Efficient methods for the addressing/decoding of a lattice-based fixed-rate, entropy-coded vector quantizer

In the quantization of a non-uniform source, the entropy coding of the quantizer output can result in a substantial decrease in bit rate. A straight-forward entropy coding scheme faces us with the problem of 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. For a memoryless source, a reasonable rule is to select 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-D subspaces. Fortunately, the selected subset has a high degree of structure which can be used to substantially decrease the complexity. We discuss a method based on dynamic programming to facilitate the search/addressing operations. We build our recursive structure required for the dynamic programming in a hierarchy of steps. This results in several benefits over the conventional trellis-based approaches. Using this structure, we develop efficient rules (based on merging the states) to substantially reduce the search/addressing complexities while keeping the degradation negligible. We choose the quantizer points from a lattice resulting in a higher granular gain in comparison with simply using the cartesian product of a set of scalar quantizers. We introduce a special class of lattices which have a low decoding complexity, and at the same time result in a noticeable granular gain. Examples are given of image coding.