Multicasting in Large Wireless Networks: Bounds on the Minimum Energy Per Bit

The authors consider scaling laws for maximal energy efficiency of communicating a message to all the nodes in a 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. In addition, they also study finite size regular networks in order to understand how regularity in node placement affects energy consumption. They first establish an information-theoretic lower bound on the minimum energy per bit for multicasting in arbitrary wireless networks when the channel state information is not available at the transmitters.