Large Deviation, Basic Information Theory for Wireless Sensor Networks
DOI : 10.3844/jmssp.2017.325.329
Journal of Mathematics and Statistics
Volume 13, Issue 4
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 πd/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.
© 2017 Kwabena Doku-Amponsah. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.