Recursively indexed differential pulse code modulation

The performance of a differential pulse code modulation (DPCM) system with a recursively indexed quantizer (RIQ) under various conditions, with first order Gauss-Markov and Laplace-Markov sources as inputs, is studied. When the predictor is matched to the input, the proposed system performs at or close to the optimum entropy constrained DPCM system. If one is willing to accept a 5 percent increase in the rate, the system is very forgiving of predictor mismatch

Source coding of composite sources with segmental fidelity measures.

This dissertation develops vector quantization theory for composite source models and segmental fidelity measures. A composite source consists of a collection of modes and a switch. At a given time the switch chooses a mode, whose output becomes the composite source output, until it chooses another. Unlike homogeneous r and om processes, composite sources can easily capture the multimodality of physical sources, such as speech and raster scanned images. Segmental fidelity measures apply different weightings to the fidelity achieved on different modes, accounting for the fact that a context sensitive user's perception of distortion is different on different modes. This dissertation presents results on designing and analyzing the performance of optimum vector quantizers in three different coding scenarios involving composite sources and three segmental fidelity measures: namely, vector quantization with no mode classifier; vector quantization with a perfect classifier; and vector quantization with an imperfect mode classifier. Specifically, (1) the optimum quantization regions and vectors are found to be nearest neighbor regions and generalized centroids, respectively; (2) algorithms for designing optimum vector quantizers are developed, exploiting the above optimality conditions; (3) Bennett and Zador-like asymptotic formulas for the performance and optimum performance, respectively, are found for large rate; (4) relations between the optimum performance for a composite source and those for its modes are found; and (5) preliminary tests on speech suggest that this approach does indeed design better quantizers than traditional approaches. Also presented is a new development of high resolution quantization theory for the traditional rth power distortion measure. This new approach is more rigorous and direct than previous work. The major contributions of this dissertation are: (1) it provides a more general framework for source coding theory, in that composite sources include homogeneous r and om processes, and segmental fidelity measures include, as well as the mean squared error distortion measure, measures devised to meet the specific tastes and needs of various users; (2) it shows that a theory of waveform source coding based on composite sources and segmental fidelity measures is both tractable and useful; and (3) it develops a rigorous and direct high resolution quantization theory.Ph.D.Electrical engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/162347/1/9001688.pd

Bennett's Integral for Vector Quantizers

This paper extends Bennett's integral from scalar to vector quantizers, giving a simple formula that expresses the rth-power distortion of a many-point vector quantizer in terms of the number of points, point density function, inertial profile and the distribution of the source. The inertial profile specifies the normalized moment of inertia of quantization cells as a function of location. The extension is formulated in terms of a sequence of quantizers whose point density and inertial profile approach known functions as the number of points increases. Precise conditions are given for the convergence of distortion (suitably normalized) to Bennett's integral. Previous extensions did not include the inertial profile and, consequently, provided only bounds or applied only to quantizers with congruent cells, such as lattice and optimal quantizers. The new version of Bennett's integral provides a framework for the analysis of suboptimal structured vector quantizers. It is shown how the loss..