The Internet and other communication networks that contain connecting nodes (terminals, computers or switches) have undergone a revolution in the past decade.
Improvements in speed and efficiency have resulted in greater throughput, or the transmission of more data, and in popular applications that use multicast addressing to transmit data from one node to multiple nodes. One example of a multicast takes place when multiple users simultaneously download the same movie from the same Web site.
Traditionally, says Zhiyuan Yan, an assistant professor of electrical and computer engineering, data transmission has occurred when each node in a communication network stores a packet of information and forwards it to the next node.
In a newer, more advanced method of data transmission, nodes combine multiple incoming packets into a single packet and pass it on. “Combine-and-forward” data transmission, also called network coding, yields significant performance improvements in multicasts.
But there is a down side, says Yan. Errors due to noise, jamming or interference can undermine the integrity of the data transmitted in network coding. This threat is particularly severe for wireless applications.
Yan’s group designs codes to detect or correct errors undermining network coding. The field is highly theoretical and mathematics-based. Yan and his students utilize three branches of mathematics – abstract algebra, finite field theory and combinatorics – to design classes of error control codes for network coding. They have led the way in adapting rank metric codes to error control in network coding. They also work with subspace codes and constant dimension codes.
“Each type of code has its own parameters,” says Yan. “We are one of the few groups working with rank metric codes and subspace codes.”
Yan’s group has published more than 50 articles in journals and conference proceedings. At IEEE’s International Symposium on Information Theory this year in Seoul, South Korea, Yan presented three papers.