Conclusions

The wrapped spherical vector quantizer for the memoryless Gaussian source achieves distortions that are in many cases lower than other published results. The operating complexity of the quantizer grows linearly with the rate, and for moderate rates is dominated by the complexity of the nearest neighbor algorithm of the underlying lattice. This complexity is comparable or slightly less than other efficient quantization techniques such as pyramid vector quantization of the Laplacian source [14], trellis coded quantization [20], and trellis coded vector quantization [26]. We note that sphere packings other than lattices may be used to create the shape codebook. In this case, more than one type of Voronoi cell results, and an average over all the different Voronoi cells is necessary to compute the MSE of the scaled packing.

Acknowledgement: The authors thank the two reviewers for a very thorough reading of this correspondence and their helpful comments.