Analytic variations on redundancy rates of renewal processes
Analytic variations on redundancy rates of renewal processes
复制标题
更新流程冗余率的分析变化
DOI：
10.1109/tit.2002.804115
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
W. Szpankowski
中科院分区：
文献类型：
--
作者：
P. Flajolet;W. Szpankowski
Csiszar和Shields（1996）证明了一类（平稳）更新过程的极大极小冗余为/spl Theta/(/spl radial /n)，其中n为块长度。这个有趣的结果为非参数过程族提供了一个非平凡的冗余界。本文给出了这种（非平稳）更新源的冗余率的精确估计，即2/(log2)/spl径向/((/spl pi//sup 2//6-1)n)+O（log n）。这个渐近展开式是由复解析方法导出的，包括生成函数表示、Mellin变换、奇点分析。还有鞍点估计。这项工作将自己置于分析信息论的框架内。
Csiszar and Shields (1996) proved that the minimax redundancy for a class of (stationary) renewal processes is /spl Theta/(/spl radic/n) where n is the block length. This interesting result provides a nontrivial bound on redundancy for a nonparametric family of processes. The present paper gives a precise estimate of the redundancy rate for such (nonstationary) renewal sources, namely, 2/(log2)/spl radic/((/spl pi//sup 2//6-1)n)+O(log n). This asymptotic expansion is derived by complex-analytic methods that include generating function representations, Mellin transforms, singularity analysis. and saddle-point estimates. This work places itself within the framework of analytic information theory.