CRII: CIF: Data compression with low distortion and finite blocklength

数据压缩系统的质量由输入和输出之间适当定义的失真度量、由系统消耗的通信量（速率）以及由编码引起的延迟来衡量。理想情况下，人们希望以尽可能低的数据速率进行传输，同时以良好的保真度进行重建，并且仅遭受短的延迟。这三个目标不可能同时实现;相反，存在一个基本的失真率延迟权衡，任何技术都无法突破。该项目旨在推进对这一基本权衡的理解。它的智力影响融合了理论上的兴趣覆盖的空间与实际考虑的有损源编码。该项目预计将产生数学工具来研究空间的有效多维覆盖，并提出简单有效的编码方案，为高清晰度内容传输的进一步技术进步提供信息。在这种情况下，以高速率为代价以低失真压缩数据。 在许多实际的数据压缩方案中，最相关的制度，它也比一般情况下更容易分析，从而产生明确的，可计算的公式，为实际的数据压缩器的设计提供有价值的见解。利用高分辨率假设提供的简化，该项目预计将提供近似的最佳有限块长度的权衡，并建议简单的编码方案，实现他们在这样的分析具有挑战性的情况下，通用的有损数据压缩，有损数据压缩与内存的源，和多端有损数据压缩。除了计划中的研究活动外，该项目还包括课程开发、研究生辅导以及向本科生和代表性不足的少数民族开展外联活动。

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.