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

TL;DR

This paper develops large deviation principles and information-theoretic results for sub-critical SINR random networks, providing insights into their probabilistic behavior and potential applications in anomaly detection.

Contribution

It introduces joint large deviation principles for empirical measures in SINR networks and establishes an asymptotic equipartition property and McMillan theorem for these models.

Findings

Established joint LDPs for empirical power and connectivity measures.

Proved an AEP for sub-critical SINR networks.

Derived a classical McMillan theorem for SINR process models.

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.