Berlekamp–Welch Algorithm

	Berlekamp–Welch Algorithm The Berlekamp–Welch algorithm, also known as the Welch–Berlekamp algorithm, is named for Elwyn R. Berlekamp and Lloyd R. Welch. This is a decoder algorithm that efficiently corrects errors in Reed–Solomon codes for an RS(''n'', ''k''), code based on the Reed Solomon original view where a message m_1, \cdots, m_k is used as coefficients of a polynomial F(a_i) or used with Lagrange interpolation In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a data set of coordinate pairs (x_j, y_j) with 0 \leq j \leq k, the x_j are called ''nodes'' an ... to generate the polynomial F(a_i) of degree < ''k'' for inputs $a_1 , \cdots, a_k$ and then $F(a_i)$ is applied to $a_, \cdots , a_n$ to create an encoded codeword $c_1, \cdots , c_n$ . The goal of the decoder is to recover the original encoding polynomial $F(a_i)$ , using the known i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Elwyn R Elwyn is an unincorporated community located in Middletown Township, Delaware County, Pennsylvania, USA. Elwyn has a latitude of 39.907N, longitude of -75.41W and an elevation of 253 feet above sea level. Elwyn is home to Elwyn Inc., a facility caring for the needs of the developmentally disabled and disadvantaged. Elwyn is named for Dr. Alfred L. Elwyn, a physician who founded ''The Pennsylvania Training School for Feeble-minded Children'' in 1852 with teacher James B. Richards. See also Media Area Media is a borough in and the county seat of Delaware County, Pennsylvania. It is located about west of Philadelphia, the sixth most populous city in the nation with 1.6 million residents as 2020. It is part of the Delaware Valley metropolita ... References External linksElwyn Inc. facility official site {{authority control Unincorporated communities in Delaware County, Pennsylvania Unincorporated communities in Pennsylvania ... [...More Info...] [...Related Items...] OR:* [Wikipedia] [Google] [Baidu]
	Lloyd R Lloyd, Lloyd's, or Lloyds may refer to: People * Lloyd (name), a variation of the Welsh word ' or ', which means "grey" or "brown" List of people with given name Lloyd List of people with surname Lloyd * Lloyd (singer) (born 1986), American singer Places United States * Lloyd, Florida * Lloyd, Kentucky * Lloyd, Montana * Lloyd, New York * Lloyd, Ohio * Lloyds, Alabama * Lloyds, Maryland * Lloyds, Virginia Elsewhere * Lloydminster, or "Lloyd", straddling the provincial border between Alberta and Saskatchewan, Canada Companies and businesses Derived from Lloyd's Coffee House Lloyd's Coffee House, a London meeting place for merchants and shipowners between about 1688 and 1774 Lloyd's of London, a British insurance market ''Lloyd's of London'' (film), a 1936 film about the insurance market Lloyd's building, its headquarters ** Lloyd's Agency Network * ''Lloyd's List'', a website and 275-year-old daily newspaper on shipping and global trade ''Lloyd's List In ... [...More Info...] [...Related Items...] OR:** [Wikipedia] [Google] [Baidu]
picture info	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. They have many applications, the most prominent of which include consumer technologies such as MiniDiscs, CDs, DVDs, Blu-ray discs, QR codes, data transmission technologies such as DSL and WiMAX, broadcast systems such as satellite communications, DVB and ATSC, and storage systems such as RAID 6. Reed–Solomon codes operate on a block of data treated as a set of 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 provided to the algorithm, or it can detect and correct combinations of erro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Lagrange Polynomial In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree of a polynomial, degree that polynomial interpolation, interpolates a given set of data. Given a data set of graph of a function, coordinate pairs (x_j, y_j) with 0 \leq j \leq k, the x_j are called ''nodes'' and the y_j are called ''values''. The Lagrange polynomial L(x) has degree \leq k and assumes each value at the corresponding node, L(x_j) = y_j. Although named after Joseph-Louis Lagrange, who published it in 1795, the method was first discovered in 1779 by Edward Waring. It is also an easy consequence of a formula published in 1783 by Leonhard Euler. Uses of Lagrange polynomials include the Newton–Cotes formulas, Newton–Cotes method of numerical integration and Shamir's Secret Sharing, Shamir's secret sharing scheme in cryptography. For equispaced nodes, Lagrange interpolation is susceptible to Runge's phenomenon of large oscillation. Definition Given a set of k + ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Finite Fields In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod when is a prime number. The ''order'' of a finite field is its number of elements, which is either a prime number or a prime power. For every prime number and every positive integer there are fields of order p^k, all of which are isomorphic. Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory. Properties A finite field is a finite set which is a field; this means that multiplication, addition, subtraction and division (excluding division by zero) are def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Coding Theory Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data. There are four types of coding: # Data compression (or ''source coding'') # Error control (or ''channel coding'') # Cryptographic coding # Line coding Data compression attempts to remove unwanted redundancy from the data from a source in order to transmit it more efficiently. For example, ZIP data compression makes data files smaller, for purposes such as to reduce Internet traffic. Data compression a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Information Theory Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering (field), information engineering, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a dice, die (with six equally likely outcomes). Some other important measures in information theory are mutual informat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]