CAREER: Coding Subspaces: Error Correction, Compression and Applications

职业：编码子空间：纠错、压缩和应用

基本信息

批准号：
1941633
负责人：
Hessam Mahdavifar
金额：
$ 64.84万
依托单位：
Regents of the University of Michigan - Ann Arbor
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-05-01 至 2024-02-29
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1941633&HistoricalAwards=false
关键词：
CAREER Coding Subspaces Error Correction

项目摘要

In today’s technological world, an enormous amount of data is being constantly generated, transmitted, received, processed, and stored at an unprecedented scale. The classical approach of representing data as blocks of information bits falls short of addressing diverse requirements, including scalability, efficiency, and reliability, of the next generation storage, computation, and communication systems. This project develops an alternative paradigm for transmission of data across massively connected wireless networks by proposing methods to embed the information into mathematical constructs called subspaces (i.e., linear-algebraic objects in a vector space), via a technique called subspace coding. While these structures capture the essence of gathered data in a wide range of signal processing applications, fundamental limits of compression as well as practical and universal techniques to attain these limits are not understood. This project characterizes a natural duality between error correction and compression in the subspace domain and proposes to leverage this connection in order to develop explicit and efficient compression mechanisms for massive data sets that exhibit certain properties. This interdisciplinary project is tied with an education plan and provides a stimulating and innovative research environment for students at all levels. Furthermore, workshops are developed as part of an active outreach program in order to introduce high school students to concepts in fields related to data science and communications, exposing them to careers essential to tomorrow’s workforce.Wireless networks are rapidly growing in size, are becoming more hierarchical, and are becoming increasingly distributed. Conventional methods including channel estimation of point-to-point links and block coding do not properly scale with the size of such massive networks. This project proposes that subspace coding in the analog domain becomes relevant for conveying information across networks in such a scenario. Furthermore, the dual problem in the compression domain is central to a wide range of applications involving large-scale raw data, often exhibiting low-dimensional structures, which require techniques for low-dimensional subspace recovery and dimensionality reduction. The specific objectives of this project are summarized as follows: (1) Provide a comprehensive framework, including a certain metric space and an analog operator channel, to study coding for wireless networks in a non-coherent fashion; (2) Construct subspace codes for analog operator channels and characterize their performance; (3) Develop techniques for low-rank subspace recovery given constrained observations; (4) Characterize fundamental limits on compression of low-rank matrices and leverage the duality with subspace codes to design explicit compression mechanisms; (5) Develop schemes for subspace-coded distributed computation to efficiently compute the outcome of algorithms operating over matrices and subspaces while minimizing the delay.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

在当今的技术世界中，大量数据正在以前所未有的规模不断生成、传输、接收、处理和存储，将数据表示为信息位块的经典方法无法满足各种需求，包括可扩展性、效率。该项目通过提出将信息嵌入到称为子空间的数学结构中的方法，开发了一种跨大规模连接的无线网络传输数据的替代范例。向量空间中的线性代数对象），通过一种称为子空间编码的技术，虽然这些结构捕获了广泛的信号处理应用中收集的数据的本质，但压缩的基本限制以及实现这些限制的实用和通用技术。该项目描述了子空间域中纠错和压缩之间的自然二元性，并建议利用这种联系来为具有某些属性的海量数据集开发明确且有效的压缩机制。教育计划并提供刺激和创新的研究此外，作为积极外展计划的一部分，举办了研讨会，旨在向高中生介绍与数据科学和通信相关领域的概念，让他们接触对未来劳动力至关重要的职业。传统的方法（包括点对点链路的信道估计和块编码）无法随着如此庞大的网络的规模而适当扩展。模拟域与跨网络传输信息相关此外，压缩域中的对偶问题是涉及大规模原始数据的广泛应用的核心，这些数据通常表现出低维结构，这需要低维子空间恢复和降维目标的技术。该项目概述如下：（1）提供一个综合框架，包括一定的度量空间和模拟运营商信道，以非相干方式研究无线网络编码；（2）为模拟运营商构建子空间代码（3））开发给定约束观测的低秩子空间恢复技术； (4) 表征低秩矩阵压缩的基本限制，并利用子空间编码的对偶性来设计显式压缩机制； (5) 开发子空间编码分布式计算方案有效计算在矩阵和子空间上运行的算法的结果，同时最大限度地减少延迟。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。