Edgar Gilbert

Edgar Nelson Gilbert (July 25, 1923 – June 15, 2013) was an American mathematician and coding theorist, a longtime researcher at Bell Laboratories whose accomplishments include the Gilbert–Varshamov bound in coding theory, the Gilbert–Elliott model of bursty errors in signal transmission, and the Erdős–Rényi model for random graphs.

Gilbert was born in 1923 in Woodhaven, New York. He did his undergraduate studies in physics at Queens College, City University of New York, graduating in 1943. He taught mathematics briefly at the University of Illinois at Urbana–Champaign but then moved to the Radiation Laboratory at the Massachusetts Institute of Technology, where he designed radar antennas from 1944 to 1946. He finished a Ph.D. in physics at MIT in 1948, with a dissertation entitled Asymptotic Solution of Relaxation Oscillation Problems under the supervision of Norman Levinson, and took a job at Bell Laboratories where he remained for the rest of his career. He retired in 1996.

He died following a fall in 2013 at Basking Ridge, New Jersey.

The Gilbert–Varshamov bound, proved independently in 1952 by Gilbert and in 1957 by Rom Varshamov, is a mathematical theorem that guarantees the existence of error-correcting codes that have a high transmission rate as a function of their length, alphabet size, and Hamming distance between codewords (a parameter that controls the number of errors that can be corrected). The main idea is that in a maximal code (one to which no additional codeword can be added), the Hamming balls of the given distance must cover the entire codespace, so the number of codewords must at least equal the total volume of the codespace divided by the volume of a single ball. For 30 years, until the invention of Goppa codes in 1982, codes constructed in this way were the best ones known.

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