Lattice-based designs of direct sum codebooks for vector quantization

Abstract

Summary form only given. A direct sum codebook (DSC) has the potential to reduce both memory and computational costs of vector quantization. A DSC consists of several sets or stages of vectors. An equivalent code vector is made from the direct sum of one vector from each stage. Such a structure, with p stages containing m vectors each, has m/sup p/ equivalent code vectors, while requiring the storage of only mp vectors. DSC quantizers are not only memory efficient, they also have a naturally simple encoding algorithm, called a residual encoding. A residual encoding uses the nearest neighbor at each stage, requiring comparison with mp vectors rather than all m/sup p/ possible combinations. Unfortunately, this encoding algorithm is suboptimal because of a problem called entanglement. Entanglement occurs when a different vector from that obtained by a residual encoding is actually a better fit for the input vector. An optimal encoding can be obtained by an exhaustive search, but this sacrifices the savings in computation. Lattice-based DSC quantizers are designed to be optimal under a residual encoding by avoiding entanglement Successive stages of the codebook produce finer and finer partitions of the space, resulting in equivalent code vectors which are points in a truncated lattice. After the initial design, the codebook can be optimized for a given source, increasing performance beyond that of a simple lattice vector quantizer. Experimental results show that DSC quantizers based on cubical lattices perform as well as exhaustive search quantizers on a scalar source.