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Lattice points enumeration for image coding

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2 Author(s)
J. Serra-Sagrista ; Dept. of Comput. Sci., Univ. Autonoma de Barcelona, Spain ; J. Borrell

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 l1 norm is more suitable than the it norm (then the classical lattice Θ series should no longer be used). In this paper we define the contour points, which count how many lattice points are at l1 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 Zd, Ad, Dd, Dd *, Dd+, Construction A and Construction B are given. These expressions pave the way for algorithms for labeling lattice points that achieve full efficiency

Published in:

Information Intelligence and Systems, 1999. Proceedings. 1999 International Conference on

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