Optimal redundant index assignment for robust vector quantization: An approach to joint source -channel coding.

Abstract

This thesis deals with the redundant index assignment (IA) problem for a type of noisy channel vector quantization (VQ) system, called a robust VQ system. We are interested in finding the optimal redundant IA, which requires the optimal choice of a channel code and an assignment of its codewords to quantization cells. For a source with arbitrary distribution and dimension, an iterative IA design algorithm, called the redundant binary switching algorithm (RBSA), is proposed. RBSA gradually searches for a locally optimum IA, either by switching codewords assigned to quantization cells or by assigning a new codeword to a cell that contributes most to channel distortion. It is a generalization of BSA previously developed to solve the non-redundant IA problem. For an <italic>i.i.d.</italic> uniform source, instead of locally optimum solutions identified by RBSA, the globally optimum performance of robust VQ system is investigated. For this global optimization, it is further assumed that quantizers are uniform scalar quantizers or the products of such, and the channel codes used in the IA are binary linear codes. The globally optimum performance is found by optimizing source-channel rate allocation, binary linear code and assignment of its codewords to quantization cells, assuming joint decoders that are optimal. As an optimization result, a table that lists the best performances, together with linear codes that achieve them, for a range of channel bit error rates and transmission rates is provided. Especially, for an integer vector source produced from the product quantizer, a theory to find analytic solutions to the assignment problem is developed, which generalizes the previous work developed by Wolf and Redinbo for a scalar source. Interestingly, we show that the optimal linear assignment for the vector source can be interpreted as the cascade of a multiplexer and the optimal linear assignment found for the scalar source. Time and frequency domain analyses are also provided to examine why an optimal linear code outperforms others when the use of optimal assignments is assumed. Especially, in the frequency domain, a measure that assesses the goodness of a linear code for our robust VQ system is suggested.