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Sufficient and necessary conditions for reliable lossless communication of two correlated sources over classes of phase asynchronous cognitive interference channels are derived. Namely, the authors consider interference channels in which one of the encoders, i.e., the secondary or cognitive user, is causally or non-causally aware of the other's message. Moreover, as a practical constraint, they assume the transmitters are not aware of the phase shifts introduced by channels. They show that, for both classes of causal and non-causal cooperation, under strong interference conditions, separate source and channel coding is optimal for reliable communication of both users.
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