Rate distortion when side information may be absent
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Sphere-packings, lattices, and groups
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Elements of information theory
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Multiple Description Lattice Vector Quantization
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High-rate quantization and transform coding with side information at the decoder
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We consider the design of lattice vector quantizers for the problem of coding Gaussian sources with uncoded side information available only at the decoder. The design of such quantizers can be reduced to the problem of finding an appropriate sublattice of a given lattice codebook. We study the performance of the resulting quantizers in the limit as the encoding rate becomes high, and we evaluate these asymptotics for three lattices of interest: the hexagonal lattice A2 , the Gosset lattice E8 , and the Leech lattice \math . We also verify these asymptotics numerically, via computer simulations based on the lattice A2 . Surprisingly, the lattice E8 achieves the best performance of all cases considered.