  The problem of network coding with multicast of a single source to multisink
has first been studied by Ahlswede, Cai, Li and Yeung in 2000, in which they
have established the celebrated max-flow mini-cut theorem on non-physical
information flow over a network of independent channels. On the other hand, in
1980, Han has studied the case with correlated multisource and a single sink
from the viewpoint of polymatroidal functions in which a necessary and
sufficient condition has been demonstrated for reliable transmission over the
network. This paper presents an attempt to unify both cases, which leads to
establish a necessary and sufficient condition for reliable transmission over a
network multicasting correlated multisource to multisink. Here, the problem of
separation of source coding and channel coding is also discussed.
