IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Entropy Bounds for Discrete Random Varibles via Coupling

IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Tightened Exponential Bounds for Discrete Time, Conditionally Symmetric Martingales with Bounded Jumps

This letter derives some new exponential bounds for discrete time, real valued, conditionally symmetric martingales with bounded jumps. The new bounds are extended to conditionally symmetric sub/ supermartingales, and are compared to some existing bounds.

IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Improved Lower Bounds on the Total Variation Distance for the Poisson Approximation

New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is ad...

IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES On Improved Bounds for Probability Metrics and f- Divergences

Derivation of tight bounds for probability metrics and f -divergences is of interest in information theory and statistics. This paper provides elementary proofs that lead, in some cases, to significant improvements over existing bounds; they also lead to the derivation of some existing bounds in a simplified way. The inequalities derived in this paper relate between the Bhattacharyya parameter,...

IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Erasure/List Random Coding Error Exponents Are Not Universally Achievable

IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES An Information-Theoretic Perspective of the Poisson Approximation via the Chen- Stein Method

The first part of this work considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of a Poisson random variable with the same mean are derived via the Chen-Stein method. The second part of this work derives new lower bounds on the total variat...