Large Deviation Principles For Empirical Measures Of Signal To Interference Noise Ratio (SINR) Graph

Abstract

We obtain a Large Deviation Principle (LDP) and Asymptotic Equipartition Property (AEP) for Critical, Super-critical and Sub-critical telecommunication network modelled as SINR random network. Given devices space D, an intensity measure _m 2 R+ is a transitional kernel Q from the space D to positive real numbers R+ and a path loss function. The study defines a Marked Poisson Point Process (MPPP). For a given MPPP and technical constant __; _ : (0;1) ! (0;1); the study defines a Marked SINR Network as a Telecommunication Network and associate it with two empirical measures; the empirical marked measure and the empirical connectivity measure on two different scales as _2a_ and _, on a topological space, where _ is the intensity measure of the PPP which defines a SINR random network. For the class of telecommunication networks, the study proves a joint LDP for the empirical measures of the telecommunication network. Using this joint LDP, the study proves Asymptotic Equipartition Property (AEP) for the stochastic telecommunication network modelled as the marked SINR network. In addition, the study proves a Local Large Deviation Principle (LLDP) and a classical McMillian Theorem for the stochastic SINR network process. Further, for a typical empirical paired measure, we deduce from local large deviation principle a bound on the cardinality of the space of marked SINR network. Note that, the LDP for the empirical measures of this stochastic SINR network modelled as Telecommunication network was derived on space of measures equipped with the _􀀀 topology, and the LLDP were deduced in the space of the SINR model process without any topological restriction. All our rate function are expressed as relative entropies of the marked SINR on the device space D.