论文标题
基于群体理论方法的泊松过程的费用延伸问题
Rate-Distortion Problems of the Poisson Process based on a Group-Theoretic Approach
论文作者
论文摘要
我们使用组理论方法研究泊松过程的率延伸问题。通过描述具有点时间或事件间（相互关系）间隔的泊松点过程的实现，并选择适当的失真度量，我们在$ \ \ \ nathbb {r}^n $中，建立了同质泊松过程的费率分数问题作为球或球体覆盖的问题。具体而言，我们研究的实现是高立方体和高效体。因此，我们将泊松过程中的三个已知率分数问题（具有不同的失真度量，但导致相同的速率函数）与laplacian-$ \ ell_1 $ rate rate-distortal问题。
We study rate-distortion problems of a Poisson process using a group theoretic approach. By describing a realization of a Poisson point process with either point timings or inter-event (inter-point) intervals and by choosing appropriate distortion measures, we establish rate-distortion problems of a homogeneous Poisson process as ball- or sphere-covering problems for realizations of the hyperoctahedral group in $\mathbb{R}^n$. Specifically, the realizations we investigate are a hypercube and a hyperoctahedron. Thereby we unify three known rate-distortion problems of a Poisson process (with different distortion measures, but resulting in the same rate-distortion function) with the Laplacian-$\ell_1$ rate-distortion problem.
