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

The article obtains large deviation asymptotic for sub-critical communication networks modeled as signal-interference-noise-ratio networks. To achieve this, we define the empirical mark measure and the empirical link measure, as well as prove joint large deviation principles(LDPs) for the two empirical measures on two different scales, i.e., $\lambda$ and $\lambda^2 a_{\lambda},$ where $\lambda$ is the intensity measure of the Poisson Point Process (PPP), which defines the SINR random network. Using the joint LDPs, we prove an Asymptotic Equipartition Property(AEP) for wireless telecommunication Networks modelled as the sub-critical SINR random networks. Further, we prove a Local Large Deviation Principle(LLDP) for the subcritical SINR random network. From the LLDPs, we prove the large deviation principle, and a classical McMillan Theorem for the stochastic SINR model processes. Note from the LLDP, for the typical empirical connectivity measure, we can deduce a bound on the cardinality of the space of SINR randomm networks. Note that, the LDPs for the empirical measures of the stochastic SINR 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.