Ergodic Fading Interference Channels: Sum-Capacity and Separability

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.