Abstract
The use of lattices as vector quantizers in still image and video compression schemes has grown increasingly in the last few years. In order to obtain a compromise between minimum distortion and bit rate, lattices have to be truncated so that the chosen lattice points, the codebook size, lie within a finite boundary. The determination of this boundary is source dependent. The geometric properties of a memoryless Laplacian source fit properly to model transform coded image statistics. In this case, the l/sub 1/ norm is more suitable than the it norm (then the classical lattice /spl Theta/ series should no longer be used). In this paper we define the contour points, which count how many lattice points are at l/sub 1/ distance m from a given lattice point; i.e., they help to establish the lattice boundary or equivalently the codebook size. Explicit combinatorial expressions for the codebook size for lattices Z/sup d/, A/sub d/, D/sub d/, D/sub d/*, D/sub d//sup +/, Construction A and Construction B are given. These expressions pave the way for algorithms for labeling lattice points that achieve full efficiency.
Published Version
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