  We characterize the capacity region of noiseless X-Channels with intermittent
connectivity and delayed channel state information at the transmitters. We
consider the general case in which each transmitter has a common message for
both receivers, and a private message for each one of them. We develop a new
set of outer-bounds that quantify the interference alignment capability of each
transmitter with delayed channel state feedback and when each receiver must
receive a baseline entropy corresponding to the common message. We also develop
a transmission strategy that achieves the outer-bounds under homogeneous
channel assumption by opportunistically treating the X-Channel as a combination
of a number of well-known problems such as the interference channel and the
multicast channel. The capacity-achieving strategies of these sub-problems must
be interleaved and carried on simultaneously in certain regimes in order to
achieve the X-Channel outer-bounds. We also extend the outer-bounds to include
non-homogeneous channel parameters.
