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:
- 金额:$ 64.84万
- 依托单位:
- 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:
- 关键词:
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,大量的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福尔斯不能满足下一代存储、计算和通信系统的各种要求,包括可扩展性、效率和可靠性。该项目通过提出将信息嵌入到称为子空间的数学构造(即,向量空间中的线性代数对象),通过称为子空间编码的技术。虽然这些结构捕获了在广泛的信号处理应用中收集的数据的本质,但是压缩的基本限制以及实现这些限制的实用和通用技术还不被理解。该项目的特点是在子空间域中的纠错和压缩之间的自然二元性,并建议利用这种连接,以开发显式和高效的压缩机制,表现出一定的属性的海量数据集。这个跨学科项目与教育计划相结合,为各级学生提供了一个激励和创新的研究环境。此外,为了向高中生介绍与数据科学和通信相关的领域的概念,使他们接触到对未来劳动力至关重要的职业,作为积极推广计划的一部分,还开发了研讨会。无线网络的规模正在迅速增长,变得更加分层,并且变得越来越分散。包括点对点链路的信道估计和分组编码的传统方法不能适当地随这种大规模网络的大小而缩放。该项目提出,在模拟域中的子空间编码成为相关的跨网络在这种情况下传递信息。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,通常表现出低维结构,这需要低维子空间恢复和降维技术。本项目的具体目标概括如下:(1)提供一个全面的框架,包括一定的度量空间和模拟运营商信道,以研究非相干方式下的无线网络编码;(2)构造模拟运营商信道的子空间码并表征其性能;(3)开发给定约束观测的低秩子空间恢复技术;(4)描述低秩矩阵压缩的基本限制,并利用子空间码的对偶性来设计显式压缩机制;(5)制定子空间方案-编码分布式计算,以有效地计算在矩阵和子空间上操作的算法的结果,同时最小化延迟。该奖项反映了NSF的法定使命,并被认为值得支持通过使用基金会的知识价值和更广泛的影响审查标准进行评估。
项目成果
期刊论文数量(15)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
A New Algebraic Approach for String Reconstruction from Substring Compositions
- DOI:10.1109/isit50566.2022.9834531
- 发表时间:2022-01
- 期刊:
- 影响因子:0
- 作者:Utkarsh Gupta;Hessam Mahdavifar
- 通讯作者:Utkarsh Gupta;Hessam Mahdavifar
Coded Computing via Binary Linear Codes: Designs and Performance Limits
- DOI:10.1109/jsait.2021.3103772
- 发表时间:2021-03
- 期刊:
- 影响因子:0
- 作者:M. Soleymani;Mohammad Vahid Jamali;Hessam Mahdavifar
- 通讯作者:M. Soleymani;Mohammad Vahid Jamali;Hessam Mahdavifar
New Packings in Grassmannian Space
格拉斯曼空间的新包装
- DOI:10.1109/isit45174.2021.9517770
- 发表时间:2021
- 期刊:
- 影响因子:0
- 作者:Soleymani, Mahdi;Mahdavifar, Hessam
- 通讯作者:Mahdavifar, Hessam
Analog Lagrange Coded Computing
- DOI:10.1109/jsait.2021.3056377
- 发表时间:2020-08
- 期刊:
- 影响因子:0
- 作者:M. Soleymani;Hessam Mahdavifar;A. Avestimehr
- 通讯作者:M. Soleymani;Hessam Mahdavifar;A. Avestimehr
Covert Millimeter-Wave Communication: Design Strategies and Performance Analysis
- DOI:10.1109/twc.2021.3123307
- 发表时间:2022-06-01
- 期刊:
- 影响因子:10.4
- 作者:Jamali, Mohammad Vahid;Mahdavifar, Hessam
- 通讯作者:Mahdavifar, Hessam
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Hessam Mahdavifar其他文献
Compound polar codes
复合极码
- DOI:
10.1109/ita.2013.6502955 - 发表时间:
2013 - 期刊:
- 影响因子:0
- 作者:
Hessam Mahdavifar;Mostafa El;Jungwon Lee;Inyup Kang - 通讯作者:
Inyup Kang
Polar Coding for Non-Stationary Channels
- DOI:
10.1109/tit.2020.3020929 - 发表时间:
2016-11 - 期刊:
- 影响因子:2.5
- 作者:
Hessam Mahdavifar - 通讯作者:
Hessam Mahdavifar
Asymptotically optimal sticky-insertion-correcting codes with efficient encoding and decoding
具有高效编码和解码的渐近最优粘性插入校正码
- DOI:
10.1109/isit.2017.8007016 - 发表时间:
2017 - 期刊:
- 影响因子:0
- 作者:
Hessam Mahdavifar;A. Vardy - 通讯作者:
A. Vardy
Matrix Completion over Finite Fields: Bounds and Belief Propagation Algorithms
有限域上的矩阵补全:界限和置信传播算法
- DOI:
- 发表时间:
2023 - 期刊:
- 影响因子:0
- 作者:
M. Soleymani;Qiang Liu;Hessam Mahdavifar;L. Balzano - 通讯作者:
L. Balzano
Projective Systematic Authentication via Reed-Muller Codes
通过 Reed-Muller 码进行投影系统认证
- DOI:
10.48550/arxiv.2404.09088 - 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
Hsuan;Hessam Mahdavifar - 通讯作者:
Hessam Mahdavifar
Hessam Mahdavifar的其他文献
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{{ truncateString('Hessam Mahdavifar', 18)}}的其他基金
CAREER: Coding Subspaces: Error Correction, Compression and Applications
职业:编码子空间:纠错、压缩和应用
- 批准号:
2415440 - 财政年份:2024
- 资助金额:
$ 64.84万 - 项目类别:
Continuing Grant
Collaborative Research: CIF: Small: Designing Plotkin Transform Codes via Machine Learning
协作研究:CIF:小型:通过机器学习设计 Plotkin 转换代码
- 批准号:
2312752 - 财政年份:2023
- 资助金额:
$ 64.84万 - 项目类别:
Standard Grant
CIF: Small: Collaborative Research: Communications in Ultra-Low-Rate Regime: Fundamental Limits, Code Constructions, and Applications
CIF:小型:协作研究:超低速率制度下的通信:基本限制、代码构造和应用
- 批准号:
1909771 - 财政年份:2019
- 资助金额:
$ 64.84万 - 项目类别:
Standard Grant
CIF: Medium: Collaborative Research: New Frontiers in Polar Coding: 5G and Beyond
CIF:媒介:协作研究:Polar 编码的新前沿:5G 及以上
- 批准号:
1763348 - 财政年份:2018
- 资助金额:
$ 64.84万 - 项目类别:
Continuing Grant
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