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

CRII：CIF：低失真和有限块长度的数据压缩

• 批准号: 1566567
• 负责人: Victoria Kostina
• 金额: $ 17.5万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-05-01 至 2018-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1566567&HistoricalAwards=false
• 关键词: CRII; CIF; Data; compression; low

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.

数据压缩系统的质量是由输入和输出之间适当定义的失真测量、系统所消耗的通信量（速率）以及编码造成的延迟来衡量的。理想情况下，人们希望以尽可能低的数据速率传输，同时以良好的保真度重建，并且只遭受短延迟。这三个目标不可能同时实现；相反，存在一种基本的扭曲率-延迟权衡，任何技术都无法打破。该项目旨在推动对这一基本权衡的理解。它的智力影响融合了对空间覆盖的理论兴趣和对有损源编码的实际考虑。该项目预计将生成数学工具，以研究有效的多维空间覆盖，并提出简单有效的编码方案，为高清内容交付的进一步技术进步提供信息。提出的技术方法的关键是对高分辨率有损数据压缩的严格分析。在这种情况下，以高速率为代价，以低失真的方式压缩数据。作为许多实际数据压缩场景中最相关的机制，它也比一般情况更容易进行分析，从而产生明确的、可计算的公式，为实际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，该项目有望提供最优有限块长度权衡的近似，并提出简单的编码方案，以在诸如通用有损数据压缩、带内存的源有损数据压缩和多终端有损数据压缩等具有分析挑战性的场景中实现它们。除了计划中的研究活动外，该项目还包括课程开发、研究生指导以及向本科生和少数族裔提供服务。