CAREER: Breaking the Barriers in Wireless Network Information Theory: A Deterministic Approach

香农的代表作《通信数学理论》（1948）是通信史上最具影响力的著作之一。在这本开创性的著作中，香农描述了在点对点信道上可靠通信的基本限制，并提供了实现它的体系结构系统设计。在过去的几十年中，将这一理论扩展到网络环境一直是信息论面临的最大挑战之一。该领域的进展有望在未来的分布式无线网络（如ad-hoc网络）设计中产生重大突破。到目前为止，大多数研究工作都是使用香农用于点对点通道的相同的通用性和准确性来解决这个问题。然而，达到这样的标准已被证明是极其困难的，在某种程度上，大多数基础网络的容量仍然未知。本研究克服了前人研究的局限性，提出了一种新的方法，该方法是基于改变焦点寻求近似解的同时保证与最优性的差距。这种方法的核心是开发简单的、确定的信道模型，这些模型捕捉无线介质的主要特征，并用于近似更复杂的模型。基于PI最近的成果，该工作开发了一个统一的框架，以利用这种强大的方法来1)近似无线网络的容量；2)研究不完全网络知识对容量的影响；3)设计对对手具有鲁棒性的协议；4)利用最新的物理层编码技术进行跨层协议设计。该项目还包括向妇女和代表性不足的少数民族提供指导和组织讲习班的重要外联方案。

Shannon's masterpiece, A Mathematical Theory of Communication (1948), is one of the most influential works in the history of communications. In this seminal work, Shannon characterized the fundamental limit for reliable communication over point-to-point channels and provided the architectural system design for achieving it. Extending this theory to network setting has been one of the greatest challenges in information theory over the past few decades. Progress in this area is expected to produce significant breakthrough in the design of distributed wireless networks of the future, such as ad-hoc networks. So far, most research efforts have approached this problem using the same generality and accuracy used by Shannon for point-to-point channels. However, meeting such a standard has proven to be extremely difficult, to the extent that the capacity of most basic networks is still unknown.This research overcomes the limitations of prior work by presenting a new approach, which is based on changing the focus to seek approximate solutions accompanied by guarantees on the gap to optimality. At the heart of this approach is the development of simple, deterministic channel models that capture the main features of the wireless medium, and are utilized to approximate more complex models. Building on recent results of the PI, the work develops a unified framework to utilize this powerful approach to 1) approximate the capacity of wireless networks; 2) study the impact of incomplete network knowledge on the capacity; 3) design protocols that are robust against adversaries; and 4) utilize recent physical layer coding techniques for cross-layer protocol design. The project also includes significant outreach program to women and under-represented minorities in the form of presenting tutorials and organizing workshops.