CAREER: Network Information Theory: Coding for Communication, Control, and Computing

尽管信息理论及其在点对点通信中的应用取得了重大进展，但管理网络上的最佳信息流的一般理论尚不存在。除了几个简单的网络模型外，由于网络中多个节点之间的竞争与合作之间的复杂权衡，一般无记忆网络的容量区域仍然未知。传感器网络、对等系统和分布式存储等现代应用进一步带来了一系列新的挑战性问题，涉及控制、估计、压缩、计算、通信和网络。该研究计划为网络上计算、控制和通信的新兴融合提供了一套通用的概念、数学和算法工具，最终目标是开发一个统一的框架来表征此类系统的基本性能限制。为了实现这一目标，我们集中讨论了代表计算、控制和通信的交集的三个具体问题--1)中继信道的容量(如何总结中继站的噪声观测：基于分布式计算的编码的列表交集技术)，2)网络控制(如何总结观测以稳定线性动力系统：用于控制的率失真编码的变种)，3)多址的冲突避免(如何从共同的随机性来源建立合作：分布式相关随机变量的生成)。新的编码方案将被提出，而经典的编码技术将被重新解释并扩展到更广泛的应用。还开发了容量区域的代数框架来检查这种编码方案的最优性。该研究方案还辅之以教育活动，其中包括为网络信息理论研究生课程开发课程和编写配套教科书。

Despite significant advances in information theory and its application to point-to-point communications, a general theory governing optimal information flow over networks does not yet exist. Except for a few simple network models, the capacity region of a general memoryless network remains unknown, due to the complex tradeoff between competition and cooperation among many nodes in the network. Modern applications such as sensor networks, peer-to-peer systems, and distributed storages further bring up a new set of challenging problems spanning control, estimation, compression, computation,communication, as well as networking. This research program provides a common set of conceptual, mathematical, and algorithmic tools for the emerging convergence of computation, control, and communication over networks, with the ultimate goal of developing a unified framework for characterizing fundamental performance limits of such systems. Towards this goal, we focus on three concrete problems representing the intersection of computation, control, and communication -- 1) the capacity of the relay channel (how to summarize the relay's noisy observation of thecodeword: a list intersection technique via coding for distributed computing), 2) networked control (how to summarize the observation to stabilize a linear dynamical system: a variant of rate distortion coding for control), 3) collision avoidance for multiple access (how to build cooperation from a common source of randomness: a distributed generation of correlated random variables). Novel coding schemes will be proposed, while classical coding techniques will be reinterpreted and extended to broader applications. An algebraic framework for capacity regions is also developed to check the optimality of such coding schemes. The research program is complemented by educational activities that include the curriculum development for a graduate course on network information theory and the writing of an accompanied textbook.