Edgar Nelson Gilbert (July 25, 1923 – June 15, 2013) was an American mathematician and coding theorist, a longtime researcher at Bell Laboratories.
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.
[3] The Gilbert–Varshamov bound, proved independently in 1952 by Gilbert and in 1957 by Rom Varshamov,[G52][4] 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.
[8] In the mathematics of shuffling playing cards, the Gilbert–Shannon–Reeds model, developed in 1955 by Gilbert and Claude Shannon[G55] and independently in unpublished work in 1981 by Jim Reeds, is a probability distribution on permutations of a set of n items that, according to experiments by Persi Diaconis, accurately models human-generated riffle shuffles.
Gilbert was able to provide upper and lower bounds for the critical range at which this network contains an infinite connected component.