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

TL;DR

This paper derives bounds on the minimum energy per bit for multicasting in large wireless networks, analyzing dense, extended, and regular networks to understand energy efficiency limits as network size grows.

Contribution

It establishes tight information-theoretic bounds on energy per bit for multicasting without channel state information, using simple flooding schemes for upper bounds.

Findings

Bounds are tight within a constant factor for dense and regular networks.

Bounds differ by a poly-logarithmic factor for extended networks.

Results hold almost surely as the number of nodes approaches infinity.

Abstract

We 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, we also study finite size regular networks in order to understand how regularity in node placement affects energy consumption. We 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. Upper bounds are 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 regular networks, and differs by a poly-logarithmic factor for extended random networks. Furthermore, we show that the proposed upper and lower bounds for random networks hold almost surely in the node locations as the number of nodes approaches infinity.