On entropy measures for dynamic network topologies: Limits to MANET

What are the fundamental limits on the communications potential of wireless networks? We contend that quantifying topological dynamics resulting from node movement enables one to: find the minimum overhead required by the network to maintain connectivity and, calculate the communication potential of the network. A mobility metric is proposed for the unbiased comparison of networks. This is an entropy measure based on the uncertainty of change in the topology of the network, and is referred to as topological uncertainty. Topological uncertainty determines the minimum overhead required by the network to correctly identify the topology and hence, provide node connectivity. We use topological uncertainty to derive fundamental bounds on the maximum bit rate available within a Mobile Ad-Hoc Networking environment. Our work demonstrates the potential of entropy measures to describe the complexities of node connectivity within wireless networks.