  Consider a multi-source network coding problem with correlated sources. While
the fundamental limits are known, achieving them, in general, involves a
computational burden due to the complex decoding process. Efficient solutions,
on the other hand, are by large based on source and network coding separation,
thus imposing strict topological constraints on the networks which can be
solved.
  In this work, we introduce a novel notion of separation of source and network
coding using G\'acs-K\"orner Common Information (CI). Unlike existing notions
of separation, the sufficient condition for this separation to hold depends on
the source structure rather than the network topology. Using the suggested
separation scheme, we tackle three important multi-source problems. The first
is the multi-source multicast. We construct efficient, zero error source codes,
and via properties of the CI completely characterize the resulting rate region.
The second is broadcast with side information. We establish a duality between
this problem and the classical problem of degraded message set broadcast, and
give two code constructions and their associated regions. Finally, we consider
the Ahlswede-Korner problem in a network, and give an efficient solution which
is tight under the CI constraints.
