Towards Asymptotic Vector Quantization
Doctoral thesis, 2001
We study topics in source coding, and vector quantization (VQ) in particular. We approach VQ from two directions: a theoretical starting point based on high rate quantization theory, and a practical based on a database desription of the signal source. The goal of this thesis is to connect these viewpoints in order to provide theoretical performance predictions of source coding systems operating on real-world sources, and to improve their design. The novel approach is to use advanced parametric models, and in particular the Gaussian mixture (GM) model, to capture source statistics from a database. The model is then utilized in design and theoretical evaluation.
The above principles are applied to speech spectrum coding. A ten-dimensional linear prediction filter source is considered. As a first step, we provide a bound on the number of bits per frame needed to achieve the benchmark: a spectral distortion (SD) equal to one dB. Together, results from high rate theory for weighted quadratic error measures, an approximation of SD to be locally quadratic, and a GM model of the source yield a bound at 22 bits for memoryless VQ.
Next, memory-based VQ is considered. High rate theory is devised for recursive VQ, and unlike previous analyses, we do not assume that unquantized history is available at the decoder. With a method to extract a GM model of the conditional source pdf, a bound at 16 bits per frame for benchmark performance is obtained.
High rate theory further provides expressions for the codevector distribution of optimal memoryless and recursive vector quantizers. With a GM model, the quantizers can be materialized. To avoid exhaustive training, random codebooks generated from GM models are used. This leads to a modest 5 % increase of SD. For some applications, the search problem persists. Therefore, structured VQ is also considered. A candidate for replacing random coding is companding VQ. A study of multidimensional companding is provided.
Modeling issues are dealt with in considerable detail. In particular, we stress modification of models and model estimation algorithms to deal with bounded support source pdfs.
Gaussian mixture models
high rate quantization