超临界通信网络的大偏差Sharron-McMillan-Breiman定理
Large Deviations, Sharron-McMillan-Breiman Theorem for Super-Critical Telecommunication Networks
摘要：
在这篇文章中，我们得到了大偏差渐近的超临界通信网络建模为信号干扰噪声比网络。为此，我们定义了经验功率测度和经验连接测度，并证明了两个经验测度在两个不同尺度上的联合大偏差原理，即$λ$和$λ^2 a_λ,$，其中$λ$是泊松点过程（PPP）的强度测度利用这个联合线性分布图，我们证明了随机通信网络的渐近均分性质被建模为SINR网络。此外，我们证明了一个局部大偏差原则（LLDP）的SINR网络。从LLDP出发，我们证明了随机SNIR网络过程的一个大偏差原理和一个经典的MacMillian定理。注意，对于随机经验连通性度量$qπ\otimesπ,$，我们可以从LLDP中推导出SINR网络空间的基数上的界限，该界限近似等于$\displaystyle e^{λ^2 a_λ\|qπ\otimesπ\|H\big(qπ\otimesπ/\|qπ\otimesπ\|\big)},$，其中网络的连通性概率$Q^{z^λ} ,$满足$ a_λ^{-1}Q^{z^λ} \to q.$。观察，随机SINR网络的经验度量的LDP是在配备有$τ-$拓扑的度量空间上获得的，LLDPs是在SINR网络过程的空间中得到的，没有任何拓扑限制。
英文摘要：
In this article we obtain large deviation asymptotics for supercritical communication networks modelled as signal-interference-noise ratio networks. To do this, we define the empirical power measure and the empirical connectivity measure, and prove joint large deviation principles(LDPs) for the two empirical measures on two different scales i.e. $λ$ and $λ^2 a_λ,$ where $λ$ is the intensity measure of the poisson point process (PPP) which defines the SINR random network.Using this joint LDPs we prove an asymptotic equipartition property for the stochastic telecommunication Networks modelled as the SINR networks. Further, we prove a Local large deviation principle(LLDP) for the SINR Network. From the LLDP we prove the a large deviation principle, and a classical MacMillian Theorem for the stochastic SNIR network processes. Note, for tupical empirical connectivity measure, $qπ\otimesπ,$ we can deduce from the LLDP a bound on the cardinality of the space of SINR networks to be approximately equal to $\displaystyle e^{λ^2 a_λ\|qπ\otimesπ\|H\big(qπ\otimesπ/\|qπ\otimesπ\|\big)},$ where the connectivity probability of the network, $Q^{z^λ} ,$ satisfies $ a_λ^{-1}Q^{z^λ} \to q.$ Observe, the LDP for the empirical measures of the stochastic SINR network were obtained on spaces of measures equipped with the $τ-$ topology, and the LLDPs were obtained in the space of SINR network process without any topological restrictions.
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