The study of certain aspects of probability with applications in communications theory

Abstract : This interim report constitutes a summary of research performed under the grant during this period. First the author presents a list of personnel involved in the research effort. In the next section the author presents a summary of research results that have been achieved. Then in the following section the author briefly comments upon the research in progress. This is followed by a list of publications supported during this grant year. Most research results are in the areas of quantization theory and detection theory. Quantization is the process by which data is reduced to a simpler, more coarse representation which is more compatible with digital processing. Loosely speaking, quantization is the heart of analog to digital conversion. It is an area which has increased in importance in the last few years due to the burgeoning advances in digital technology. The typical goal of quantization is to reduce data to a simplier representation without causing much distortion; that is, the output of a quantizer should be close to the input, with some appropriate measure of distance. Another research area in which we have recently obtained results is the area of signal detection. The detection problem is modeled as a test between two statistical hypotheses; we assume that under the null hypothesis noise alone is being observed, and under the alternate hypothesis a signal plus noise is being observed. We considered discrete time detection.