Staggered lattices in multiple description quantization

We investigate using a lattice and a staggered version of it for balanced multiple description quantization at high-resolution. By letting one side quantizer use a lattice codebook, and the other side quantizer use a codebook based on the same lattice with a slight shift, the joint quantizer as the central quantizer can naturally achieve a performance improvement over the side quantizers. Application of such a structure is meaningful when the side quantizers´ distortions are of (equal) primary concern. Another immediate application of such a structure is when a refinement stage is added to further reduce the central distortion. We analyze the performance of this structure for these two applications, and then evaluate the root lattices A_n, D_n (with dimension less than 9), E₆, E₇, E₈ and their duals. The results suggest that these two applications in fact lead to different choices of lattices: while the former requires good lattices in terms of their normalized second moments of inertia, the latter appears to perform better when the staggering of lattices generates more cells by intersection of the Voronoi regions of the two lattices. These observations also suggest a suboptimal but simple multiple description quantization scheme using lattices.