Efficient algorithms for fixed-rate entropy-coded vector quantization

Abstract

In quantization of any source with a nonuniform probability density function, the entropy coding of the quantizer output can result in a substantial decrease in bit rate. A straight-forward entropy coding scheme presents us with the problem of the variable data rate. A solution in a space of dimensionality N is to select a subset of elements in the N- fold cartesian product of a scalar quantizer and represent them with code-words of the same length. A reasonable rule is to select the N-fold symbols of the highest probability. For a memoryless source, this is equivalent to selecting the N-fold symbols with the lowest additive self-information. The search/addressing of this scheme can no longer be achieved independently along the one-dimensional subspaces. In the case of a memoryless source, the selected subset has a high degree of structure which can be used to substantially decrease the complexity. In this work, a dynamic programming approach is used to exploit this structure. We build our recursive structure required for the dynamic programming in a hierarchy of stages. This results in several benefits over the conventional trellis-based approaches. Using this structure, we develop efficient rules (based on aggregating the states) to substantially reduce the search/addressing complexities while keeping the degradation negligible.

This research was supported by a grant from the Canadian Institute for Telecommunications Research under the NCE program of the Government of Canada and also by a funding from INRS-Telecommunications