CIF: Small: Algebraic Network Information Theory

在过去十年中，受移动视频等数据密集型应用的推动，对数据服务的需求呈指数级增长，预计未来十年将加速增长。为了满足这种需求，新的基础设施正在快速建设，从而导致更密集、更复杂的部署。与此同时，移动处理能力急剧增加，这为将更复杂的通信技术纳入开发标准打开了大门。在这种背景下，网络信息理论作为一个强大的理论框架，用于评估跨复杂网络拓扑的技术，并为实际部署设定基准。最近的研究发现了一些经典框架之外的技术实例，并利用多用户通信固有的代数结构来获得更高的性能。本计划将发展一种结合经典与现代通讯技术的代数网路资讯理论，并可作为未来资讯处理网路的基础。该项目还包括一些教育和推广活动，包括研讨会、暑期学校和教程。这个项目的目的是采取一个全面的观点，代数的信息理论技术，有效地跨网络通信。总体目标是从联合典典性和离散无记忆通道和源的可访问概念开始发展代数网络信息理论。该项目分为三个重点。第一部分概述了基于联合典型化以及代数填充和覆盖引理的统一问题陈述。第二个重点是对最佳解码极限的基本理解。最后，第三个推力旨在从基于格的代码中传输几何见解，以获得线性代码的新边界和算法。

The demand for data services has grown exponentially over the past decade, driven by data-hungry applications such as mobile video, and is forecasted to accelerate through the next decade. To keep up with this demand, new infrastructure is being built at a rapid pace, leading to denser, more complex deployments. Concurrently, mobile processing power has increased dramatically, which opens the door for the inclusion of more sophisticated communication techniques as part of developing standards. Within this context, network information theory acts as a powerful theoretical framework for assessing techniques across complex network topologies and setting benchmarks for practical deployments. Recent efforts have uncovered examples of techniques that sit outside this classical framework, and exploit the algebraic structure inherent to multi-user communication to attain higher performance. This project will develop an algebraic network information theory that unifies classical and modern communication techniques, and can serve as a foundation for future information-processing networks. The project is complemented by several educational and outreach activities, including workshops, summer schools, and tutorials.This project aims to take a comprehensive view of algebraic, information-theoretic techniques for efficient communication across networks. The overarching goal is to develop an algebraic network information theory starting from the accessible concepts of joint typicality and discrete memoryless channels and sources. The project is organized into three thrusts. The first thrust outlines a unifying problem statement based on joint typicality as well as algebraic packing and covering lemmas. The second thrust pursues a fundamental understanding of the limits of optimal decoding. Finally, the third thrust aims to transport geometric insights from lattice-based codes to obtain new bounds and algorithms for linear codes.