Also known as: Richard Hamming
Richard Hamming (1915–1998) was an American mathematician who created the first practical error-correcting codes — the Hamming codes — launching the field of coding theory on which all reliable digital radio, storage, and networking now depends.1
Life and work
Richard Wesley Hamming was born in Chicago in 1915, took a bachelor’s degree from the University of Chicago, a master’s from Nebraska, and a PhD in mathematics from the University of Illinois in 1942. During the Second World War he was recruited to the Manhattan Project at Los Alamos, where he ran the mechanical calculating machines that carried out the physicists’ computations — an early, formative encounter with computing as an industrial process. In 1946 he joined Bell Telephone Laboratories, then at the height of its influence, sharing an environment with Claude Shannon, John Tukey, and others, and he stayed for thirty years. After retiring from Bell Labs in 1976 he taught at the Naval Postgraduate School in Monterey, where his lectures on “The Art of Doing Science and Engineering” and his talk “You and Your Research” became famous meditations on how to do work that matters.
The story behind his most famous invention is well known. Bell Labs’ relay computers ran batch jobs over the weekend, and when the machine detected a parity error it simply halted and moved on, wasting the whole run. Hamming, frustrated at arriving on Monday to find his job aborted, reasoned that if the machine could detect an error it ought to be able to locate and correct it, and over 1947–1950 he worked out how.
Contribution
Hamming’s construction arranges several parity checks so that each data bit is covered by a distinct combination of them. When an error occurs, the pattern of failed checks — read as a binary number, the “syndrome” — points directly to the position of the flipped bit, which the decoder simply inverts. The classic Hamming(7,4) code protects four data bits with three parity bits and corrects any single-bit error in the seven; adding one more overall parity bit lets it also detect (without correcting) any double error. Underlying all of this is the concept he formalised, the Hamming distance — the number of bit positions in which two codewords differ. A code that keeps all its valid codewords at least distance three apart can always correct one error, because any single flip still leaves the received word closest to the original.2 That geometric way of thinking about codes as points spread out in a space became the organising idea of the whole discipline, generalised soon after in the richer Golay code and later in the algebraic codes that dominate modern systems.
Hamming’s 1950 paper appeared just two years after Shannon’s, and the two are complementary: Shannon proved good codes must exist, while Hamming actually built one and gave engineers the tools to reason about it.
Legacy
Hamming received the ACM Turing Award in 1968 and the IEEE Hamming Medal, established in his honour, is awarded annually for contributions to information sciences and systems. His single error-correcting codes are still used directly in computer memory (SECDED ECC) and in many communication headers, and the distance concept underpins every block code that followed, from BCH and Reed–Solomon to the modern LDPC codes associated with Robert Gallager. In land-mobile radio the lineage is very concrete: P25 uses Hamming and Golay codes to protect its control and signalling words, so a decoder such as GopherTrunk is, at the bit level, running exactly the kind of syndrome-based forward error correction Hamming invented to keep his weekend computer runs from dying on a single flipped bit.
Sources
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Richard Hamming — Wikipedia, for biography and his creation of the first practical error-correcting codes. ↩
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Richard W. Hamming — A.M. Turing Award — ACM, for the Hamming codes, Hamming distance, and his 1968 Turing Award. ↩