Rates of convergence in adaptive universal vector quantization

Abstract

We consider the problem of adaptive universal quantization. By adaptive quantization we mean quantization for which the delay associated with encoding the jth sample in a sequence of length n is bounded for all n>j. We demonstrate the existence of an adaptive universal quantization algorithm for which any weighted sum of the rate and the expected mean square error converges almost surely and in expectation as O(√(log log n/log n)) to the corresponding weighted sum of the rate and the distortion-rate function at that rate.