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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.
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