Collaborative Research: The Role of Feedback in Two-Way Communication Networks

许多常见的通信情况是通过固有的双向信道，例如电话系统、数字用户线路（DSL）、蜂窝网络和因特网。 事实上，即使是最终目标是单向传递信息的“点对点”系统，由于反馈的存在，也往往产生双向通信的情况。在这样的系统中，可以从信道的另一端接收反馈，该反馈可以用于改善通信质量。 虽然反馈存在于许多通信系统中，并且以某些原始形式如在信道估计和自动重复请求中使用，但是其使用背后的理论远未完成。 本研究探讨了反馈在双向通信网络中的作用，并为设计鲁棒和高效的通信系统提供了架构级的指导。虽然积极的结果导致通信系统设计的新方法，消极的结果防止过度工程，并允许在简单和模块化的实现更有信心。 与此同时，反馈是生物和人工控制系统、学习机器和通信网络中的关键概念。更深入地理解反馈在一个领域的作用（通信）将导致更好地理解反馈在更广泛的多学科背景下的作用。具体地说，这项研究侧重于并开发新的方法来解决以下领域出现的问题：1）具有记忆的单用户信道的反馈容量（新的编码定理的基础上有向信息，因果条件，和香农战略，以及发展的具体计划，以实现基本的限制），2）具有反馈的多用户信道（强调多路存取频道和广播频道：基本极限的表征以及实际编码方案的构造），3）双向信道（如Blackwell-Shannon二进制乘法信道）的容量区域（动态规划和无限维凸优化），4）信道不确定性下的鲁棒反馈编码技术（通用解码方案），以及5）具有噪声反馈的可靠通信（关于信道码和网络协议的跨层设计的新观点）。 在许多反馈通信问题中，Massey的有向信息扮演了Shannon的互信息的角色。 因此，有向信息的作用是研究一般因果推理问题的一个基本概念。 例子包括赌博在赛马市场的因果边信息和它的双重源编码。

Many common communication situations are over inherently two-way channels, such as telephone systems, digital subscriber lines (DSL), cellular networks, and the Internet. In fact, even `point-to-point' systems, where the end goal is to transfer information in one direction, often give rise to two-way communication scenarios due to the presence of feedback. In such systems, one can receive feedback from the other end of the channel, which can be used to improve the quality of communication. Although feedback is present in many communication systems, and is being used in certain primitive forms as in channel estimation and automatic repeat request, the theory behind its use is far from complete. This research investigates the role of feedback in two-way communication networks and provides architecture-level guidance for designing robust and efficient communication systems. While positive results lead to novel approaches to communication systems design, negative results prevent over-engineering and allow more confidence in simple and modular implementations. At the same time, feedback is a pivotal concept in biological and artificial control systems, learning machines, and communication networks. A deeper understanding of the role of feedback in one area (communication) will lead to a better understanding of the role of feedback in a broader multidisciplinary context.Concretely, this research focuses on and develops new approaches for tackling problems arising in the following areas: 1) feedback capacity of single-user channels with memory (new coding theorems based on directed information, causal conditioning, and Shannon strategy, as well as the development of concrete schemes for achieving the fundamental limits), 2) multiple-user channels with feedback (emphasis on multiple access channels and broadcast channels: characterization of fundamental limits as well as the construction of practical coding schemes), 3) capacity region of the two-way channel such as the Blackwell-Shannon binary multiplying channel (dynamic programming and infinite-dimensional convex optimization), 4) robust feedback coding techniques under channel uncertainty (universal decoding schemes), and 5) reliable communication with noisy feedback (new perspectives on cross-layer design of channel codes and network protocols). Massey's directed information takes the role of Shannon's mutual information in many feedback communication problems. Thus the role of directed information is investigated as a fundamental notion in general causal inference problems. Examples include gambling in horse-race markets with causal side information and its dual in source coding.