arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1512.08050cs.ITmath.IT
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大偏差,无线传感器网络的基本信息论

Large deviation, Basic Information Theory for Wireless Sensor Networks

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摘要:

在这篇文章中,我们证明了Shannon-MacMillan-Breiman定理的无线传感器网络建模为有色几何随机图。对于大的$n,$,我们表明,无线传感器网络组成的$n$传感器在$[0,1]^d$连接的平均数量的链接顺序$n\log n $可以编码约$[n(\log n )^2π^{d/2}/(d/2)!]\,\mathcal{H}$位,其中$\mathcal{H}$是一个明确定义的熵。在这个过程中,我们得到了一个联合大偏差原则(LDP)的\emph{empirical sensor measure}和\emph{the empirical link measure}的彩色随机几何图模型。

英文摘要:

In this article, we prove Shannon-MacMillan-Breiman Theorem for Wireless Sensor Networks modelled as coloured geometric random graphs. For large $n,$ we show that a Wireless Sensor Network consisting of $n$ sensors in $[0,1]^d$ connected by an average number of links of order $n\log n $ can be coded by about $[n(\log n )^2π^{d/2}/(d/2)!]\,\mathcal{H}$ bits, where $\mathcal{H}$ is an explicitly defined entropy. In the process, we derive a joint large deviation principle (LDP) for the \emph{empirical sensor measure} and \emph{the empirical link measure} of coloured random geometric graph models.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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