CIF: Small: Algebraic Network Information Theory

过去十年，在移动视频等数据密集型应用的推动下，对数据服务的需求呈指数级增长，预计未来十年还将加速增长。为了跟上这种需求，新的基础设施正在快速建设，这导致了更密集、更复杂的部署。与此同时，移动处理能力大幅提高，这为将更复杂的通信技术作为开发标准的一部分打开了大门。在这种背景下，网络信息理论充当了一个强大的理论框架，用于评估复杂网络拓扑中的技术并为实际部署设定基准。最近的努力揭示了位于这一经典框架之外的技术的例子，并利用多用户通信所固有的代数结构来获得更高的性能。该项目将发展一种代数网络信息理论，将古典和现代通信技术统一起来，并可作为未来信息处理网络的基础。该项目还包括几项教育和推广活动，包括讲习班、暑期学校和教程。该项目旨在全面了解代数和信息理论技术，以便在网络上进行有效的沟通。主要目标是从联合典型性和离散无记忆通道和来源的可访问概念开始，发展一种代数网络信息理论。这个项目被组织成三个项目。第一个要点概述了基于联合典型性以及代数填充和覆盖引理的统一问题陈述。第二个推动力是追求对最佳译码极限的基本理解。最后，第三个推力旨在传递基于格码的几何见解，以获得线性码的新的界和算法。

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.