Optimality and Suboptimality of Multiple-Description Vector Quantization With a Lattice Codebook

Abstract

The asymptotic analysis of multiple-description vector quantization (MDVQ) with a lattice codebook for sources with smooth probability density functions (pdfs) is considered in this correspondence. Goyal et al. (2002) observed that as the side distortion decreases and the central distortion correspondingly increases, the quantizer cells farther away from the coarse lattice points shrink in a spatially periodic pattern. In this correspondence, two special classes of index assignments are used along strategic groupings of central quantizer cells to derive a straightforward asymptotic analysis, which provides an analytical explanation for the aforementioned observation. MDVQ with a lattice codebook was shown earlier to be asymptotically optimal in high dimensions, with a curious converging property, that the side quantizers achieve the space filling advantage of an n-dimensional sphere instead of an n-dimensional optimal polytope. The analysis presented here explains this behavior readily. While central quantizer cells on a uniform lattice are asymptotically optimal in high dimensions, the present authors have shown that by using nonuniform rather than uniform central quantizer cells, the central-side distortion product in an MDSQ can be reduced by 0.4 dB at asymptotically high rate. The asymptotic analysis derived here partially unifies these previous results in the same framework, though a complete characterization is still beyond reach.