Sharp Bounds on the Entropy of the Poisson Law and Related Quantities
arXiv:1001.2897 · doi:10.1109/TIT.2010.2044057
Abstract
One of the difficulties in calculating the capacity of certain Poisson channels is that H(lambda), the entropy of the Poisson distribution with mean lambda, is not available in a simple form. In this work we derive upper and lower bounds for H(lambda) 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 Harremoes and Ruzankin (2004). Bounds on the entropy of the binomial also follow easily.
To appear, IEEE Trans. Inform. Theory
References in corpus (3)
Cited by in corpus (14)
- Thinning, Entropy and the Law of Thin Numbers
- Coding Theorems for Noisy Permutation Channels
- Entropy Bounds for Discrete Random Variables via Maximal Coupling
- Squeezing-enhanced communication without a phase reference
- On Approaching the Ultimate Limits of Photon-Efficient and Bandwidth-Efficient Optical Communication
- An Information-Theoretic Perspective of the Poisson Approximation via the Chen-Stein Method
- On the Entropy of Sums of Bernoulli Random Variables via the Chen-Stein Method
- Sensing Method for Two-Target Detection in Time-Constrained Vector Poisson Channel
- Interactive Computation of Type-Threshold Functions in Collocated Broadcast-Superposition Networks
- Entropy and thinning of discrete random variables
- Bounds for some entropies and special functions
- Concavity of some entropies
- On the Shannon entropy of the number of vertices with zero in-degree in randomly oriented hypergraphs
- Sharp estimates for Gowers norms on discrete cubes