Large Deviation, Basic Information Theory for Wireless Sensor Networks

In this research paper, we establish Shannon-McMillan-Breiman Theorem for Wireless Sensor Networks modelled as Coloured Geometric Random Networks. For, large n we show that a Wireless Sensor Network consisting of n sensors in [0; 1]^d linked by an expected number of edges of order n log n can be transmitted by approximately [n(log n)² π^d/2/(d/2)!] H bits, where H is an entropy defined explicitly from the parameters of the Coloured Geometric Random Network. In the process, we derive a joint Large Deviation Principle (LDP) for the empirical sensor measure and the empirical link measure of coloured random geometric network models.