The quality of data compression systems is gauged by an appropriately defined distortion measure between the input and the output, by the amount (rate) of communication expended by the system, and also by the delay due to coding. Ideally, one would like to transmit at as low data rate as possible, while reconstructing with good fidelity, and suffering only a short delay. All three goals cannot be met at the same time; rather, there exists a fundamental distortion-rate-delay trade-off, unbreachable by any technology. This project aims to advance the state of the art in the understanding of that fundamental trade-off. Its intellectual impact fuses theoretical interest in coverings of space with practical considerations of lossy source coding. The project is expected to generate mathematical tools to study efficient multidimensional coverings of space, and suggest simple and efficient coding schemes informing further technological progress in high definition content delivery.
The key to the proposed technical approach is a rigorous analysis of high resolution lossy data compression. In that regime, the data is compressed with low distortion at the expense of a high rate. The most relevant regime in many practical data compression scenarios, it also lends itself to analysis more easily than the general case, giving rise to explicit, computable formulas that provide valuable insights into the design of practical data compressors. Leveraging the simplifications afforded by the high resolution assumption, the project is expected to provide approximations to the optimal finite blocklength trade-offs and suggests simple coding schemes that achieve them in such analytically challenging scenarios as universal lossy data compression, lossy data compression of sources with memory, and multiterminal lossy data compression. In addition to the planned research activities, the project includes curricular development, graduate student mentoring, and outreach to undergraduates and under-represented minorities.
