Mathematical Theories of Communication: Old and New

Reliable and efficient digital communication is possible today largely due to some wonderful successes in mathematical modelling and analysis. A legendary figure in this space is Claude Shannon (1916-2001) who laid out the mathematical foundations of communication in his seminal 1948 treatise, where among other contributions he gave a mathematical definition of “entropy” and coined the now ubiquitous term “bit” (for binary digit). But Shannon’s theory is not the last word in communication. Communication extends to settings well beyond the carefully designed full information exchange model explored in Shannon’s work. In this talk I will try to describe some of the many extensions that have been explored in the interim period including communication complexity (Yao 1980) that explores how it might be possible to achieve effective communication without a full exchange; interactive communication (Schulman 1992) which explores how to cope with errors in an interactive setting, and some of our own work on uncertain communication, which explores how shared context can make communication more effective, even if the context is shared only loosely.

Madhu Sudan

Harvard

Madhu Sudan is a Gordon McKay Professor in the John A. Paulson School of Engineering and Applied Sciences at Harvard University, where he has been since 2015. Madhu got his Bachelor’s degree from IIT Delhi in 1987, and his PhD from UC Berkeley in 1992. From 1992 to 2015, Madhu worked at IBM Research (Research Staff Member 1992-1997), at MIT (Associate Professor 1997-2000, Professor 2000-2011, Fujitsu Chair Professor 2003-2011, CSAIL Associate Director 2007-2009, Adjunct Professor 2011-2015), and at Microsoft Research (Principal Researcher, 2009-2015). He is a recipient of the Nevanlinna Prize awarded by the International Mathematical Union for outstanding contributions to mathematics of computer and information science, and the Infosys Foundation Prize in Mathematical Sciences. Madhu is also a fellow of the Association for Computing Machinery, the Institute of Electrical and Electronics Engineers and the American Mathematical Society. Additionally, he is a member of the American Academy of Arts and Sciences and the National Academy of Sciences.

Madhu’s research interests revolve around mathematical studies of communication and computation. Specifically, his research focuses on concepts of reliability and mechanisms that are, or can be, used by computers to interact reliably with each other. His research draws on tools from computational complexity, which studies efficiency of computation, and many areas of mathematics including algebra and probability theory. He is best known for his works on probabilistic checking of proofs, and on the design of list-decoding algorithms for error-correcting codes. His current research interests include property testing—which is the study of sublinear time algorithms to estimate properties of massive data, and communication amid uncertainty—a mathematical study of the role of context in communication.