NationMaster - Encyclopedia: Error checking

In computer science and information theory, error correction consists of using methods to detect and/or correct errors in the transmission or storage of data by the use of some amount of redundant data and (in the case of transmission) the selective retransmission of incorrect segments of the data. In general, error correction requires more redundant bits than error detection. Image File history File links Please see the file description page for further information. ... In telecommunication, an error-detecting system is a system employing an error-detecting code and so arranged that any signal detected as being in error is either deleted from the data delivered to the data sink, in some cases with an indication that such deletion has taken place, or delivered... Wikibooks Wikiversity has more about this subject: School of Computer Science Open Directory Project: Computer Science Collection of Computer Science Bibliographies Belief that title science in computer science is inappropriate Categories: Computer science | Academic disciplines ... Information theory is a branch of the mathematical theory of probability and mathematical statistics that quantifies the concept of information. ... In laymans terms, a method is a codified series of steps taken to complete a certain task or to reach a certain objective. ... A datum is a statement accepted at face value (a given). Data is the plural of datum. ... In telecommunication, a redundancy check is extra data added to a message for the purposes of error detection and error correction. ...

Error-correction methods are chosen depending on the error characteristics of the transmission or storage medium, such that errors are almost always detected and corrected with a minimum of redundant data stored or sent.

The minimum amount of redundant data is one bit. A common method of error detection uses one bit of each byte of data as a parity bit. However, that this only provides error-detection, and not error-correction: if a single bit error occurs, we do not know which bit is in error. Worse, this method will only detect about half of all errors. In telecommunication, a redundancy check is extra data added to a message for the purposes of error detection and error correction. ... A bit (abbreviated b) is the most basic information unit used in computing and information theory. ... This article refers to the unit of binary information. ... Parity is a concept of equality of status or functional equivalence. ...

The most obvious method of error-correction is to repeat each unit of data multiple redundant times. However, it is possible to detect and correct errors with far less redundant data. In telecommunication, a redundancy check is extra data added to a message for the purposes of error detection and error correction. ...

Information theory tells us that whatever be the probability of error in transmission or storage, it is possible to construct error-correcting codes in which the likelihood of failure is arbitrarily low, although this requires adding increasing amounts of redundant data to the original, which might not be practical when the error probability is very high. Shannon's theorem sets an upper bound to the error correction rate that can be achieved using a fixed amount of redundancy, but does not tell us how to construct such an optimal encoder. In telecommunication, a redundancy check is extra data added to a message for the purposes of error detection and error correction. ... In information theory, the Shannon-Hartley theorem states the maximum amount of error-free digital data (that is, information) that can be transmitted over a communication link with a specified bandwidth in the presence of noise interference. ...

Hamming codes allow any single bit error in a block to be detected and corrected. Other block error-correcting codes, such as Reed-Solomon codes transform a chunk of bits into a (longer) chunk of bits in such a way that errors up to some threshold in each block can be detected and corrected. In telecommunication, a Hamming code is an error-correcting code named after its inventor, Richard Hamming. ... In information theory and coding, an error-correcting code or ECC is a code in which each data signal conforms to specific rules of construction so that departures from this construction in the received signal can generally be automatically detected and corrected. ... Reed-Solomon error correction is a coding scheme which works by first constructing a polynomial from the data symbols to be transmitted and then sending an over-sampled plot of the polynomial instead of the original symbols themselves. ...

However, in practice errors often occur in bursts rather than at random. This is often compensated for by shuffling (interleaving) the bits in the message after coding. Then any burst of bit-errors is broken up into a set of scattered single-bit errors when the bits of the message are unshuffled (de-interleaved) before being decoded. In telecommunication, an error burst is a contiguous sequence of symbols, received over a data transmission 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. ...

List of error-correction methods

Categories: Articles to be merged | Error detection and correction Alamouti Coding is a spatial-time block code (STBC) which exploits the spatial diversity at the transmitter for a two-transmitter(antenna) system. ... A check bit is a single bit that is added to a byte or string as a part of an error detection (or sometimes error_correction) system. ... A check digit is a form of redundancy check used for error detection, the decimal equivalent of a binary checksum. ... In telecommunication, a convolutional code is a type of error-correction code in which (a) each m-bit information symbol (each m-bit string) to be encoded is transformed into an n-bit symbol, where m/n is the code rate (n >= m) and (b) the transformation is a function... In general, an erasure code transforms a message of n blocks, into one with > n blocks such that the original message can be recovered from a subset of those blocks. ... In telecommunication, forward error correction (FEC) is a system of error control for data transmission wherein the receiving device has the capability to detect and correct fewer than a predetermined number or fraction of bits or symbols corrupted by transmission errors. ... In telecommunication, a Hagelbarger code is a convolutional code that enables error bursts to be corrected provided that there are relatively long error-free intervals between the error bursts. ... In telecommunication, a Hamming code is an error-correcting code named after its inventor, Richard Hamming. ... In information theory, a low-density parity-check code (LDPC code) is a code that uses a sparse parity-check matrix. ... In computing and telecommunication, a parity bit is a binary digit that takes on the value zero or one to satisfy a constraint on the overall parity of a binary number. ... Reed-Solomon error correction is a coding scheme which works by first constructing a polynomial from the data symbols to be transmitted and then sending an over-sampled plot of the polynomial instead of the original symbols themselves. ... A Sparse graph code is a code which is represented by a sparse graph. ... Turbo codes are a class of recently-developed high-performance error correction codes finding use in deep-space satellite communications and other applications where designers seek to achieve maximal information transfer over a limited-bandwidth communication link in the presence of data-corrupting noise. ...

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List of error-correction methods