Extension of two-stage vector quantization-lattice vector quantization

This paper is the extension of two-stage vector quantization–(spherical) lattice vector quantization (VQ–(S)LVQ) recently introduced by Pan and Fischer [1]. First, according to high resolution quantization theory, generalized vector quantization–lattice vector quantization (G-VQ–LVQ) is formulated in order to release the constraint of the spherical boundary for the second-stage lattice vector quantization (LVQ), which would provide possibilities of improving this kind of two-stage unstructured/structured quantizer by using more efficient LVQ. Second, among G-VQ–LVQ, vector quantization–pyramidal lattice vector quantization (VQ–PLVQ) is developed which is slightly superior or comparable to VQ–(S)LVQ in performance but has a much lower complexity. Simulation results show that for memoryless sources, VQ–PLVQ achieves a rate-distortion performance that is among the best of the fixed-rate quantization that we found in the literature. Therefore, VQ–PLVQ is an attractive alternative to VQ–(S)LVQ in practice. Third, transform VQ–PLVQ (TVQ–PLVQ) is proposed for sources with memory. For encoding 16-D vectors of the Gauss–Markov source, T-VQ–PLVQ has an advantage of close to 1.0 dB over VQ–PLVQ and is about 0.5 dB better than VQ–(S)LVQ.