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

同步是数据可靠传输的重要组成部分。本文利用几何学和组合编码理论的方法研究了多址信道中避免冲突的问题.集合差系是一种组合结构，它被用来设计具有良好同步特性的码.无逗号码在没有字同步的情况下在冲突信道上传输的协议的组织中发挥作用。 群测试技术在故障检测、差错控制码和实验设计等方面有着广泛的应用，近年来，群测试在多路访问通信、遗传信息分析、染色体作图和DNA文库筛选等方面的应用越来越多。该项目探讨了最佳2阶段测试方案和组合设计之间的联系，最大限度地减少了预期的测试次数，以及通过序列或超序列重建序列的算法。 数据包丢失是Internet传输中常见的错误来源，这重新引起了对删除校正码的兴趣。 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佳长度的界，以及构造满足吉尔伯特界的好的2-删除纠错码，以及构造产生最佳删除-插入纠错码的有序Steiner系统。 拟议的研究计划提出了一个很好的机会，介绍研究生和上层本科生使用计算机学习和解决问题，涉及大规模的代数和组合运算应用于数据结构的强大规模，并利用计算机作为学习和解决现实世界中出现的问题的工具，在科学和工程的各个领域今天的信息时代。

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.