CAREER: Harnessing Interference Structure in Networks

无线网络是移动互联网的结构。高速、无处不在的无线接入日益成为从通信到商业、医疗和教育等重要应用的一项使能技术。因此，就用户数量和数据速率而言，为无线网络的可持续增长创造一条途径至关重要。这项工作面临的一个主要挑战是干扰：由于无线信道是共享介质，同时传输相互干扰。这种现象通常被理论家和实践者视为有害的，而现代无线协议的设计是为了避免干扰。在该范例中，无线信道是具有有限容量的固定资源，这意味着随着更多用户加入网络，每个用户的最大数据速率直线下降。然而，干扰信号不仅仅是额外的噪声，它们代表了来自其他用户的数据，并且具有相当大的可利用的结构。本研究追求一种基于干扰的代数结构的多用户通信的新方法。关键的见解是，接收器可以首先对所有发送的码字的线性组合进行解码，然后才在数字域中求解其所需的码字。在许多重要的网络场景中，与传统方法相比，这一强大的技术可产生显著更高的数据速率。该项目利用这项技术来揭示受干扰的规范无线网络的基本容量限制，并建立可有效接近这些限制的编码策略的体系结构原则。它利用组合优化中的现代工具来解决当该技术应用于复杂的无线网络时出现的资源分配问题，例如分布式多天线系统。更广泛地说，这项研究为解决分散信息处理、压缩和解码中的挑战性问题的代数网络信息理论奠定了基础。该项目结合了几项推广工作，包括针对高中生的蜂窝通信互动演示、教程和研讨会组织。

Wireless networks are the fabric of the mobile Internet. High-speed, ubiquitous wireless access is increasingly an enabling technology for important applications ranging from communication to commerce, medicine, and education. It is thus critical to create a pathway for sustainable wireless network growth in terms of the number of users and their data rates. A major challenge facing this effort is interference: since the wireless channel is a shared medium, simultaneous transmissions interfere with one another. This phenomenon is conventionally viewed as harmful by theorists and practitioners alike, and modern wireless protocols are designed to avoid interference. Within this paradigm, the wireless channel is a fixed resource with a finite capacity, meaning that as more users join a network, the maximum data rate per user plummets. However, interfering signals are not just additional noise; rather, they represent data from other users and possess considerable structure which can be exploited.This research pursues a novel approach to multi-user communication based on harnessing the algebraic structure of interference. The key insight is that it is possible for a receiver to first decode linear combinations of all transmitted codewords and only afterwards solve for its desired codeword in the digital domain. In many important network scenarios, this powerful technique yields significantly higher data rates compared to conventional approaches. This project leverages this technique to uncover the fundamental capacity limits of canonical wireless networks subject to interference as well as establish architectural principles for coding strategies that can efficiently approach these limits. It draws upon modern tools from combinatorial optimization to solve the resource allocation problems that emerge when this technique is applied to complex wireless networks, such as distributed multiple antenna systems. More broadly, this research lays the foundation for an algebraic network information theory to tackle challenging problems in decentralized information processing, compression, and decoding. This project incorporates several outreach efforts including interactive presentations on cellular communication for high school students, tutorials, and workshop organization.