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Reed–Solomon Error Correction
In information theory and coding theory, Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon in 1960. They have many applications, including consumer technologies such as MiniDiscs, CDs, DVDs, Blu-ray discs, QR codes, Data Matrix, data transmission technologies such as DSL and WiMAX, Broadcasting, broadcast systems such as satellite communications, Digital Video Broadcasting, DVB and ATSC Standards, ATSC, and storage systems such as RAID 6. Reed–Solomon codes operate on a block of data treated as a set of finite field, finite-field elements called symbols. Reed–Solomon codes are able to detect and correct multiple symbol errors. By adding check symbols to the data, a Reed–Solomon code can detect (but not correct) any combination of up to erroneous symbols, ''or'' locate and correct up to erroneous symbols at unknown locations. As an erasure code, it can correct up to erasures at locations that are known and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irving S
Irving may refer to: People *Irving (name), including a list of people with the name Fictional characters * Irving, the main character's love interest in Cathy (comic strip) * Lloyd Irving, the main protagonist in the ''Tales of Symphonia'' video game * Irving, A recycling collecting chuggington, chugger Places Canada * Irving Nature Park, a park in Saint John, N.B. United States *Irving, California, former name of Irvington, California *Irving, Illinois *Irving, Iowa *Irving (Duluth), Minnesota *Irving, New York *Irving, Texas *Irving, Wisconsin, a town **Irving (community), Wisconsin, an unincorporated community *Irving Park, Chicago, Illinois * Irving Township, Montgomery County, Illinois * Irving Township, Michigan * Irving Township, Minnesota * Lake Irving, a lake in Minnesota Companies * Irving Group of Companies, Canadian conglomerate based in Saint John, New Brunswick, controlled by the Irving family, including: ** J. D. Irving, a conglomerate with holdings in forestry, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Video Broadcasting
Digital Video Broadcasting (DVB) is a set of international open standards for digital television. DVB standards are maintained by the DVB Project, an international industry consortium, and are published by a Joint Technical Committee (JTC) of the European Telecommunications Standards Institute (ETSI), European Committee for Electrotechnical Standardization (CENELEC) and European Broadcasting Union (EBU). Transmission DVB systems distribute data using a variety of approaches, including: * Satellite: DVB-S, DVB-DSNG, DVB-S2, DVB-S2X and DVB-SH ** DVB-SMATV for distribution via SMATV * Cable: DVB-C, DVB-C2 * Terrestrial television: DVB-T, DVB-T2 ** Digital terrestrial television for handhelds: DVB-H, DVB-SH * Microwave: using DTT ( DVB-MT), the MMDS ( DVB-MC), and/or MVDS standards ( DVB-MS) These standards define the physical layer and data link layer of the distribution system. Devices interact with the physical layer via a synchronous parallel interface ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extended Euclidean Algorithm
In arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers ''a'' and ''b'', also the coefficients of Bézout's identity, which are integers ''x'' and ''y'' such that : ax + by = \gcd(a, b). This is a certifying algorithm, because the gcd is the only number that can simultaneously satisfy this equation and divide the inputs. It allows one to compute also, with almost no extra cost, the quotients of ''a'' and ''b'' by their greatest common divisor. also refers to a very similar algorithm for computing the polynomial greatest common divisor and the coefficients of Bézout's identity of two univariate polynomials. The extended Euclidean algorithm is particularly useful when ''a'' and ''b'' are coprime. With that provision, ''x'' is the modular multiplicative inverse of ''a'' modulo ''b'', and ''y'' is the modular multiplicative inverse of ''b'' mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Massey
James Lee Massey (February 11, 1934 – June 16, 2013) was an American information theorist and cryptographer, Professor Emeritus of Digital Technology at ETH Zurich. His notable work includes the application of the Berlekamp–Massey algorithm to linear codes, the design of the block ciphers IDEA (with Xuejia Lai, based on the Lai-Massey scheme) and SAFER, and the Massey-Omura cryptosystem (with Jim K. Omura). Biography Massey was born in Wauseon, Ohio. As a child, after the death of his father in Ohio, he moved with his mother and brother to Mendota, Illinois. At age 14, his family moved to Ottawa, Illinois. After graduating from St. Bede Academy, he entered the University of Notre Dame. He received a B.S. in electrical engineering from Notre Dame in 1956 and was granted an NSF Fellowship. After three years of military service, he began graduate studies in 1959 at MIT, where he concentrated on coding theory and was awarded a Ph.D. in 1962, with John Wozencraft as his advis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elwyn Berlekamp
Elwyn Ralph Berlekamp (September 6, 1940 – April 9, 2019) was a professor of mathematics and computer science at the University of California, Berkeley.Elwyn Berlekamp listing at the Department of Mathematics, . Berlekamp was widely known for his work in computer science, and . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyclic Code
In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting codes that have algebraic properties that are convenient for efficient error detection and correction. Definition Let \mathcal be a linear code over a finite field (also called '' Galois field'') GF(q) of block length n. \mathcal is called a cyclic code if, for every Code word (communication), codeword c=(c_1,\ldots,c_n) from \mathcal, the word (c_n,c_1,\ldots,c_) in GF(q)^n obtained by a circular shift, cyclic right shift of components is again a codeword. Because one cyclic right shift is equal to n-1 cyclic left shifts, a cyclic code may also be defined via cyclic left shifts. Therefore, the linear code \mathcal is cyclic precisely when it is invariant under all cyclic shifts. Cyclic codes have some additional structural constraint on the codes. They are based on Galois fields and because of their structural properti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel Gorenstein
Daniel E. Gorenstein (January 1, 1923 – August 26, 1992) was an American mathematician best remembered for his contribution to the classification of finite simple groups. Gorenstein mastered calculus at age 12 and subsequently matriculated at Harvard University, where he earned his bachelor's and master's degrees. During the Second World War, he taught mathematics to military personnel. After the war, he stayed at Harvard and earned his PhD 1950 under the supervision of Oscar Zariski. In his dissertation, Gorenstein introduced a duality principle for plane curves that motivated Alexander Grothendieck's introduction of Gorenstein rings. Gorenstein held posts at Clark University and Northeastern University, before moving to Rutgers University in 1969, where he remained for the rest of his life. He became the founding director of the Center for Discrete Mathematics and Theoretical Computer Science ( DIMACS) at Rutgers in 1989, and remained at this post until his death. He was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BCH Codes
In coding theory, the Bose–Chaudhuri–Hocquenghem codes (BCH codes) form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field (also called a ''Galois field''). BCH codes were invented in 1959 by French mathematician Alexis Hocquenghem, and independently in 1960 by Raj Chandra Bose and D. K. Ray-Chaudhuri. The name ''Bose–Chaudhuri–Hocquenghem'' (and the acronym ''BCH'') arises from the initials of the inventors' surnames (mistakenly, in the case of Ray-Chaudhuri). One of the key features of BCH codes is that during code design, there is a precise control over the number of symbol errors correctable by the code. In particular, it is possible to design binary BCH codes that can correct multiple bit errors. Another advantage of BCH codes is the ease with which they can be decoded, namely, via an algebraic method known as syndrome decoding. This simplifies the design of the decoder for these codes, using small low ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MIT Lincoln Laboratory
The MIT Lincoln Laboratory, located in Lexington, Massachusetts, is a United States Department of Defense federally funded research and development center chartered to apply advanced technology to problems of national security. Research and development activities focus on long-term technology development as well as rapid system prototyping and demonstration. Its core competencies are in sensors, integrated sensing, signal processing for information extraction, decision-making support, and communications. These efforts are aligned within ten mission areas. The laboratory also maintains several field sites around the world. The laboratory transfers much of its advanced technology to government agencies, industry, and academia, and has launched more than 100 start-ups. History Origins At the urging of the United States Air Force, the Lincoln Laboratory was created in 1951 at the Massachusetts Institute of Technology (MIT) as part of an effort to improve the U.S. air defense syste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BCH Code
In coding theory, the Bose–Chaudhuri–Hocquenghem codes (BCH codes) form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field (also called a '' Galois field''). BCH codes were invented in 1959 by French mathematician Alexis Hocquenghem, and independently in 1960 by Raj Chandra Bose and D. K. Ray-Chaudhuri. The name ''Bose–Chaudhuri–Hocquenghem'' (and the acronym ''BCH'') arises from the initials of the inventors' surnames (mistakenly, in the case of Ray-Chaudhuri). One of the key features of BCH codes is that during code design, there is a precise control over the number of symbol errors correctable by the code. In particular, it is possible to design binary BCH codes that can correct multiple bit errors. Another advantage of BCH codes is the ease with which they can be decoded, namely, via an algebraic method known as syndrome decoding. This simplifies the design of the decoder for these codes, using small ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Burst Error
In telecommunications, a burst error or error burst is a contiguous sequence of symbols, received over a communication channel, such that the first and last symbols are in error and there exists no contiguous subsequence of ''m'' correctly received symbols within the error burst. The integer parameter ''m'' is referred to as the ''guard band'' of the error burst. The last symbol in a burst and the first symbol in the following burst are accordingly separated by ''m'' correct symbols or more. The parameter ''m'' should be specified when describing an error burst. Channel model The Gilbert–Elliott model is a simple channel model introduced by Edgar Gilbert and E. O. Elliott that is widely used for describing burst error patterns in transmission channels and enables simulations of the digital error performance of communications links. It is based on a Markov chain In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erasure Code
In coding theory, an erasure code is a forward error correction (FEC) code under the assumption of bit erasures (rather than bit errors), which transforms a message of ''k'' symbols into a longer message (code word) with ''n'' symbols such that the original message can be recovered from a subset of the ''n'' symbols. The fraction ''r'' = ''k''/''n'' is called the code rate. The fraction ''k’/k'', where ''k’'' denotes the number of symbols required for recovery, is called reception efficiency. The recovery algorithm expects that it is known which of the ''n'' symbols are lost. History Erasure coding was invented by Irving Reed and Gustave Solomon in 1960. There are many different erasure coding schemes. The most popular erasure codes are Reed-Solomon coding, Low-density parity-check code (LDPC codes), and Turbo codes. As of 2023, modern data storage systems can be designed to tolerate the complete failure of a few disks without data loss, using one of 3 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
