Efficient algorithms for fixed-rate entropy-coded vector quantization

In the 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 straightforward entropy coding scheme presents us with the problem of the variable data rate. A solution in a space of dimensionality N is to select of subset of elements in the N-fold cartesian product of a scaler 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. 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.<
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