Security in the context of future communication challenges and compressive sensing

本提案建议继续共同努力，应对和解决通信技术发展中的关键挑战-审查未来移动的电话和量子技术中的物理安全层，这些技术提供了无条件安全通信的前景。压缩感知是这里要利用的主要工具：事实上，在最初的两年里，很明显，压缩感知和安全的概念比最初预期的更加紧密地交织在一起，这将在提案中列出。它汇集了来自电气工程和移动的电话通信，量子信息科学和应用数学的重要专业知识;两位主要研究人员在现代信号处理和特别是压缩传感研究方面都有大量的记录。在该提案的核心是显着的数学方法发展的层次结构，结构化的问题，超越低秩和稀疏的情况下和新的双线性问题的情况下，在一个交换阅读，以及在非交换的类似物，自然出现在量子设置。从理论上讲，新的快速和内存经济的方法将成为关注的焦点。

The present proposal suggests a continuing concerted effort to tackle and resolve key challenges in the development of communication technologies - examining physical layers of security in future mobile phone and quantum technologies that offer the perspective of unconditionally secure communication. Compressed sensing is the main tool to be exploited here: In fact, in the first two years, it has become clear that notions of compressed sensing and security are even much more closely intertwined than originally anticipated, in a "dichotomy" that will be laid out in the proposal. It brings together significant expertise from electrical engineering and mobile phone communication, quantum information science, and applied mathematics collaboratively; with both principal investigators having a substantial track record in research on modern signal processing and specifically compressed sensing. At the heart of the proposal is significant mathematical method development of hierarchical structures, structured problems beyond low-rank and sparse situations and novel instances of bi-linear problems, in a commutative reading as well as in non-commutative analogs that naturally arise in the quantum settings. Algorithmically, new fast and memory-economical methods will be in the focus of attention.