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

许多常见的通信情况都是在固有的双向通道上进行的，例如电话系统、数字用户线路（DSL）、蜂窝网络和Internet。事实上，即使是“点对点”系统，其最终目标是在一个方向上传递信息，也经常由于反馈的存在而产生双向通信场景。在这样的系统中，一个人可以从信道的另一端接收反馈，这可以用来提高通信质量。虽然反馈存在于许多通信系统中，并以某些原始形式用于信道估计和自动重复请求，但其使用背后的理论还远远不够完整。本研究探讨了反馈在双向通信网络中的作用，并为设计健壮和高效的通信系统提供了架构级指导。虽然积极的结果导致通信系统设计的新方法，但消极的结果防止过度工程，并允许对简单和模块化实施更有信心。同时，反馈是生物和人工控制系统、学习机和通信网络中的关键概念。深入了解反馈在一个领域（沟通）中的作用，将有助于更好地了解反馈在更广泛的多学科背景下的作用。具体而言，本研究关注并开发了解决以下领域问题的新方法：1)具有内存的单用户信道的反馈能力（基于定向信息、因果条件反射和香农策略的新编码定理，以及实现基本限制的具体方案的开发），2)具有反馈的多用户信道（重点是多址信道和广播信道）。3)双向信道的容量区域，如Blackwell-Shannon二进制乘法信道（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（信道编码和网络协议跨层设计的新视角）。在许多反馈沟通问题中，梅西的定向信息代替了香农的互信息。因此，定向信息作为一般因果推理问题中的一个基本概念被研究。例子包括在赛马市场的赌博与因果侧信息及其在源编码中的对偶。

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.