Multicasting in large random wireless networks: Bounds on the minimum energy per bit

We consider scaling laws for maximal energy efficiency of communicating a message to all the nodes in a random wireless network, as the number of nodes in the network becomes large. Two cases of large wireless networks are studied dense random networks and constant density (extended) random networks. We first establish an information-theoretic lower bound on the minimum energy per bit for multicasting that holds for arbitrary wireless networks when the channel state information is not available at the transmitters. These lower bounds are then evaluated for two cases of random networks. Upper bounds are also obtained by constructing a simple flooding scheme that requires no information at the receivers about the channel states or the locations and identities of the nodes. The gap between the upper and lower bounds is only a constant factor for dense random networks and differs by a poly-logarithmic factor for extended random networks. Furthermore, the proposed upper and lower bounds hold almost surely in the node locations as the number of nodes approaches infinity.