  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. This setting yields precise asymptotic characterization in the
high-rate regime. We also describe a simple and asymptotically optimal
algorithm for solving this problem. Performance of this algorithm is studied
and compared with several known solutions.
