CAREER: Information Transmission and Optimal Estimation: Fundamentals and Applications

通信技术是推动现代社会进步的主要动力。通信的根本问题一方面是信号的检测和估计问题，另一方面是信息的有效表示和传输问题。本研究将信息论和估计论视为一枚硬币的两面，系统地探讨了两者之间的基本关系，并研究了它们在未来有线、无线和光通信系统设计和优化中的应用。第一部分的灵感来自于与高斯和泊松信道中互信息和估计误差相关的基本公式。研究人员研究了这些公式的操作意义和推广；它们在信息不平等中的应用；以及估计在通过时变渠道有效传递信息方面的一般作用。研究的第二部分涉及为提高效率而探索越来越高维度的空间的通信系统(例如，在编码、扩频、多路复用方面)。这项研究的灵感来自于启发式结果(通过统计物理)，该结果表明线性系统的输入信号的多维渐近解耦。利用为稀疏系统发展的严密技术，研究了解耦结果的一系列猜想推广，以及与信息论中的渐近均分性质有关的大系统的自平均现象。该计划还包括培训学生进行研究，并扩大西北大学信息科学课程的范围。

Communication technology is a major driving force for advances in the modern society. The fundamental problem of communication is on one hand a problem of signal detection and estimation, and on the other a problem of efficient information representation and transmission.Regarding information theory and estimation theory as two sides of the same coin, this research systematically explores the fundamental relationship between the two theories, and studies their application to the design and optimization of future wired, wireless and optical communication systems.This research is divided into two parts. Part I is inspired by fundamental formulas which relate the mutual information and estimation errors in Gaussian and Poisson channels. The investigators study the operational meaning and generalizations of the formulas; their application to information inequalities; and the general role of estimation in efficient information transmission through time-varying channels. Part II of the research is concerned with communication systems which explore spaces of increasingly high dimensions for efficiency (e.g., in coding, spreading, multiplexing). The research is inspired by heuristic results (via statistical physics) which show that the multiple dimensions of the input signal to a linear system decouple asymptotically. Equipped with rigorous techniques developed for sparse systems, a series of conjectured generalizations of the decoupling result are studied, as well as the self-averaging phenomenon of large systems, which is related to the asymptotic equipartition property in information theory. The program also includes training students in research and broadening the scope of information science curricula at Northwestern.