Diversity and degrees of freedom of cooperative wireless networks

Two key parameters in the outage characterization of a wireless fading network are the diversity and the degrees of freedom (DOF). These two quantities represent the two end-points of the diversity multiplexing gain tradeoff. In this paper, we present max-flow min-cut type theorems for computing both the diversity and the DOF of arbitrary single-source single-sink networks with nodes possessing multiple antennas. We also show that an amplify-and-forward protocol is sufficient to achieve the same. The DOF characterization is obtained using a conversion to a deterministic wireless network for which the capacity was recently found. This conversion is operational in the sense that a capacity-achieving scheme for the deterministic network can be converted into a DOF-achieving scheme for the fading network. We also show that the diversity result easily extends to multi-source multi-sink networks whereas the DOF result extends to a single-source multi-cast network. Along the way, we prove that the zero error capacity of the deterministic network is the same as its isin-error capacity.