CIF: AF: Small: Data Processing Against Synchronization Errors

CIF：AF：小：针对同步错误的数据处理

基本信息

批准号：
2006455
负责人：
Mahdi Cheraghchi Bashi Astaneh
金额：
$ 48.92万
依托单位：
Regents of the University of Michigan - Ann Arbor
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-10-01 至 2023-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2006455&HistoricalAwards=false
关键词：
CIF AF Small Data Processing

项目摘要

This research project addresses fundamental challenges caused by imperfect or lacking synchronization in communications and information systems. Timing disparity, for example, between a sender and receiver pair or different components of a high-throughput processing unit may cause these errors. In such cases, the communicated symbols may be missed or registered multiple times by the receiver unit. In high-speed optical communications, data is encoded in the form of intensity variations of light beams. As photons travel through the communications medium, they may be absorbed or arrive at the destination in an unpredictable order. The photon detecting receiver will then need to translate the unreliable photon counts over time to the precise digital data being sent. More recently, reliable and extremely compact storage of massive digital data in DNA molecules has been an active subject of study. In such applications, the stored information is retrieved via existing DNA sequencing technologies that are also prone to synchronization errors. The scientific impacts of the project span the above-mentioned technologies that are of key significance to the processing, transmission, and storage of massive data. Educational aspects of the project include training postgraduate and undergraduate students and incorporating elements of the project into coursework.The above examples divide the specific goals of the project into three main categories. First, Shannon capacity of the deletion channel, as well as related communications channels, will be studied. A main goal will be to obtain provable and improved bounds on the information capacity. Second, Shannon capacity of the Poisson channel, a classical model for optical communications, will be studied. The project sets forth the novel hypothesis that the deletion and Poisson capacity problems, two of the longest-standing open problems in classical information theory since the 1960s, have remained unresolved due to shared mathematical difficulties, and thus should be studied with a shared perspective. Finally, the project studies the complexity of the trace reconstruction problem which provides a mathematical model to study the capacity of DNA storage systems.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.

该研究项目解决了由于通信和信息系统不完善或缺乏同步而造成的根本挑战。例如，发送器和接收器对之间或高吞吐量处理单元的不同组件之间的定时差异可能会导致这些错误。在这种情况下，所传送的符号可能会被接收器单元丢失或多次记录。在高速光通信中，数据以光束强度变化的形式编码。当光子穿过通信介质时，它们可能会被吸收或以不可预测的顺序到达目的地。然后，光子检测接收器需要将不可靠的光子计数随时间转换为正在发送的精确数字数据。最近，在 DNA 分子中可靠且极其紧凑地存储大量数字数据已成为一个活跃的研究课题。在此类应用中，存储的信息是通过现有的 DNA 测序技术检索的，但这些技术也容易出现同步错误。该项目的科学影响涵盖了上述对海量数据的处理、传输和存储具有关键意义的技术。该项目的教育方面包括培训研究生和本科生以及将项目的要素纳入课程作业中。上述示例将该项目的具体目标分为三个主要类别。首先，将研究删除通道以及相关通信通道的香农容量。主要目标是获得可证明的和改进的信息容量界限。其次，将研究光通信经典模型泊松信道的香农容量。该项目提出了一个新颖的假设，即删除问题和泊松容量问题是 20 世纪 60 年代以来经典信息论中最长期存在的两个开放问题，由于共同的数学困难而仍未得到解决，因此应该以共同的视角进行研究。最后，该项目研究了痕迹重建问题的复杂性，为研究 DNA 存储系统的容量提供了一个数学模型。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进行评估，被认为值得支持标准。