  This work addresses the cooperation facilitator (CF) model, in which network
nodes coordinate through a rate limited communication device. For independent
multiple-access channel (MAC) encoders, the CF model is known to show
significant rate benefits, even when the rate of cooperation is negligible.
Specifically, the benefit in MAC sum-rate, as a function of the cooperation
rate $C_{CF}$, sometimes has an infinite slope at $C_{CF}=0$. This work studies
the question of whether cooperation through a CF can yield similar
infinite-slope benefits when applied to internal network encoders in which
dependence among MAC transmitters can be established without the help of the
CF. Towards this end, this work studies the CF model when applied to relay
nodes of a single-source, single-terminal, diamond network consisting of a
broadcast channel followed by a MAC. In the relay channel with orthogonal
receiver components, careful generalization of the
partial-decode-forward/compress-forward lower bound to the CF model yields
sufficient conditions for an infinite-slope benefit. Additional results include
derivation of a family of diamond networks for which the infinite-slope
rate-benefit derives directly from the properties of the corresponding MAC
component when studied in isolation.
