Lattice quantization with side information

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 Λ₂₄. 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