  The sum-capacity for specific sub-classes of ergodic fading Gaussian two-user
interference channels (IFCs) is developed under the assumption of perfect
channel state information at all transmitters and receivers. For the
sub-classes of uniformly strong (every fading state is strong) and ergodic very
strong two-sided IFCs (a mix of strong and weak fading states satisfying
specific fading averaged conditions) the optimality of completely decoding the
interference, i.e., converting the IFC to a compound multiple access channel
(C-MAC), is proved. It is also shown that this capacity-achieving scheme
requires encoding and decoding jointly across all fading states. As an
achievable scheme and also as a topic of independent interest, the capacity
region and the corresponding optimal power policies for an ergodic fading C-MAC
are developed. For the sub-class of uniformly weak IFCs (every fading state is
weak), genie-aided outer bounds are developed. The bounds are shown to be
achieved by treating interference as noise and by separable coding for
one-sided fading IFCs. Finally, for the sub-class of one-sided hybrid IFCs (a
mix of weak and strong states that do not satisfy ergodic very strong
conditions), an achievable scheme involving rate splitting and joint coding
across all fading states is developed and is shown to perform at least as well
as a separable coding scheme.
