Working Paper Article Version 1 This version is not peer-reviewed

# Large Deviations and Information theory for Sub-Critical SINR Randon Network Models

Version 1 : Received: 11 April 2021 / Approved: 13 April 2021 / Online: 13 April 2021 (09:17:54 CEST)

How to cite: Sakyi-Yeboah, E.; Andam, P.S.; Asiedu, L.; Doku-Amponsah, K. Large Deviations and Information theory for Sub-Critical SINR Randon Network Models. Preprints 2021, 2021040331 Sakyi-Yeboah, E.; Andam, P.S.; Asiedu, L.; Doku-Amponsah, K. Large Deviations and Information theory for Sub-Critical SINR Randon Network Models. Preprints 2021, 2021040331

## Abstract

The article obtains large deviation asymptotic for sub-critical communication networks modelled as signal-interference-noise-ratio(SINR) random networks. To achieve this, we define the empirical power measure and the empirical connectivity measure, as well as prove joint large deviation principles(LDPs) for the two empirical measures on two different scales. Using the joint LDPs, we prove an Asymptotic equipartition property(AEP) for wireless telecommunication Networks modelled as the subcritical SINR random networks. Further, we prove a Local Large deviation principle(LLDP) for the sub-critical SINR random network. From the LLDPs, we prove the large deviation principle, and a classical McMillan Theorem for the stochastic SINR model processes. Note that, the LDPs for the empirical measures of this stochastic SINR random network model were derived on spaces of measures equipped with the $\tau-$ topology, and the LLDPs were deduced in the space of SINR model process without any topological limitations. We motivate the study by describing a possible anomaly detection test for SINR random networks.

## Keywords

Large deviation principle; Sub-critical SINR random network model; Poisson point process; Empirical power measure; Empirical connectivity measure; Relative entropy; Kullback action

## Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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