CIF:Medium:Collaborative Research: Geometric Network Information Theory

通信网络的激增意味着其效率和安全性现在几乎影响到我们日常生活的各个方面。在社会层面，可靠和高效的网络对技术发展、国民经济增长和国防至关重要。有鉴于此，理解网络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，信息理论长期以来一直面临着一个挑战，即系统地将其成功扩展到经典的点对点信息交换之外。尽管自1948年该领域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，即使是像三节点中继信道这样的基本网络，也仍然是开放的。传统的信息理论方法量化网络的基本性能限制往往失败，因为目前的信息理论工具集是不够完善，以表征紧张局势出现在网络中，由于竞争的目标。 超越传统的方法，这个项目将研究的作用，从几何和功能分析的不平等，可以在表征信息措施之间的紧张局势。该研究项目将与强大的大学间教育计划相结合，其中包括联合和协作的学生和博士后研究人员提供咨询。

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.