|
Burst Error-correcting Code
In coding theory, burst error-correcting codes employ methods of correcting burst errors, which are errors that occur in many consecutive bits rather than occurring in bits independently of each other. Many codes have been designed to correct random errors. Sometimes, however, channels may introduce errors which are localized in a short interval. Such errors occur in a burst (called burst errors) because they occur in many consecutive bits. Examples of burst errors can be found extensively in storage mediums. These errors may be due to physical damage such as scratch on a disc or a stroke of lightning in case of wireless channels. They are not independent; they tend to be spatially concentrated. If one bit has an error, it is likely that the adjacent bits could also be corrupted. The methods used to correct random errors are inefficient to correct burst errors. Definitions A burst of length Say a codeword C is transmitted, and it is received as Y = C + E. Then, the error vector ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 computer data storage, 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 detection and correction, Error control (or ''channel coding'') # Cryptography, Cryptographic coding # Line code, Line coding Data compression attempts to remove unwanted redundancy from the data from a source in order to transmit it more efficiently. For example, DEFLATE data compression makes files small ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Division Theorem
In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder exist and are unique, under some conditions. Because of this uniqueness, ''Euclidean division'' is often considered without referring to any method of computation, and without explicitly computing the quotient and the remainder. The methods of computation are called integer division algorithms, the best known of which being long division. Euclidean division, and algorithms to compute it, are fundamental for many questions concerning integers, such as the Euclidean algorithm for finding the greatest common divisor of two integers, and modular arithmetic, for which only remainders are considered. The operation consisting of computing only t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Code Rate
In telecommunication and information theory, the code rate (or information rateHuffman, W. Cary, and Pless, Vera, ''Fundamentals of Error-Correcting Codes'', Cambridge, 2003.) of a forward error correction code is the proportion of the data-stream that is useful (non- redundant). That is, if the code rate is k/n for every bits of useful information, the coder generates a total of bits of data, of which n-k are redundant. If is the gross bit rate or data signalling rate (inclusive of redundant error coding), the net bit rate (the useful bit rate exclusive of error correction codes) is \leq R \cdot k/n. For example: The code rate of a convolutional code will typically be , , , , , etc., corresponding to one redundant bit inserted after every single, second, third, etc., bit. The code rate of the octet oriented Reed Solomon block code denoted RS(204,188) is 188/204, meaning that redundant octets (or bytes) are added to each block of 188 octets of useful information. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error-correcting Codes With Feedback
In mathematics, computer science, telecommunication, information theory, and searching theory, error-correcting codes with feedback are error correcting codes designed to work in the presence of feedback from the receiver to the sender.See and . Problem Alice (the sender) wishes to send a value ''x'' to Bob (the receiver). The communication channel between Alice and Bob is imperfect, and can introduce errors. Solution An error-correcting code is a way of encoding ''x'' as a message such that Bob will successfully understand the value ''x'' as intended by Alice, even if the message Alice sends and the message Bob receives differ. In an error-correcting code with feedback, the channel is two-way: Bob can send feedback to Alice about the message he received. Noisy feedback In an error-correcting code without noisy feedback, the feedback received by the sender is always free of errors. In an error-correcting code with noisy feedback, errors can occur in the feedback, as w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Detection And Correction
In information theory and coding theory with applications in computer science and telecommunications, error detection and correction (EDAC) or error control are techniques that enable reliable delivery of digital data over unreliable communication channels. Many communication channels are subject to channel noise, and thus errors may be introduced during transmission from the source to a receiver. Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases. Definitions ''Error detection'' is the detection of errors caused by noise or other impairments during transmission from the transmitter to the receiver. ''Error correction'' is the detection of errors and reconstruction of the original, error-free data. History In classical antiquity, copyists of the Hebrew Bible were paid for their work according to the number of stichs (lines of verse). As the prose books of the Bible were hardly ever w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross-interleaved Reed–Solomon Coding
In the compact disc system, cross-interleaved Reed–Solomon code (CIRC) provides error detection and error correction. CIRC adds to every three data bytes one redundant parity byte. Overview Reed–Solomon codes are specifically useful in combating mixtures of random and burst errors. CIRC corrects error bursts up to 4000 data bits in sequence (2.5 mm in length as seen on CD surface) and compensates for error bursts up to 12,000 bits (7.5 mm) that may be caused by minor scratches. Characteristics * High random error correctability * Long burst error correctability * In case the burst correction capability is exceeded, interpolation may provide concealment by approximation * Simple decoder strategy possible with reasonably-sized external random access memory * Very high efficiency * Room for future introduction of four audio channels without major changes in the format (as of 2024, this has not been implemented). Interleave Errors found in compact discs (CDs) are a c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forward Error Correction
In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is that the sender encodes the message in a redundant way, most often by using an error correction code, or error correcting code (ECC). The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors. Therefore a reverse channel to request re-transmission may not be needed. The cost is a fixed, higher forward channel bandwidth. The American mathematician Richard Hamming pioneered this field in the 1940s and invented the first error-correcting code in 1950: the Hamming (7,4) code. FEC can be applied in situations where re-transmissions are costly or impossible, such as one-way communication links or when transmitting to multiple receivers in m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Row And Column Major Order
Row or ROW may refer to: Exercise * Rowing, or a form of aquatic movement using oars * Row (weight-lifting), a form of weight-lifting exercise Mathematics and informatics * Row vector, a 1 × ''n'' matrix in linear algebra * Row(s) in a table (information), a data arrangement with rows and columns * Row (database), a single, implicitly structured data item in a database table * Tone row, an arrangement of the twelve notes of the chromatic scale Places * Rów, Pomeranian Voivodeship, north Poland * Rów, Warmian-Masurian Voivodeship, north Poland * Rów, West Pomeranian Voivodeship, northwest Poland * Roswell International Air Center's IATA code * Row, a former spelling of Rhu, Dunbartonshire, Scotland * The Row (Lyme, New York), a set of historic homes * The Row, Virginia, an unincorporated community * Rest of the world (RoW) * The Row or The Row Fulton Market, 900 West Randolph, a Chicago Skyscraper on Chicago's Restaurant Row Other * Reality of Wrestling, an American profess ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
