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, strongly less noisy and 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.