On universal quantization by randomized uniform/lattice quantizers

Uniform quantization with dither, or lattice quantization with dither in the vector case, followed by a universal lossless source encoder (entropy coder), is a simple procedure for universal coding with distortion of a source that may take continuously many values. The rate of this universal coding scheme is examined, and we derive a general expression for it. An upper bound for the redundancy of this scheme, deened as the diierence between its rate and the minimal possible rate, given by the rate distortion function of the source, is derived. This bound holds for all distortion levels. Furthermore, we present a composite upper bound on the redundancy as a function of the quantizer resolution which leads to a tighter bound in the high rate (low distortion) case.