Degradedness Under Cooperation

We study cooperation problems in broadcast and relay networks, where the receivers do not satisfy the classical physical degradedness assumptions. New notions of degradedness, \emph{strongly less noisy} and \emph{strongly more capable} are introduced. We show that under these conditions, decode and forward (D\&F) is optimal for classes of cooperative systems with limited conference rates, thus yielding new capacity results for these systems. In particular, we derive bounds on the capacity region of a class of broadcast channels with cooperation, that are tight on part of the capacity region. It is shown that the cut-set bound is tight for classes of primitive relay and diamond channels, beyond the physically or stochastically degraded models.