An Algorithm for Quantization of Discrete Probability Distributions

We study the problem of quantization of discrete probability distributions, arising in universal coding, as well as other applications. We show, that in many situations this problem can be reduced to the covering problem for the unit simplex, yielding precise characterization in the high-rate regime. Our main contribution is a simple and asymptotically optimal algorithm for solving this problem. Performance of this algorithm is studied and compared with several known solutions.