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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...
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