Phase asynchronous cognitive interference channels: Lossless source-channel separation theorems

Sufficient and necessary conditions for reliable lossless communication of two correlated sources over classes of phase asynchronous cognitive interference channels are derived. Namely, we 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, we assume the transmitters are not aware of the phase shifts introduced by channels. We show that, for both classes of causal and noncausal cooperation, under strong interference conditions, separate source and channel coding is optimal for reliable communication of both users. Also, we derive necessary and sufficient conditions for reliable communication of the cognitive radio transmission while the primary is able to maintain the same information rate it could reliably send in the absence of the secondary. To the best of our knowledge, this is the first work to find fundamental limits of lossless reliable communication for cognitive interference channels.