CIF:Medium:Collaborative Research: Geometric Network Information Theory

通信网络的激增意味着它们的效率和安全性现在几乎影响到我们日常生活的方方面面。在社会层面上，可靠和高效的网络对技术发展、国家经济增长和国防至关重要。有鉴于此，理解联网设备的基本信息限制的问题现在比以往任何时候都更加尖锐。不幸的是，系统地将其成功扩展到经典的点对点信息交换之外，一直是信息论中的一个长期挑战。尽管该领域自1948年成立以来进行了大量的研究工作，但大多数网络设置的信息限制，甚至对于像三节点中继通道这样基本的网络，到目前为止仍然是开放的。该项目旨在改变当今信息论中分析许多网络问题的方式。量化网络基本性能极限的传统信息论方法经常失败，因为当前的信息论工具集没有足够精细地描述由于竞争目标而在网络中出现的紧张局势。除了传统的方法外，这个项目将研究几何和泛函分析中的不平等在表征信息度量之间的紧张关系方面所起的作用。该研究项目将与强大的大学间教育计划相辅相成，其中包括联合和合作的学生和博士后研究人员建议。

The proliferation of communication networks means that their efficiency and security now affects almost all aspects of our daily lives. At the societal level, reliable and efficient networks are of central importance to technological development, national economic growth and national defense. In light of this, the problem of understanding fundamental information limits of networked devices is more acute now than ever. Unfortunately, it has been a longstanding challenge in information theory to systematically extend its success beyond classical point-to-point exchanges of information. Despite significant research effort since the inception of the field in 1948, the information limits for most network settings, even for networks as fundamental as a three node relay channel, have remained open to date.This project aims to change the way many network problems are analyzed today in information theory. Traditional information-theoretic approaches for quantifying fundamental performance limits of networks often fail because the current toolset of information theory is not sufficiently refined to characterize tensions that emerge in networks due to competing objectives. Looking beyond traditional methods, this project will study the role that inequalities from geometric and functional analysis can play in characterizing tensions between information measures. The research project will be complemented with a strong inter-university education program, which includes joint and collaborative student and post-doctoral researcher advising.