources (DMCS) over a cooperative relay network.
Necessary conditions with cut-set interpretation are presented. A \emph{Joint
source-Wyner-Ziv encoding/sliding window decoding} scheme is proposed, in which
decoding at each receiver is done with respect to an ordered partition of other
nodes. For each ordered partition a set of feasibility constraints is derived.
Then, utilizing the sub-modular property of the entropy function and a novel
geometrical approach, the results of different ordered partitions are
consolidated, which lead to sufficient conditions for our problem. The proposed
scheme achieves operational separation between source coding and channel
coding. It is shown that sufficient conditions are indeed necessary conditions
in two special cooperative networks, namely, Aref network and finite-field
deterministic network. Also, in Gaussian cooperative networks, it is shown that
reliable transmission of all DMCS whose Slepian-Wolf region intersects the
cut-set bound region within a constant number of bits, is feasible. In
particular, all results of the paper are specialized to obtain an achievable
rate region for cooperative relay networks which includes relay networks and
two-way relay networks.
