The project develops foundations for the recently booming applied mathematics field of network coding. Network coding offers the promise of improved performance over traditional network routing techniques used in practical engineering applications. Emphasis is placed on the fundamental theory of communication in networks that allow coding in addition to routing. Applications include improved throughput in packet networks and power savings in wireless ad hoc networks. The work exploits the diverse mathematical, engineering, and computer science background from the investigator's previous work and involves mathematical analysis, algorithm design, and computer simulation. The main topic areas investigated are: the role of alphabet size and error correcting codes in network coding, techniques for computing or bounding network capacities, determining the scalar or vector solvability of networks, theoretically achievable rates under a limitation of the number of network nodes that can perform coding, and bi-directional networks.
This project has applications to practical engineering problems involving packet switched networks, such as sensor networks, military battlefield networks, and local area networks. The most prominent example is the Internet, which is used on a daily basis by billions of people for sending email, downloading images and video, transferring data, and many other applications. This project studies the theoretical foundations of how information can be sent across such networks using mathematical combinations of data rather than just routing of data. Specifically, the project studies the fundamental limits of data transmission, the best methods to transmit such data, and variations on the types of networks used. The project includes graduate student participation as well as some undergraduate and high school student contributions, with emphasis on the interconnection between mathematics, engineering, and computer science.
