CIF: Small: Collaborative Research:A Reductionist View of Network Information Theory

现代社会的进步与我们的通信系统的进步日益交织在一起。从娱乐到商业，从交通到医疗保健，一切都依赖于我们高效可靠的沟通能力。随着所有这些领域的进步，通信需求也在不断增加。满足这些需求的关键是对如何建立更好的通信网络以及如何更有效地运营我们拥有的网络的不断增长和不断增长的理解。虽然我们对通信网络的一小部分了解很多，但令人惊讶的是，我们对如何更有效地运营整个网络知之甚少。本项目旨在解决这一重大而关键的目标，通过寻求揭示网络设计选择的含义，了解这些含义之间的共性和差异，并扩展有效操作这些系统所需的理论和技术，并了解其性能的限制。网络信息理论文献考虑了在各种系统模型和约束条件下通信系统的代码设计和性能限制。虽然仔细阅读文献会发现许多常见的工具和策略，但每个新问题都会产生自己的新理论。这项工作采用系统的方法来揭示隐藏的潜在共性，这些共性连接着信息理论问题的解决方案。这种方法的核心是简化论证，它推导出不同信息理论问题的解决方案之间的关系。在这种情况下，我们的框架将注意力从传统的解决示例网络转移到建立问题解决方案之间的联系。这项工作分为三个重点。第一部分考察了网络建模假设，目的是确定每个假设对网络的信息理论可解性有多大影响，提炼出对可解性影响很小或没有影响的方面，并将广泛的通信问题类别简化为其基本代表性核心。第二个重点是从单个网络特征转移到特征之间的比较，以便理解位于广泛的网络信息理论问题核心的共同的、未解决的挑战，并使用这些共性来开发问题和解决方案的分类。最后，随着前两个重点将注意力转向具有代表性的例子和共同的挑战，现有的代码设计和容量计算工具通过将其应用于新的通信场景而得到增强和扩大，其中还原论证证明了两者之间的联系。

Advances in modern society are increasingly intertwined with those of our communication systems. Everything from entertainment to business to transportation to healthcare itself relies on our ability to communicate efficiently and reliably. With progress in all of these domains come increasing communication demands. The key to meeting those demands is an ever increasing and growing understanding of how to build better communication networks and how to operate the ones that we have more effectively. While much is known about small parts of our communication networks, surprisingly little is known about how to operate the network as a whole more efficiently. This project sets out to tackle that monumental and critical goal, by seeking to uncover the implications of network design choices, understand the commonalities and differences among these implications, and expand the theory and techniques needed both to operate these systems efficiently and to understand the limits of their performance.The network information theory literature considers code design and performance limits for communication systems under a wide variety of system models and constraints. While a careful reading of the literature reveals many common tools and strategies, each new problem engenders its own new theory. This work takes a systematic approach towards uncovering the hidden underlying commonalities that connect the solutions of information theoretic problems. Central to this approach are reduction arguments that derive relationships between the solutions to different information theoretic problems. In such, our framework shifts attention from the traditional focus on solving example networks to a focus on building connections between problem solutions. The work is organized in three thrusts. The first examines network modeling assumptions with the goal of determining how much each assumption impacts the information theoretic solvability of networks, distilling out aspects that have little or no impact on solvability, and simplifying broad classes of communication problems down to their essential representative core. The second thrust moves from individual network characteristics to comparisons between characteristics in order to understand the common, unsolved challenges that lie at the heart of a wide range of network information theoretic questions and use these commonalities to develop a taxonomy of problems and solutions. Finally, as the first two thrusts steer attention towards representative examples and common challenges, existing tools for code design and capacity calculation are enhanced and amplified by applying them to new communication scenarios for which reductive arguments demonstrate a connection.