OPTIMIZATION OF LATTICES FOR QUANTIZATION

A training algorithm for the design of lattices for vector quantizatio n is presented, The algorithm uses a steepest descent method to adjust a generator matrix, in the search for a lattice whose Voronoi regions have minimal normalized second moment. The numerical elements of the found generator matrices are interpreted and translated into exact val ues. Experiments show that the algorithm is stable, in the sense that several independent runs reach equivalent lattices. The obtained latti ces reach as low second moments as the best preciously reported lattic es, or even lower. Specifically, we report lattices in nine and ten di mensions with normalized second moments of 0.0716 and 0.0708, respecti vely, and nonlattice tessellations in seven and nine dimensions with 0 .0727 and 0.0711, which improves on previously known values, The new n ine- and ten-dimensional lattices suggest that Conway and Sloane's con jecture on the duality between the optimal lattices for packing and qu antization might be false. A discussion of the application of lattices in vector quantizer design for various sources, uniform and nonunifor m, is included.