Edgar Gilbert

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Edgar Nelson Gilbert (born July 25, 1923 in Woodhaven , Queens , New York City - † June 15, 2013 in Basking Ridge , New Jersey ) was an American mathematician who is best known for his contributions to coding theory .

Life

Gilbert went to the Franklin K. Lane High School in Brooklyn (completion 1940) and studied physics at Queens College of the City University of New York with the Bachelor Accounts 1943. He then taught briefly at the University of Illinois . During the Second World War he worked on radar antennas in the Radiation Laboratory of the Massachusetts Institute of Technology (MIT), where he received his doctorate in 1948 under Norman Levinson ( Asymptotic Solution of Relaxation Oscillation Problems ). He then worked at Bell Laboratories until his retirement in 1996 . He died as a result of a fall.

In September 1948 he married Mina Young (died 2000) and had a son and a daughter. He lived in Whippany for most of the time before moving to Fellowship Village in Basking Ridge in 2008.

In 1974 he became a Fellow of the IEEE .

plant

He wrote 85 research papers in the fields of information theory and coding theory, graph theory, combinatorics, optimization and probability theory.

In the coding theory comes from him (1952) and independently Rom Rubenowitsch Warschamow (Varshamov, 1957) the Gilbert-Varshamov bound (the approaches of Gilbert and Varshamov are different and also lead to slightly different results). It ensures the existence of good error-correcting codes depending on the code parameters (length, dimension and Hamming distance) via a lower limit for the size of the code.

In 1960, independently of EO Elliott (1963), he introduced a model for errors occurring in groups ( bursts ) in transmission channels (Gilbert-Elliott model).

Independently of Paul Erdős and Alfréd Rényi , he introduced the Erdős – Rényi model of random graphs in 1959 .

With Claude Shannon he developed a model for shuffling cards (riffle shuffle) in 1955 at Bell Labs in an unpublished memorandum ( Theory of shuffling ). Since Jim Reeds also introduced it in 1981 in an unpublished work, it is called the Gilbert-Shannon-Reeds model.

In 1967 he developed a model for cracks that grow randomly in the plane according to a Poisson distribution and that grow until they meet another crack (Gilbert tessellation). He also worked on the Steiner tree problem , which he related to network flows, and various combinatorial problems.

Web links

Individual evidence

  1. ↑ Edgar Gilbert in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ^ Gilbert, A comparison of signaling alphabets, Bell System Technical Journal, Volume 31, 1952, pp. 504-522
  3. ↑ Martin Bossert, Kanalcodierung, Oldenbourg 2013, p. 141
  4. ↑ Gilbert, Capacity of a burst-noise channel, Bell System Technical Journal, Volume 39, 1960, pp. 1253-1265
  5. ↑ Erdös, Renyi, On Random Graphs I, Publicationes Mathematicae, Volume 6, 1959, pp. 290-297.
  6. ↑ Gilbert, Random Graphs, Annals of Mathematical Statistics, Volume 30, 1959, pp. 1141-1144
  7. ^ Gilbert, Random plane networks and needle-shaped crystals, in: B. Noble, Applications of Undergraduate Mathematics in Engineering, New York: Macmillan 1967
personal data
SURNAME Gilbert, Edgar
ALTERNATIVE NAMES Gilbert, Edgar Nelson (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH July 25, 1923
PLACE OF BIRTH Woodhaven , New York
DATE OF DEATH June 15, 2013
Place of death Basking Ridge , New Jersey