Frame-Based Kernel Analysis and Algorithms for Fast Recovery of Erasures and Multiplexing

用于快速恢复擦除和复用的基于帧的内核分析和算法

基本信息

批准号：
1403400
负责人：
Deguang Han
金额：
$ 16.35万
依托单位：
The University of Central Florida Board of Trustees
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2014
资助国家：
美国
起止时间：
2014-09-01 至 2018-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1403400&HistoricalAwards=false
关键词：
Frame Based Kernel Analysis Algorithms

项目摘要

Accurate transmission of messages is critical in many areas of application in our information-based society. But a message can be distorted in many ways, often arriving with erasures in parts of the message. In such cases, most frame-based methods to restore the message have been aimed at either fast reconstruction of the message (but allowing approximation errors) or perfect reconstruction (but usually with expensive computational cost). In this project the investigator targets problems related to both fast and accurate recovery of the lost data from either known or unknown locations in the message. This has direct applications in information technology, biotechnology, and communications, particularly in multiplexing where expensive channels are shared and the multiplexed data are used to enhance coding security. Students will be trained in the course of this project.The principal investigator and his students work on three fundamental questions concerning the use of frames for fast and accurate recovery of signals with erasures: (i) Develop new approaches to the problem of recovering signals from the frame coefficients when there are erasures at either known or unknown locations. The investigation includes both theoretical analysis and new algorithms. The main objective is to characterize and identify the encoding frames that ensure fast and perfect recovery of the erasures for almost all input signals when erasures occur at possibly unknown locations. (ii) Develop theory and algorithms for optimal superframes and erasure recovery in channel-sharing applications. Multiplexing combines several messages into a single one, which must then be decoded -- that is, its separate component messages must be extracted. Multiplexing usually is done to share an expensive resource, such as a channel, or to enhance the security of the component messages. The investigator studies conditions on superframes that allow perfect recovery from erasures while maintaining information security among the receivers of the different component messages. (iii) Study spectrally optimal frames. The chief aim here is to characterize spectrally k-uniform or near k-uniform frames. Additionally, the investigator continues to work on problems related to the theory of frame dilations and its connections to the Similarity Problem.

在我们基于信息的社会中，许多应用领域的准确传输至关重要。但是，一条消息可能会以多种方式扭曲，经常在消息的部分内容中擦除。在这种情况下，恢复消息的大多数基于框架的方法都是针对消息的快速重建（但允许近似错误）或完美的重建（但通常具有昂贵的计算成本）。在该项目中，研究者针对与消息中已知或未知位置的丢失数据的快速和准确恢复有关的问题。这在信息技术，生物技术和通信中具有直接应用程序，尤其是在共享昂贵的渠道并使用多重数据的多重渠道中，用于增强编码安全性。学生将在该项目的过程中接受培训。主要研究人员和他的学生研究了三个基本问题，涉及使用框架快速准确地恢复具有擦除的信号：（i）在已知或已知位置擦除时从框架系数中恢复信号的新方法。调查包括理论分析和新算法。主要目的是表征和确定编码框架，以确保在可能未知位置发生擦除时，几乎所有输入信号的擦除快速恢复。（ii）开发理论和算法，用于最佳的超级帧和在渠道共享应用中删除恢复。多路复用将几个消息组合到一个消息中，然后必须解码，即必须提取其单独的组件消息。多路复用通常是为了共享昂贵的资源，例如通道，或增强组件消息的安全性。研究者研究了超级帧的条件，这些条件允许从擦除中恢复完美，同时保持不同组件消息的接收器之间的信息安全性。（iii）研究方面最佳的框架。这里的主要目的是表征频谱K-均匀的或接近K均匀框架。此外，研究者继续致力于与框架扩张理论及其与相似性问题的联系有关的问题。