Theory of lattice-based fine-coarse vector quantization

The performance of a lattice-based fast vector quantization (VQ) method, which yields rate-distortion performance to that of an optimal VQ, is analyzed. The method, which is a special case of fine-coarse vector quantization (FCVQ), uses the cascade of a fine lattice quantizer and a coarse optimal VQ to encode a given source vector. The second stage is implemented in the form of a lookup table, which needs to be stored at the encoder. The arithmetic complexity of this method is essentially that of lattice VQ. Its distortion can be made arbitrarily close to that of an optimal VQ, provided sufficient storage for the table is available. It is shown that the distortion of lattice-based FCVQ is larger than that of full search quantization by an amount that decreases as the square of the diameter of the lattice cells, and it provides exact formulas for the asymptotic constant of proportionality in terms of the properties of the lattice, coarse codebook, and source density. It is shown that the excess distortion asymptotically equals that of the fine quantizer. Simulation results indicate how small the lattice cells must be in order for the asymptotic formulas to be applicable