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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.

在我们的信息社会中，信息的准确传输在许多应用领域中至关重要。但是一条信息可以在很多方面被歪曲，经常在部分信息中出现擦除。在这种情况下，大多数基于帧的恢复消息的方法都旨在快速重建消息（但允许近似误差）或完美重建（但通常计算成本昂贵）。在这个项目中，研究人员的目标是从消息中的已知或未知位置快速准确地恢复丢失的数据。这在信息技术、生物技术和通信中具有直接应用，特别是在其中共享昂贵信道并且复用数据用于增强编码安全性的复用中。学生将在这个项目的过程中进行培训。主要研究员和他的学生工作的三个基本问题，关于使用帧的快速和准确的恢复信号与擦除：（一）开发新的方法来恢复信号的帧系数时，在已知或未知的位置有擦除的问题。调查包括理论分析和新的算法。其主要目的是表征和识别编码帧，以确保快速和完美的恢复几乎所有的输入信号时，擦除发生在可能的未知位置的擦除。 (ii)开发信道共享应用中最佳超帧和擦除恢复的理论和算法。多路复用将多个消息组合成一个消息，然后必须对其进行解码-也就是说，必须提取其单独的组成消息。多路复用通常用于共享昂贵的资源（如通道），或增强组件消息的安全性。研究人员研究超帧的条件，允许完美的恢复，同时保持信息安全的接收器之间的不同组件的消息。(iii)研究频谱最优帧。这里的主要目的是刻画谱k-一致或近k-一致框架。此外，研究人员继续研究与框架扩张理论及其与相似性问题的联系有关的问题。