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37 relations: ASCII, Bell Labs, Bell System Technical Journal, Bit, Block code, Cambridge, Cambridge University Press, Code rate, Coding theory, Decoding methods, Dual code, ECC memory, Electromechanics, Generator matrix, Golay code, Hadamard code, Hamming bound, Hamming distance, Hamming(7,4), Identity matrix, John Wiley & Sons, Linear code, Linear independence, Low-density parity-check code, Mathematics, New Jersey, Parity (mathematics), Parity bit, Parity-check matrix, Punched card, Punched tape, Reed–Muller code, Reed–Solomon error correction, Repetition code, Richard Hamming, Telecommunication, Turbo code.
ASCII
ASCII, abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication.
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Bell Labs
Nokia Bell Labs (formerly named AT&T Bell Laboratories, Bell Telephone Laboratories and Bell Labs) is an American research and scientific development company, owned by Finnish company Nokia.
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Bell System Technical Journal
The Bell System Technical Journal was a periodical publication by the American Telephone and Telegraph Company (AT&T) in New York devoted to the scientific and engineering aspects of electrical communication.
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Bit
The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications.
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Block code
In coding theory, a block code is any member of the large and important family of error-correcting codes that encode data in blocks.
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Cambridge
Cambridge is a university city and the county town of Cambridgeshire, England, on the River Cam approximately north of London.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Code rate
In telecommunication and information theory, the code rate (or information rate) of a forward error correction code is the proportion of the data-stream that is useful (non-redundant).
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Coding theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications.
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Decoding methods
In coding theory, decoding is the process of translating received messages into codewords of a given code.
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Dual code
In coding theory, the dual code of a linear code is the linear code defined by where is a scalar product.
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ECC memory
Error-correcting code memory (ECC memory) is a type of computer data storage that can detect and correct the most common kinds of internal data corruption.
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Electromechanics
In engineering, electromechanics combines processes and procedures drawn from electrical engineering and mechanical engineering.
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Generator matrix
In coding theory, a generator matrix is a matrix whose rows form a basis for a linear code.
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Golay code
Golay code may refer to.
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Hadamard code
The Hadamard code is an error-correcting code named after Jacques Hadamard that is used for error detection and correction when transmitting messages over very noisy or unreliable channels.
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Hamming bound
In mathematics and computer science, in the field of coding theory, the Hamming bound is a limit on the parameters of an arbitrary block code: it is also known as the sphere-packing bound or the volume bound from an interpretation in terms of packing balls in the Hamming metric into the space of all possible words.
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Hamming distance
In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different.
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Hamming(7,4)
In coding theory, Hamming(7,4) is a linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits.
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Identity matrix
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.
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John Wiley & Sons
John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.
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Linear code
In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword.
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Linear independence
In the theory of vector spaces, a set of vectors is said to be if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be.
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Low-density parity-check code
In information theory, a low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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New Jersey
New Jersey is a state in the Mid-Atlantic region of the Northeastern United States.
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Parity (mathematics)
In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.
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Parity bit
A parity bit, or check bit, is a bit added to a string of binary code to ensure that the total number of 1-bits in the string is even or odd.
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Parity-check matrix
In coding theory, a parity-check matrix of a linear block code C is a matrix which describes the linear relations that the components of a codeword must satisfy.
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Punched card
A punched card or punch card is a piece of stiff paper that can be used to contain digital data represented by the presence or absence of holes in predefined positions.
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Punched tape
Punched tape or perforated paper tape is a form of data storage, consisting of a long strip of paper in which holes are punched to store data.
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Reed–Muller code
Reed–Muller codes are a family of linear error-correcting codes used in communications.
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Reed–Solomon error correction
Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon in 1960.
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Repetition code
In coding theory, the repetition code is one of the most basic error-correcting codes.
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Richard Hamming
Richard Wesley Hamming (February 11, 1915 – January 7, 1998) was an American mathematician whose work had many implications for computer engineering and telecommunications.
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Telecommunication
Telecommunication is the transmission of signs, signals, messages, words, writings, images and sounds or information of any nature by wire, radio, optical or other electromagnetic systems.
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Turbo code
In information theory, turbo codes (originally in French Turbocodes) are a class of high-performance forward error correction (FEC) codes developed around 1990–91 (but first published in 1993), which were the first practical codes to closely approach the channel capacity, a theoretical maximum for the code rate at which reliable communication is still possible given a specific noise level.
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References
[1] https://en.wikipedia.org/wiki/Hamming_code
