UNIVERSITY OF CALIFORNIA, SAN DIEGO Quantization Over Noisy Channels and Bit Allocation

OF THE DISSERTATION Quantization Over Noisy Channels and Bit Allocation by Benjamin Farber Doctor of Philosophy in Electrical Engineering (Communication Theory and Systems) University of California, San Diego, 2005 Professor Kenneth Zeger, Chair In this dissertation we study two problems related to scalar quantization, namely quantization over a noisy channel and bit allocation. Scalar quantizers have been extensively studied for the case of a noiseless channel. However, their structure and performance is not well understood when operating over a noisy channel. The bit allocation problem is how to allocate a limited number of bits to a set of scalar quantizers so as to minimize the sum of their mean squared errors. We first examine scalar quantizers with uniform encoders and channel optimized decoders for uniform sources and binary symmetric channels. We calculate the point density functions and the mean squared errors for several different index assignments. We also show that the Natural Binary Code is mean squared optimal among all possible index assignments, for all bit error rates, and all quantizer transmission rates. In contrast, we find that almost all index assignments perform poorly and have degenerate