* A full list of authors:ĚýRichard Blahut, Douglas Chan, Jun Chen, Jackie Xing, William Levy, Luis Lastras, Yasutada Oohama, Raymond Yeung, and Zhen Zhang
Toby Berger was born and raised in New York City. He received his Bachelor’s degree in electrical engineering from Yale University in 1962 and his PhD degree in applied mathematics from Harvard University in 1966. At Harvard, he studied with Don Tufts. Among Tufts’ students, others known in this community are John Proakis and Terry Fine.
While studying at Harvard, Toby was working at Raytheon as a research scientist. He remained there until 1968 when he was recruited by Fred Jelinek to the EE Faculty at Cornell University, where he started his academic career. When Toby joined, Terry Fine and Neil Sloane were already on the Faculty. Sloane left for Bell Labs in 1969 and Jelinek left for IBM T.J. Watson Research Lab in 1972. With Terry, Toby started a golden era of information theory at Cornell. For a long period of time, Dick Blahut, an early PhD student of Toby, was an adjunct professor at Cornell, visiting from IBM, Owego.
Though subsequently built a very successful career in information theory, Toby was not an information theorist to start with. His PhD advisor Don Tufts received his PhD degree from MIT, advised by Norbert Wiener and Yuk-Wing Lee. Wiener was a legendary applied mathematician, perhaps best known in this community for the filter bearing his name. Lee was a PhD student of Wiener and he authored a book on statistical communication theory which is still in print.
Toby’s exceptional talent in explaining difficult concepts through writing has long been recognized in the field. Among the books he authored, his graduate level textbook Rate Distortion Theory: A Mathematical Basis for Data Compression published in 1971 is a classic and remains a useful reference after 50 years. To fully appreciate his achievement in writing this book, one has to specially note that he finished the book within five years after his PhD and that his PhD thesis was on a totally different subject (Nyquist sampling).
Besides this book, Toby also wrote two highly acclaimed tutorial papers, one on multiterminal source coding (1977) and the other on performance analysis of multiple access protocols (1981). These two pieces of writing had inspired numerous young researchers and given them the handle to work on these problems. At the 50th anniversary of information theory, Toby was entrusted, together with Jerry Gibson, with the task of chronicling in the Special 50th Anniversary Commemorative Issue of the IT Transactions the history of the theory of lossy source coding, to which he had made consistent and profound contributions. These include, for example, the CEO problem he formulated that has received a lot of attention in this community.
Toby graduated a total of 43 PhD students, 41 from Cornell University and 2 from University of Virginia. Each graduate student of Toby probably had a different learning experience with him, because he provided each of them a unique environment that fits his/her needs. Instead of working on problems he prescribed, his students enjoyed the freedom to work on problems they came up with by themselves. There is one thing in common though: he would spend hours and hours to work with each of his students individually to perfect his/her writing. His famous statement “Information theory is beautiful” also resonated well with many of his students, and eventually became a motto for many successful careers in the field.
Quite possibly due to his influence, a few of Toby’s students are also technical book authors. Dick Blahut has authored more than 10 books on very diverse subjects. Among these, Theory and Practice of Error Control Codes is a coding theory classic. Raymond Yeung’s two books on information theory and network coding are widely used textbooks in the field. Zhongxing Ye has authored a number of books (in Chinese) on information theory and related topics, with a few of them being very popular in China. They all continue Toby's tradition of rigorous writing.
Toby started to interact with the Japanese information theory community in the late 1970s. He presented a new problem of statistical inference in the framework of multiterminal source coding at the Â鶹´«Ă˝AV 7th Spring Workshop on Information Theory held at Mt. Kisco, NY in 1979. This problem was followed up by Shun'ichi Amari, Te Sun Han, and Kingo Kobayashi, resulting in many papers in the IT Transactions. This problem turns out to be closely related to the theory of information geometry pioneered by Amari. In 1980/81, Toby visited Suguru Arimoto at Osaka University for two months, supported by the Japan Society for the Promotion of Science.
In the early 1980’s, Toby received a fellowship from the Ministry of Education of China to give a series of lectures on information theory at South China Institute of Technology that attracted attendants across the country. It was a time when there was very little contact between China and the West. Three of the attendants subsequently became his PhD students.
In the 1990’s, Toby became interested in applications of information theory and multiple access theory. He founded the DISCOVERY Lab at Cornell in the mid-1990s to conduct research on practical methods for video conferencing over the telephone line, whose bandwidth was less than 1% of what we are used to nowadays. Sightspeed, a spinoff company from the DISCOVERY Lab, was acquired by Logitech in 2008 for $30 million. In the 1990s, Toby and his students were also granted a few patents on online compression of human signatures. In 2017 he co-founded with his student a Wi-Fi networks technology company, Cayuga Wireless, that is based on their multiple access research for multiuser physical layers.
At Cornell, Toby became the first Irwin and Joan Jacobs Professor of Engineering.
He taught a large number of undergraduate and graduate courses. Among the graduate courses he developed was “Bio-Information Theory,” first offered in 2001 and was the first regular course on the subject ever offered in a university. This course was part of his effort to help launch the interdisciplinary merger of information theory and biology, specifically neuroscience, around the turn of the century. The title of his 2002 Shannon Lecture was “Living Information Theory.” Based on this lecture, he published a tutorial paper with the same title in the Society’s Newsletter in 2003.
During his Cornell years, Toby was very active doing consulting work for IBM and Bell Labs. At IBM, he did a lot of unpublished work with Dick Blahut on various digital communication problems. At Bell Labs, he was a frequent visitor to the information theory group headed by Aaron Wyner.
In 1998 Toby took a sabbatical year at the University of Virginia. Here he began his collaboration with a neuroscientist, William “Chip” Levy. The collaboration was particularly successful because of their shared belief that information theory could be used to understand evolved communication and computation by neurons of the brain. They continued their research collaboration until his retirement.
Due to a family reason, Toby retired from Cornell in 2006 and joined University of Virginia. Bio-information theory continued to be his main research interest for the rest of his career. He remained very active in research until he finally retired at the age of 79, when most of his earlier students had already retired.
During his tenure at Virginia, Toby enjoyed teaching various graduate courses. The harmonica playing before finals and the home-made cookies from his wife Florence after exams were and will always be remembered as the sweetest treat.
Toby was deeply intrigued and amazed by the energy efficiency of information processing in the human brain. In particular, he thought it was fascinating that the 100 billion neurons composing the human brain consumed about 20 watts of power, whereas the IBM simulated cat visual cortex was 109 times more costly per neuron. This had led to his seminal 2010 IT Transactions paper, in which he laid the mathematical foundation of energy efficient neural computation and communication, i.e., the maximum bits-per-Joule (bpJ) theory. Through a subsequent collaboration with Terry Sejnowski – a pioneer in computational neuroscience, Toby helped bridge the gap between information theory and neuroscience, widening the scope of his theory and its potential range of applications.
Toby served the Â鶹´«Ă˝AV Information Theory Group in various capacities, including President (1979) and Editor-in-Chief (1987-89). He was also a Co-Chair of the 1977 Â鶹´«Ă˝AV International Symposium on Information Theory which was held in Ithaca, NY.
Toby was recognized by numerous awards. These include the 1982 Frederick E. Terman Award of the American Society for Engineering Education for outstanding young electrical engineering educator, the 2002 Claude E. Shannon Award, the 2006 Â鶹´«Ă˝AV Leon K. Kirchmayer Graduate Teaching Award, and the 2011 Â鶹´«Ă˝AV Richard W. Hamming Medal. He was a Member of the US National Academy of Engineering and a Life Fellow of the Â鶹´«Ă˝AV.
An outstanding researcher and educator of our time, Toby Berger will be remembered for his technical legacy. For those who know him, he will also be remembered for his harmonica playing, his enthusiasm in tennis, his generosity, his humility, and his humanity toward the underprivileged.
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