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A two-stage vector quantization-lattice vector quantization is introduced that uses an unstructured codebook in the first stage and a lattice codebook in the second stage. Joint optimum two-stage encoding is accomplished by exhaustive search of the parent codebook of the two-stage product code. Due to the relative ease of lattice vector quantization, optimum encoding is feasible for moderate encoding rates and vector dimensions. For memoryless Gaussian and Laplacian sources, the signal-to-noise ratio performance is superior to equivalent-delay encoding results previously reported. For Gaussian sources with memory, the effectiveness of the encoding method is dependent on the feasibility of using a large enough first-stage vector quantizer codebook to exploit most of the source memory.
The encoding of vector quantization-lattice vector quantization has two concatenated mappings: quantization and enumeration encoding. Efficient enumeration encoding and decoding algorithms are developed for vector quantization-lattice vector quantization, as well as for spherical cubic and $D\sb{L}$ lattice quantization.
Two vector quantization schemes are developed for intraframe encoding of the speech line spectrum pairs. A two-stage vector quantizer-lattice vector quantizer has been modified for the weighted mean squared error distortion measure. Compared to two recently popular vector quantization encoding schemes, the vector quantization-lattice vector quantization has 2 to 3 bits/vector performance advantage over the split vector quantization, and has 1 to 3 bits/vector performance advantage over multistage vector quantization. The vector quantizer-lattice vector quantizer has a moderate computational complexity. Three trellis codes are also developed without and with linear and non-linear prediction. The trellis coded vector quantization with non-linear prediction provides line spectrum pair encoding performance similar to the split vector quantizer.
A set of hybrid transformations is derived for encoding the speech reflection coefficients using vector quantization, and offers a small encoding advantage over the commonly used arcsine transformation and the log area ratios.