Coding of Brownian Motion by Quantization of Exit Times

We present a concrete coding scheme for standard linear Brownian motion. The coding error under sup-norm decays like O(r(-1/2)) in the entropy r, and is thus rate-optimal. Moreover, the multiplicative constant lies below the theoretical maximum, and thus improves the known results. The scheme is based on a novel technique for quantizing the exit times of Brownian motion within a random error.