Ergodic two-user interference channels: Is separability optimal?

The optimality of separable encoding and decoding over parallel channels (fading states) for ergodic fading two-user interference channels (IFCs) is studied using a one-sided IFC as a model. For an ergodic fading one-sided IFC with non-fading direct links and a fading cross-channel link, it is shown that separability can be strictly suboptimal except for the cases where all the parallel channels are of the same type, i.e., all of them are either strong but not very strong or very strong channels. A recent result on the sum-capacities of classes of ergodic strong and very strong IFCs is used to show that encoding and decoding jointly over all parallel channels is optimal when either the strong or very strong interference conditions hold on average over all channels.