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