Asymptotic performance of multiple description lattice quantizers

The high-rate squared-error distortions of a balanced multiple description lattice vector quantizer are analyzed for a memoryless source with probability density function p, differential entropy h(p) < infinity, and lattice codebook Lambda. For any a is an element of (0, 1) and rate pair (R,R), it is shown that the two-channel distortion (d) over bar (0) and the channel 1 (or channel 2) distortion (d) over bar (s) satisfy lim(R --> infinity) (d) over bar (0)2(2R(1+a)) = G(Lambda )2(2h(p))/4 and lim(R --> infinity) (d) over bar (s)2(2R(1-a)) = G(S-L)2(2h(p)), where G(Lambda) is the normalieed second moment of a Voronoi cell of the lattice Lambda and G(S-L) is the normalized second moment of a sphere in L dimensions.