Source Coding and Simulation

源代码和模拟

• 批准号: 0846199
• 负责人: Robert Gray
• 金额: --
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2011-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0846199&HistoricalAwards=false
• 关键词: Source; Coding; Simulation

The intimate connection between source coding (data compression,quantization) and simulation (the generation of a signal with prescribed distributions from a purely random mechanism such as coin flips) has been known for over three decades. Recent results suggest even deeper connections with potentially significant implications for the related problems of compression code design, modeling random processes for the analysis and design of signal processing and coding systems, and understanding the nature and structure of mathematical models of random processes capturing the important properties of signals arising in the real world. This research is concerned with developing precise results characterizing and applying these connections to obtain new insight, theory, and algorithms.In 1977 the performance of an optimized source coding system was shown to be bounded by the quality of a constrained simulation of the source, with equality under certain conditions. In 2008 this connection was strengthened by a precise formulation and proof of an information theoretic ``folk theorem'' stating that source coding systems performing near the Shannon optimum yield bit streams that are ``nearly coin flips'' in the rigorous sense of closeness in Ornstein's d-bar process distance. Together these results imply that source coding systems --- including digital speech, audio, image, and video communication and storage systems --- and simulation systems --- comprising stationary codings or filterings of iid bits --- are mathematically approximately equivalent systems, and hence the theory and design algorithms appropriate for one yield corresponding results for the other. This project exploits these connections to develop new theory and design algorithms for codes for compression, simulation, and modeling based on known distributions and on distributions learned from data.

信源编码（数据压缩、量化）和模拟（从一个纯粹的随机机制（如硬币翻转）中产生具有规定分布的信号）之间的密切联系已经被人们了解了三十多年。 最近的研究结果表明，甚至更深的连接与潜在的重大影响的相关问题的压缩码设计，建模随机过程的分析和设计的信号处理和编码系统，并了解的性质和结构的随机过程的数学模型捕捉的重要性质的信号出现在真实的世界。本研究关注的是开发精确的结果表征和应用这些连接，以获得新的见解，理论和算法。在1977年的性能优化的源编码系统被证明是有界的质量的一个约束模拟的来源，在一定条件下的平等。 在2008年，这种联系被一个精确的公式和一个信息理论的“民间定理”的证明所加强，该定理指出，在香农最优附近执行的信源编码系统产生的比特流在严格意义上是“几乎硬币翻转”在奥恩斯坦的d-bar过程距离的接近度。这些结果一起意味着源编码系统-包括数字语音、音频、图像和视频通信和存储系统-和仿真系统-包括iid比特的固定编码或滤波-在数学上是近似等价的系统，因此适合于一个的理论和设计算法产生对应于另一个的结果。该项目利用这些联系开发新的理论和设计算法，用于基于已知分布和从数据中学习的分布的压缩，仿真和建模代码。