Large Deviation, Basic Information Theory for Wireless Sensor Networks

Journal of Mathematics and Statistics

Doku-Amponsah, Kwabena¹ 

关键词: Shannon-McMillian-Breiman Theorem;    Joint Large Deviation Principle;    Coloured Geometric Random Graph;    Empirical Sensor Measure;    Empirical Link Measure;    Wireless Sensor Networks;    Sensor Law;    Near Entropy;    Relative Entropy Sensor Graph;    Mathematics Subject Classification: 94A15;    94A24;    60F10;    05C80;   

DOI  :  10.3844/jmssp.2017.325.329

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

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.

【 授权许可】

CC BY