Large Deviation, Basic Information Theory for Wireless Sensor Networks

Kwabena Doku-Amponsah
2017 Journal of Mathematics and Statistics  
In this article, we prove Shannon-MacMillan-Breiman Theorem for Wireless Sensor Networks modelled as coloured geometric random graphs. For large n, we show that a Wireless Sensor Network consisting of n sensors in [0,1]^d connected by an average number of links of order n n can be coded by about [n( n )^2π^d/2/(d/2)!] H bits, where H is an explicitly defined entropy. 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 graph models.
doi:10.3844/jmssp.2017.325.329 fatcat:ihwwhp6v2ve5jl73b2q2pmrxze