Though the cost of storing and transmitting information continues to decrease, such reductions seem only to stimulate demand for information and, consequently, for further developments in data compression. The first goal of this research is to advance the theory and practice of quantization as a lossy data compression methodology, for sources such as speech, images, video and music. Synchronization is a key issue in data compression systems that operate in environments where decoding may begin at an arbitrary point in the compressed stream of bits, or where the compressed stream may be corrupted by insertion, deletion or substitution errors. The second goal of this research is to develop a theory of data synchronization that takes into account the users need to know the time indices of the data, as well as its values.
The quantization theory to be developed will increase the qualitative and quantitative understanding of how the performance of lossy compression systems relates to their complexity, with the goal of enabling better systems to be designed. The methodology is largely, but not exclusively, based on high resolution theory techniques and concepts. The focus is primarily on vector quantization, both as a practical technique and as a paradigm for studying fundamental issues. Though synchronization methods have been much developed, there is no theory for the analysis and design of synchronization codes that, in addition to permitting the decoder to synchronize with the encoder, enable it to produce estimates of the time indices of the data it decodes. This research will develop such a theory. It will focus on optimizing the tradeoffs among coding efficiency (rate), resynchronization delay, and the production of timing information. The application of such methods to coding for channels with insertion, deletion and substitution errors will also be investigated.
