Toward a Fundamental Theory of Gaussian Source-Channel Networks

走向高斯源通道网络的基本理论

• 批准号: 355601-2013
• 负责人: Chen, Jun
• 金额: $ 2.11万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=595701
• 关键词: Toward; Fundamental; Theory; Gaussian; Source

Research over the past six decades has led to a deep understanding of the point-to-point communication problem. However, the architecture of modern communication systems typically involves networks, rather than isolated direct connections of individual sources to individual destinations. The long-term goal of this research program is to develop a similarly comprehensive understanding of complex communication networks. As an important step toward this goal, the proposed research is intended to provide a theoretical framework for characterizing fundamental performance limits of Gaussian source-channel networks (i.e., network models that consist of vector Gaussian channels with quadratic cost constraint and vector Gaussian sources with quadratic distortion measure) and the structure of associated coding schemes. This theoretical framework is envisaged to contain three major components: reduction techniques, extremal inequalities, and nonlinear methods. Specifically, reduction techniques are used to convert the given Gaussian source-channel network to an equivalent model with a statistical structure that is more amenable to analysis, then the performance limit of the equivalent model is bounded with the aid of extremal inequalities, and finally nonlinear methods are invoked to prove the tightness of the resulting bound. The proposed research will enrich the fundamentals of network information theory through the introduction of new analysis techniques and the solution of important open problems. It will also advance the understanding of complex networked systems, suggesting both specific coding schemes and broad architectural principles. The development of reduction techniques has the potential to provide a bridge between information theory and theoretical computer science. Extremal inequalities obtained through this project are of independent mathematical interest and are likely to find applications beyond information theory. On the education front, this project will provide a valuable research and learning environment for graduate students in the rapidly progressing field of network information theory, and contribute to course development and training of undergraduate students.

过去六十年的研究使人们对点对点通信问题有了深刻的理解。然而，现代通信系统的架构通常涉及网络，而不是各个源到各个目的地的隔离的直接连接。该研究项目的长期目标是对复杂的通信网络有一个类似的全面了解。作为实现这一目标的重要一步，拟议的研究旨在提供一个理论框架，用于表征高斯源-信道网络的基本性能极限（即，由具有二次成本约束的矢量高斯信道和具有二次失真度量的矢量高斯源组成的网络模型）以及相关联的编码方案的结构。这个理论框架被设想包含三个主要组成部分：减少技术，极值不等式，和非线性方法。具体来说，减少技术被用来转换给定的高斯源通道网络的等效模型与统计结构，更适合分析，然后的等效模型的性能限制是有界的援助极值不等式，最后调用非线性方法来证明所得到的界的紧密性。拟议的研究将丰富网络信息理论的基础，通过引入新的分析技术和重要的开放问题的解决方案。它还将促进对复杂网络系统的理解，提出具体的编码方案和广泛的架构原则。约简技术的发展有可能在信息论和理论计算机科学之间架起一座桥梁。通过该项目获得的极值不等式具有独立的数学兴趣，并且可能会在信息论之外找到应用。在教育方面，本计划将为研究生在迅速发展的网络信息理论领域提供一个有价值的研究和学习环境，并有助于课程开发和本科生的培养。