O que (quem) é Hamming code - definição

ERROR CORRECTING HAMMING CODE

Hamming coding; Hamming's code; Hamming matrix; SEC-DED; SECDED; Hamming Code; Single-error correction and double-error detection; Single-error correction, double-error detection; Single error correction and double error detection; Hamming codes

Hamming code

<algorithm> Extra, redundant bits added to stored or transmitted data for the purposes of {error detection and correction}. Named after the mathematician Richard Hamming, Hamming codes greatly improve the reliability of data, e.g. from distant space probes, where it is impractical, because of the long transmission delay, to correct errors by requesting retransmission. [Detail? Connection with Hamming Distance?] (2002-07-02)

Richard Hamming

AMERICAN MATHEMATICIAN AND INFORMATION THEORIST

Richard W. Hamming; Richard W Hamming; Richard Wesley Hamming; Hamming, Richard Wesley; Hamming, Richard; Richard Hammering; R. W. Hammering

<person> Professor Richard Wesley Hamming (1915-02-11 - 1998-01-07). An American mathematician known for his work in information theory (notably {error detection and correction}), having invented the concepts of Hamming code, Hamming distance, and Hamming window. Richard Hamming received his B.S. from the University of Chicago in 1937, his M.A. from the University of Nebraska in 1939, and his Ph.D. in mathematics from the University of Illinois at Urbana-Champaign in 1942. In 1945 Hamming joined the Manhattan Project at Los Alamos. In 1946, after World War II, Hamming joined the {Bell Telephone Laboratories} where he worked with both Shannon and John Tukey. He worked there until 1976 when he accepted a chair of computer science at the Naval Postgraduate School at Monterey, California. Hamming's fundamental paper on error-detecting and error-correcting codes ("Hamming codes") appeared in 1950. His work on the IBM 650 leading to the development in 1956 of the L2 programming language. This never displaced the workhorse language L1 devised by Michael V Wolontis. By 1958 the 650 had been elbowed aside by the 704. Although best known for error-correcting codes, Hamming was primarily a numerical analyst, working on integrating differential equations and the Hamming spectral window used for smoothing data before Fourier analysis. He wrote textbooks, propounded aphorisms ("the purpose of computing is insight, not numbers"), and was a founder of the ACM and a proponent of open-shop computing ("better to solve the right problem the wrong way than the wrong problem the right way."). In 1968 he was made a fellow of the {Institute of Electrical and Electronics Engineers} and awarded the Turing Prize from the Association for Computing Machinery. The Institute of Electrical and Electronics Engineers awarded Hamming the Emanuel R Piore Award in 1979 and a medal in 1988. http://www-gap.dcs.st-and.ac.uk/Richard Hamminghistory/Mathematicians/Hamming.html. http://zapata.seas.smu.edu/Richard Hamminggorsak/hamming.html. http://webtechniques.com/archives/1998/03/homepage/. [Richard Hamming. Coding and Information Theory. Prentice-Hall, 1980. ISBN 0-13-139139-9]. (2003-06-07)

Hamming, Richard

AMERICAN MATHEMATICIAN AND INFORMATION THEORIST

Richard W. Hamming; Richard W Hamming; Richard Wesley Hamming; Hamming, Richard Wesley; Hamming, Richard; Richard Hammering; R. W. Hammering

Richard Hamming

Wikipédia

Hamming code

In computer science and telecommunication, Hamming codes are a family of linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By contrast, the simple parity code cannot correct errors, and can detect only an odd number of bits in error. Hamming codes are perfect codes, that is, they achieve the highest possible rate for codes with their block length and minimum distance of three.Richard W. Hamming invented Hamming codes in 1950 as a way of automatically correcting errors introduced by punched card readers. In his original paper, Hamming elaborated his general idea, but specifically focused on the Hamming(7,4) code which adds three parity bits to four bits of data.

In mathematical terms, Hamming codes are a class of binary linear code. For each integer r ≥ 2 there is a code-word with block length n = 2^r − 1 and message length k = 2^r − r − 1. Hence the rate of Hamming codes is R = k / n = 1 − r / (2^r − 1), which is the highest possible for codes with minimum distance of three (i.e., the minimal number of bit changes needed to go from any code word to any other code word is three) and block length 2^r − 1. The parity-check matrix of a Hamming code is constructed by listing all columns of length r that are non-zero, which means that the dual code of the Hamming code is the shortened Hadamard code, also known as a Simplex code. The parity-check matrix has the property that any two columns are pairwise linearly independent.

Due to the limited redundancy that Hamming codes add to the data, they can only detect and correct errors when the error rate is low. This is the case in computer memory (usually RAM), where bit errors are extremely rare and Hamming codes are widely used, and a RAM with this correction system is a ECC RAM (ECC memory). In this context, an extended Hamming code having one extra parity bit is often used. Extended Hamming codes achieve a Hamming distance of four, which allows the decoder to distinguish between when at most one one-bit error occurs and when any two-bit errors occur. In this sense, extended Hamming codes are single-error correcting and double-error detecting, abbreviated as SECDED.

https://en.wikipedia.org/wiki/Hamming code

Exemplos de pronúncia para Hamming code

1. And so Richard Hamming of Hamming code, you know,

How to Have a Bad Career _ David Patterson _ Talks at Google