Performance improvement of vector quantizer with reflection group for uniform distribution on hyperspace

Abstract

A two-stage vector quantizer (kaleidoscope vector quantizer: KVQ) using multidimensional symmetry which has a reflection group is proposed as a high-speed vector quantizer (VQ) for vectors following a uniform distribution on a hypersphere. The first-stage VQ of this method is a lattice quantizer on a hypersphere based on a reflection group and plays a central role in achieving higher dimensions and higher rates. The last-stage VQ is a full-search vector quantizer and plays the roles of repartitioning and reforming the Voronoi regions and improving the quantization properties. In this method, the code vectors are assigned only inside the first-stage Voronoi regions. In this paper, a unified-region KVQ is proposed as a method for improving the quantization characteristic in the high dimensions of KVQ. This method also assigns the code vectors of the last-stage VQ to the boundary surfaces of the Voronoi regions of the first-stage VQ. By using this method, the multiple Voronoi regions in the first-stage VQ are merged and repartitioned, and the degree of freedom in the code vector assignment is increased. Simulation tests were conducted on Gaussian vectors and showed that the quantization characteristics equivalent to the full-search VQ were obtained in the range of 16 dimensions and a rate of about 2.5 bits/sample. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(3): 26–35, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20261