This project is concerned with the theory and design of structured vector quantizers for the compression and storage of analog sources such as speech, images, video, and music. Vector quantization is a class of techniques that holds significant promise for significant gains over recent compression techniques. The difficulty with vector quantizers is the high degree of complexity involved in implementations. The focus of this project is the development of a theory of reduced complexity vector quantizers. Asymptotic quantization theory is to be further developed and used to analyze the performance of moderate to high rate structured quantizers. New methods for analyzing the performance of low rate quantizers are being studied. The fundamental limits of performance versus structure are being explored.