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 (see IEEE Trans. Inform. Theory, vol.41, p.155, 1995). 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.