Sharp Bounds on the Entropy of the Poisson Law and Related Quantities
Sharp Bounds on the Entropy of the Poisson Law and Related Quantities
复制标题
泊松定律和相关量的熵的锐界
DOI：
10.1109/tit.2010.2044057
复制
发表时间：
2010
影响因子：
2.5
通讯作者：
Yaming Yu
中科院分区：
文献类型：
--
作者：
J. Adell;A. Lekuona;Yaming Yu
计算某些泊松信道容量的困难之一在于，均值为λ的泊松分布的熵H(λ)无法以简单形式给出。在本文中，我们推导出了H(λ)的上下界，这些界渐近紧密且易于计算。此类界的推导仅涉及简单的概率和分析工具。这补充了克内斯尔（1998年）、雅凯和斯潘科夫斯基（1999年）以及弗拉若莱（1999年）的渐近展开式。同样的方法给出了二项分布和泊松分布之间相对熵D(n, p)的紧密界，从而改进了哈勒莫伊斯和鲁赞金（2004年）的工作。二项分布熵的界也很容易得出。
One of the difficulties in calculating the capacity of certain Poisson channels is that H(¿), the entropy of the Poisson distribution with mean ¿, is not available in a simple form. In this paper, we derive upper and lower bounds for H(¿) that are asymptotically tight and easy to compute. The derivation of such bounds involves only simple probabilistic and analytic tools. This complements the asymptotic expansions of Knessl (1998), Jacquet and Szpankowski (1999), and Flajolet (1999). The same method yields tight bounds on the relative entropy D(n, p) between a binomial and a Poisson, thus refining the work of Harremoe¿s and Ruzankin (2004). Bounds on the entropy of the binomial also follow easily.