U. S.-Russian Collaborative Research: Codes for Multiple-Access Channels, Genetic Testing, Deletion-Insertion Correction, and Synchronization

美俄合作研究：多通道编码、基因检测、删除插入校正和同步

• 批准号: 0310632
• 负责人: Vladimir Tonchev
• 金额: --
• 依托单位: Michigan Technological University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-06-01 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0310632&HistoricalAwards=false
• 关键词: U.; S.; Russian; Collaborative; Research

Synchronization is an important component of reliabledata transmission. The problem of avoiding conflicts in asynchronousmultiple-access channels is investigated by utilizing methods fromalgebraic and combinatorial coding theory.Difference systems of sets are combinatorial structuresthat are being used to facilitate the design of codes with goodsynchronization properties. Comma-free codes are brought into play in the organization of protocols for transmission over collision channels in the absence of word synchronization. Group testing techniques have numerous applications in fault detection, error-control codes, and experimental designs.In recent years, group testing has been studied in connection with emerging new applications in multi-access communications,the analysis of genetic information, chromosome mapping,and DNA library screening. This project explores the link between optimal 2-stage testing schemes and combinatorial designs that minimize the expected number of tests, as well as algorithms for the reconstruction of sequences by their subsequences or super-sequences. Packet loss is a common source of errors in Internet transmissions that has renewed the interest in deletion-correcting codes. The research concerning deletion and insertion correcting codes will focus on finding bounds on the optimal size of a code with prescribed error-correcting capacity, as well asconstructions of good 2-deletion-correcting codes that exceedthe Gilbert bound, and constructions of ordered Steinersystems that yield optimal deletion-insertion correctingcodes. The proposed research program presents an excellent opportunity for introducing graduate and upper level undergraduatestudents to the use of computers for learning and solving problemsthat involve large scale algebraic and combinatorial operations applied on data structures of formidable size, and utilizingthe computer as a tool for learning and solving real-world problemsthat arise in various areas of science and engineeringof today's information age.

同步是可靠数据传输的重要组成部分。利用几何和组合编码理论的方法，研究了异步多址信道中避免冲突的问题。集合的差系是一种组合结构，用来帮助设计具有良好同步特性的码。无逗号代码在协议的组织中发挥作用，以便在没有字同步的情况下通过冲突信道进行传输。组测试技术在故障检测、差错控制编码和实验设计中有着广泛的应用。近年来，组测试在多址通信、遗传信息分析、染色体作图和DNA文库筛选等领域得到了新的应用。这个项目探索了最优的两阶段测试方案和最小化预期测试数量的组合设计之间的联系，以及通过它们的子序列或超序列重建序列的算法。分组丢失是互联网传输中常见的错误来源，这重新引起了人们对删除纠错码的兴趣。关于删除和插入纠错码的研究将集中在寻找具有指定纠错能力的码的最优大小的界，以及构造超出Gilbert界的好的2-删除纠错码，以及构造产生最优删除-插入纠错码的有序Steiners系统。拟议的研究计划提供了一个极好的机会，向研究生和本科生介绍使用计算机学习和解决问题，这些问题涉及在巨大规模的数据结构上应用大规模代数和组合运算，并将计算机用作学习和解决当今信息时代科学和工程各个领域出现的现实世界问题的工具。