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\log n $ can be coded by about $[n(\log n )^2\pi^{ d/2}/(d/2)!]\,\mathcal{ H}$ bits, where $\mathcal{ H}$ is an explicitly defined entropy. In the process, we derive a joint large deviation principle (LDP) for the \emph{ empirical sensor measure} and \emph{ the empirical link measure} of coloured random geometric graph models.
Categories: cs.IT math.IT