Communications Theory
The research of communicaton theory covers a wide range of topics on channel coding theory, information theory, mathematical theory of switching, and mathematical tools for performance analysis, etc. The study of communication theory deals with the fundamental aspects of information as an entity, and uses mathematical tools and techniques to derive the limits of information coding, data compression, transmission efficiency, and network performance, etc.
Research Projects
1. Asynchronous Communications
Inspired by data retrieval in a storage system, such as a CD player or a magnetic recording system, we look at the problem of reliable communication through a channel for which the clock of the transmitter and of the receiver are not synchronized. We are interested in determining the capacity of such channels.
2. Information Inequalities
Inequalities involving Shannon's information measures, termed information inequalities, are fundamental in information theory. We developed a software called ITIP that can prove most information inequalities known in the literature. Research results on this problem have fundamental implications in information theory and probability theory.
3. Network Coding Theory
Traditionally, the role of the nodes in a network is to route and/or to replicate information. We introduced a new concept called network coding, which refers to coding at the nodes of a network. We showed that bandwidth can be saved with network coding if information is multicast in a network.
4. Switching Networks by Algebraic Principles
Switching theory has been evolving toward a branch of mathematics with significant applications to telecommunications. The project was developed a new platform for algebraic studies of switching networks.
Sporadic ad hoc results are pieced together into general algebraic principles. Generality grows with the mathematical rigor in formulation and derivation.
5. Prime Factorization Theory of Networks
This theory deals with the partitioning of a network into factors, i.e., subnetworks with restrictions on the shape and the size. Classical results in matching theory are extended and recast in terms of a prime factorization theory of networks. Prime factorization means recursive factoring until it cannot be further factored.