Multiple-Description Vector Quantization with Lattice Codebooks: Design and Analysis

The problem of designing a multiple-description vector quantizer with lattice codebook [Lambda] is considered. A general solution is given to a labeling problem which plays a crucial role in the design of such quantizers. Numerical performance results are obtained for quantizers based on the lattices [A.sub.2] and [Z.sup.i], i = 1, 2, 4, 8, that make use of this labeling algorithm. The high-rate squared-error distortions for this family of L-dimensional vector quantizers are then analyzed for a memoryless source with probability density function (pdf) p and differential entropy h(p) [is less than] [infinity]. For any a [element of] (0, 1) and rate pair (R, R), it is shown that the two-channel distortion [[bar]d.sub.0] and the channel 1 (or channel 2) distortion [[bar]d.sub.s] satisfy [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where G([Lambda]) is the normalized second moment of a Voronoi cell of the lattice [Lambda] and G ([S.sub.L]) is the normalized second moment of a sphere in L dimensions. Index Terms--Cubic lattice, hexagonal lattice, lattice quantization, multiple descriptions, quantization, source coding, vector quantization.