Source–Channel Communication Over Phase-Incoherent Multiuser Channels

We study the transmission of two correlated and memoryless sources (U₁, U₂) over several multiuser phase asynchronous channels. Namely, we consider a multiple access relay channel (MARC) with causal, and a MARC with non-causal unidirectional cooperation between encoders, referred to as phase-incoherent causal (respectively, non-causal) cognitive MARCs. We also consider phase-incoherent interference channel models with and without relay, in the same context. In all cases, the input signals are assumed to undergo non-ergodic phase shifts, which are unknown to the transmitters and known to the receivers as a realistic assumption. Both necessary and sufficient conditions in order to reliably send the correlated sources to the destinations are derived. In particular, for all of the channel models, by using a key lemma, we first derive an outer bound for reliable communication. Then, using separate source and channel coding and under specific gain conditions, we establish the same region as the inner bound. We thus conclude that without the knowledge of the phase shifts at transmitters, and under specific gain conditions, separation is optimal.