Chernoff - Bounds Wolfgang Mulzer

Chernoff Bounds

If m = 2, i.e., P = (p, 1 − p) and Q = (q, 1 − q), we also write DKL(p‖q). The Kullback-Leibler divergence provides a measure of distance between the distributions P and Q: it represents the expected loss of efficiency if we encode an m-letter alphabet with distribution P with a code that is optimal for distribution Q. We can now state the general form of the Chernoff Bound: Theorem 1.1. Let X1...

Five Proofs of Chernoff's Bound with Applications

We discuss five ways of proving Chernoff’s bound and show how they lead to different extensions of the basic bound.

The Number of Combinatorially Different Convex Hulls of Points in Lines ∗

Given a sequenceR of planar lines in general position, we can obtain a point set by picking exactly one point from each line in R. We provide exponential upper and lower bounds on the number of combinatorially different convex hulls for point sets that are generated in this manner.

Tolerated Tverberg Partitions: An Algorithmic Approach

Chernoff bounds on pairwise error probabilities of space-time codes

We derive Chernoff bounds on pairwise error probabilities of coherent and noncoherent space-time signaling schemes. First, general Chernoff bound expressions are derived for a correlated Ricean fading channel and correlated additive Gaussian noise. Then, we specialize the obtained results to the cases of space-timeseparable noise, white noise, and uncorrelated fading. We derive approximate Cher...