# Claude Shannon 1916-2001

Look at a compact disc under a microscope and you will see music represented as a sequence of pits, or in mathematical terms, as a sequence of 0's and 1's, commonly referred to as bits. The foundation of our Information Age is this transformation of speech, audio, images and video into digital content, and the man who started the digital revolution was Claude Shannon, who died February 24, at the age of 84, after a long struggle with Alzheimer's disease.

Shannon arrived at the revolutionary idea of digital representation by sampling the information source at an appropriate rate, and converting the samples to a bit stream. He characterized the source by a single number, the entropy, adapting a term from statistical mechanics, to quantify the information content of the source. For English language text, Shannon viewed entropy as a statistical parameter that measured how much information is produced on the average by each letter. He also created coding theory, by introducing redundancy into the digital representation to protect against corruption. If today you take a compact disc in one hand, take a pair of scissors in the other hand, and score the disc along a radius from the center to the edge, then you will find that the disc still plays as if new.

Before Shannon, it was commonly believed that the only way of achieving arbitrarily small probability of error in a communication channel was to reduce the transmission rate to zero. All this changed in 1948 with the publication of A Mathematical Theory of Communication, where Shannon characterized a channel by a single parameter; the channel capacity, and showed that it was possible to transmit information at any rate below capacity with an arbitrarily small probability of error. His method of proof was to show the existence of a single good code by averaging over all possible codes. His paper established fundamental limits on the efficiency of communication over noisy channels, and presented the challenge of finding families of codes that achieve capacity. The method of random coding does not produce an explicit example of a good code, and in fact it has taken fifty years for coding theorists to discover codes that come close to these fundamental limits on telephone line channels.

The importance of Shannon's work was recognized immediately. According to a 1953 issue of Fortune Magazine: "It may be no exaggeration to say that man's progress in peace, and security in war, depend more on fruitful applications of information theory than on physical demonstrations, either in bombs or in power plants, that Einstein's famous equation works". In fact his work has become more important over time with the advent of deep space communication, wireless phones, high speed data networks, the Internet, and products like compact disc players, hard drives, and high speed modems that make essential use of coding and data compression to improve speed and reliability.

Shannon grew up in Gaylord Michigan, and began his education at the University of Michigan, where he majored in both Mathematics and Electrical Engineering. As a graduate student at MIT, his familiarity with both the mathematics of Boolean Algebra and the practice of circuit design produced what H. H. Goldstine called: "one of the most important master's theses ever written ... a landmark in that it changed circuit design from an art to a science". This thesis, A Symbolic Analysis of Relay and Switching Circuits, written in 1936, provided mathematical techniques for building a network of switches and relays to realize a specific logical function, such as a combination lock. It won the Alfred Noble Prize of the combined engineering societies of the USA and is fundamental in the design of digital computers and integrated circuits.

Shannon's interest in circuit design was not purely theoretical, for he also liked to build, and his sense of play is evident in many of his creations. In the 1950's, when computers were given names like ENIAC (Electronic Numerical Integrator and Calculator) Shannon built a computer called THROBAC I ( THrifty ROman-numeral BAckward-looking Computer), which was able to add, subtract, multiply and even divide numbers up to 85 working only with Roman numerals. His study in Winchester Mass. was filled with such devices, including a maze-solving mechanical mouse and a miraculous juggling machine. Traversing the ceiling was a rotating chain, like those at dry cleaners, from which were suspended the gowns from a score of honorary doctorates. They made a splendid sight flying around the room.

Shannon's 1941 doctoral dissertation, on the mathematical theory of genetics, is not as well known as his master's thesis, and in fact was not published until 1993, by which time most of the results had been obtained independently by others. After graduating from MIT, Shannon spent a year at the Institute for Advanced Study, and this is the period where he began to develop his theoretical framework that lead to his 1948 paper on communication in the presence of noise. He joined Bell Labs in 1941, and remained there for 15 years, after which he returned to MIT. During World War II his work on encryption led to the system used by Roosevelt and Churchill for transoceanic conferences, and inspired his pioneering work on the mathematical theory of cryptography.

It was at Bell Labs that Shannon produced the series of papers that transformed the world, and that transformation continues today. In 1948, Shannon was connecting information theory and physics by developing his new perspective on entropy and its relation to the laws of thermodynamics. That connection is evolving today , as others explore the implications of quantum computing, by enlarging information theory to treat the transmission and processing of quantum states.

Shannon must rank near the top of the list of the major figures of Twentieth Century science, though his name is relatively unknown to the general public. His influence on everyday life, which is already tremendous, can only increase with the passage of time.

Robert Calderbank and Neil J. A. Sloane

Robert Calderbank and Neil J. A. Sloane are with the Information Sciences Research Lab, AT&T Shannon Research and Technology Center, Florham Park NJ 07932-0971, USA.