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

Michigan Technological University, Houghton MI

Investigators

Abstract

Synchronization is an important component of reliable data transmission. The problem of avoiding conflicts in asynchronous multiple-access channels is investigated by utilizing methods from algebraic and combinatorial coding theory. Difference systems of sets are combinatorial structures that are being used to facilitate the design of codes with good synchronization 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 as constructions of good 2-deletion-correcting codes that exceed the Gilbert bound, and constructions of ordered Steiner systems that yield optimal deletion-insertion correcting codes. The proposed research program presents an excellent opportunity for introducing graduate and upper level undergraduate students to the use of computers for learning and solving problems that involve large scale algebraic and combinatorial operations applied on data structures of formidable size, and utilizing the computer as a tool for learning and solving real-world problems that arise in various areas of science and engineering of today's information age.