Rate of convergence to Poisson law in terms of information divergence

The precise bounds on the information divergence from a binomial distribution to the accompanying Poisson law are obtained. As a corollary, an upper bound for the total variation distance between the distributions is established, which in a large range of change of the parameters of the distributions is better than those already known.

[1]  P. Hall,et al.  On the rate of Poisson convergence , 1984, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  Oliver Johnson,et al.  Entropy and the law of small numbers , 2005, IEEE Transactions on Information Theory.

[3]  P. Deheuvels,et al.  A Semigroup Approach to Poisson Approximation , 1986 .

[4]  Peter Harremoës,et al.  Binomial and Poisson distributions as maximum entropy distributions , 2001, IEEE Trans. Inf. Theory.

[5]  Thomas L. Marzetta,et al.  Capacity of a Mobile Multiple-Antenna Communication Link in Rayleigh Flat Fading , 1999, IEEE Trans. Inf. Theory.

[6]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[7]  Babak Hassibi,et al.  How much training is needed in multiple-antenna wireless links? , 2003, IEEE Trans. Inf. Theory.

[8]  Harish Viswanathan,et al.  Optimal placement of training for frequency-selective block-fading channels , 2002, IEEE Trans. Inf. Theory.

[9]  Elza Erkip,et al.  On Channel State Information in Multiple Antenna Block Fading Channels , 2000 .

[10]  E. N.,et al.  The Calculus of Finite Differences , 1934, Nature.

[11]  Ron Goldman,et al.  Poisson approximation , 2000, Proceedings Geometric Modeling and Processing 2000. Theory and Applications.

[12]  Sergio VerdÂ,et al.  Fading Channels: InformationTheoretic and Communications Aspects , 2000 .

[13]  E. L. Presman.  Approximation in Variation of the Distribution of a Sum of Independent Bernoulli Variables with a Poisson Law , 1986 .

[14]  John M. Cioffi,et al.  Block transmission over dispersive channels: transmit filter optimization and realization, and MMSE-DFE receiver performance , 1996, IEEE Trans. Inf. Theory.

[15]  Amiel Feinstein,et al.  Information and information stability of random variables and processes , 1964 .

[16]  J. Cavers.  An analysis of pilot symbol assisted modulation for Rayleigh fading channels (mobile radio) , 1991 .

[17]  Anna Scaglione,et al.  Filterbank Transceivers Optimizing Information Rate in Block Transmissions over Dispersive Channels , 1999, IEEE Trans. Inf. Theory.

[18]  Shlomo Shamai,et al.  Fading channels: How perfect need "Perfect side information" be? , 2002, IEEE Trans. Inf. Theory.

[19]  Károly Jordán.  Calculus of finite differences , 1951 .

[20]  Anna Scaglione,et al.  Redundant filterbank precoders and equalizers-part I , 1998 .

[21]  Peter Harremoës,et al.  Refinements of Pinsker's inequality , 2003, IEEE Trans. Inf. Theory.

[22]  Hikmet Sari,et al.  Transmission techniques for digital terrestrial TV broadcasting , 1995, IEEE Commun. Mag..

[23]  L. Hanzo,et al.  Adaptive multicarrier modulation: a convenient framework for time-frequency processing in wireless communications , 2000, Proceedings of the IEEE.

[24]  Georgios B. Giannakis,et al.  Optimal training and redundant precoding for block transmissions with application to wireless OFDM , 2002, IEEE Trans. Commun..

[25]  Oliver Johnson.  Convergence to the Poisson Distribution , 2004 .

[26]  R. Negi,et al.  Pilot Tone Selection For Channel Estimation In A Mobile Ofdm System * , 1998, International 1998 Conference on Consumer Electronics.

[27]  T. A. Azlarov,et al.  Refinements of Yu. V. Prokhorov's theorems on the asymptotic behavior of the binomial distribution , 1987 .

[28]  Narayan B. Mandayam,et al.  DIMACS Series in Discrete Mathematics and Theoretical Computer Science Pilot Assisted Estimation of MIMO Fading Channel Response and Achievable Data Rates , 2022 .