This is an expository talk on the theory of network coding (NC) with a wide variety of applications to multicast, peer-to-peer communications, wireless networks, sensor networks, personal communications, etc. NC is a paradigm shift in the mode of data transport from the traditional store-and-forward. Linear NC makes the hardware/software implementation feasibly fast for practical applications, while Theorem of Linear NC guarantees the best possible throughput. The wide applicability of NC has generated interest in multi-disciplinary research among computer science, information/coding theory, matrix theory, networking, operations research, and switching. The closing part of the talk extends linear NC to convolutional NC.
Professor Bob Li received the PhD degree in math from UC Berkeley in 1974. He taught applied math at MIT in 1974-76 and math/statistics/CS at U. Illinois, Chicago in 1976-79. After working on switching systems and theoretic research at Bell Labs/Bellcore for a decade, he became Chair Professor of Information Engineering at CUHK in 1989. He was the featured scientist of Scientific American in the Chinese 7/2007 issue. Currently he also serves as a “111 Great Master of Science” for a base of the IGAT Program of Ministry of Education, as well as various types of honorary professors at Peking U, BUPT, National Tsing Hua U, and Xidian University.
Bob Li is a cofounder of the theory of network coding. The Li-Yeung-Cai paper “Linear Network Coding” won the IEEE Information Theory Society Paper Award of Year 2005. The book “Algebraic Switching Theory and Broadband Applications” (2000-01) establishes switching theory as a new branch of applied algebra. The “algebraic switching fabric” has been adopted by the “Metro switch” project of ITRI (2002-04). His “martingale of patterns” (1980) engenders an active research area with applications to genetITCS and communications. He holds 30 US patents.
Based on his previous work, he is composing the talk series “A Dialogue between mathematics and Engineering.” It includes today’s talk.