  The problem of interference management is considered in the context of a
linear interference network that is subject to long term channel fluctuations
due to shadow fading. The fading model used is one where each link in the
network is subject independently to erasure with probability p. It is assumed
that each receiver in the network is interested in one unique message, which is
made available at M transmitters. Optimal schemes from a Degrees of Freedom
(DoF) viewpoint are analyzed for the setting of no erasures, and new schemes
are proposed with better average DoF performance at higher probabilities of
erasure. Additionally, for M=1, the average per user DoF is characterized for
every value of p, and optimal message assignments are identified. For M>1, it
is first established that there is no strategy for assigning messages to
transmitters in networks that is optimal for all values of p. The optimal
cooperative zero-forcing scheme for M=2 is then identified, and shown to be
information-theoretically optimal when the size of the largest subnetwork that
contains no erased links is at most five.
