Lattice and trellis quantization with lattice- and trellis-bounded codebooks-High-rate theory for memoryless sources

High-rate lattice and trellis quantizers for nonuniform sources are introduced and analyzed. The performance of these quantizers is determined by two separable quantities, the granular gain and the boundary gain, which are determined by the shapes of the granular cells and of the support region, respectively. The granular gain and boundary gain are the duals of shaping and coding gain in data transmission applications. Using this duality, it is shown for Gaussian sources that the ultimate achievable boundary gain with high-rate lattice-bounded lattice codebooks is the same as the ultimate gain that can be obtained from variable-rate entropy coding. It is observed that if lattice codebooks can achieve the ultimate granular gain of 0.255 b per dimension, then lattice-bounded lattice codebooks can approach the rate-distortion limit. The performance of lattice quantizers is compared to that of optimum vector quantizers