Backward Error Correction Wiki
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citations to reliable sources. Unsourced material may be challenged and removed. (August 2008) (Learn how and when to remove this template message) In information theory and coding theory with forward and backward error correction applications in computer science and telecommunication, error detection and correction or error
Error Correction Code Wiki
control are techniques that enable reliable delivery of digital data over unreliable communication channels. Many communication channels are subject hamming distance error correction 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 error correction and detection the original data in many cases. Contents 1 Definitions 2 History 3 Introduction 4 Implementation 5 Error detection schemes 5.1 Repetition codes 5.2 Parity bits 5.3 Checksums 5.4 Cyclic redundancy checks (CRCs) 5.5 Cryptographic hash functions 5.6 Error-correcting codes 6 Error correction 6.1 Automatic repeat request (ARQ) 6.2 Error-correcting code 6.3 Hybrid schemes 7 Applications 7.1 Internet 7.2 Deep-space telecommunications 7.3 Satellite
Error Correction Code
broadcasting (DVB) 7.4 Data storage 7.5 Error-correcting memory 8 See also 9 References 10 Further reading 11 External links Definitions[edit] The general definitions of the terms are as follows: 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[edit] The modern development of error-correcting codes in 1947 is due to Richard W. Hamming.[1] A description of Hamming's code appeared in Claude Shannon's A Mathematical Theory of Communication[2] and was quickly generalized by Marcel J. E. Golay.[3] Introduction[edit] The general idea for achieving error detection and correction is to add some redundancy (i.e., some extra data) to a message, which receivers can use to check consistency of the delivered message, and to recover data determined to be corrupted. Error-detection and correction schemes can be either systematic or non-systematic: In a systematic scheme, the transmitter sends the original data, and attaches a fixed number of check bits (or parity data), which are derived from the data bits by some determinis
BCH code Reed–Solomon code Block length n Message length k Distance n − k + 1 Alphabet size q = pm ≥ n (p prime) Often n = q − 1. Notation [n, k, n − error correction techniques k + 1]q-code Algorithms Decoding Berlekamp–Massey Euclidean et al. Properties Maximum-distance separable code v error detection and correction in computer networks t e Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon
Error Detection And Correction Using Hamming Code Example
in 1960.[1] They have many applications, the most prominent of which include consumer technologies such as CDs, DVDs, Blu-ray Discs, QR Codes, data transmission technologies such as DSL and WiMAX, broadcast systems such https://en.wikipedia.org/wiki/Error_detection_and_correction as DVB and ATSC, and storage systems such as RAID 6. They are also used in satellite communication. In coding theory, the Reed–Solomon code belongs to the class of non-binary cyclic error-correcting codes. The Reed–Solomon code is based on univariate polynomials over finite fields. It is able to detect and correct multiple symbol errors. By adding t check symbols to the data, a Reed–Solomon code can https://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_correction detect any combination of up to t erroneous symbols, or correct up to ⌊t/2⌋ symbols. As an erasure code, it can correct up to t known erasures, or it can detect and correct combinations of errors and erasures. Furthermore, Reed–Solomon codes are suitable as multiple-burst bit-error correcting codes, since a sequence of b+1 consecutive bit errors can affect at most two symbols of size b. The choice of t is up to the designer of the code, and may be selected within wide limits. Contents 1 History 2 Applications 2.1 Data storage 2.2 Bar code 2.3 Data transmission 2.4 Space transmission 3 Constructions 3.1 Reed & Solomon's original view: The codeword as a sequence of values 3.1.1 Simple encoding procedure: The message as a sequence of coefficients 3.1.2 Systematic encoding procedure: The message as an initial sequence of values 3.1.3 Theoretical decoding procedure 3.2 The BCH view: The codeword as a sequence of coefficients 3.2.1 Systematic encoding procedure 3.3 Duality of the two views - discrete Fourier transform 3.4 Remarks 4 Properties 5 Error correction algorithms 5.1 Peterson–Gorenstein–Zierler decoder 5.1.1 Syndrome decoding 5.1.2 Error locators and error values 5.1.3 Error locator polynomial 5.1.4 Obtain the error locators
page's history now serves to provide attribution for that content in the latter page, and it must not be deleted so long as the latter page exists. The former page's talk page https://en.wikipedia.org/wiki/Talk%3AForward_error_correction can be accessed at Talk:Interleaving. WikiProject Telecommunications (Rated Start-class) TelecommunicationsWikipedia:WikiProject TelecommunicationsTemplate:WikiProject TelecommunicationsTelecommunications articles https://www.scribd.com/document/145654486/Wiki-Error-Detection-and-Correction Telecommunication portal v t e This article is within the scope of WikiProject Telecommunications, a collaborative effort to improve the coverage of Telecommunications on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks. Start This article error correction has been rated as Start-Class on the project's quality scale. ??? This article has not yet received a rating on the project's importance scale. Contents 1 Software patents 2 Weird 3 Incomplete text 4 What is forward? 5 Merge? 6 Retransmission!? 7 Most recent development? 8 Relevance of reference 9 Dubious 10 MLC NAND 11 FEQ vs. FEC 12 Simplified Layman's terms explanation 13 Rewrite backward error correction 14 2/3 FEC and 3/4 FEC 15 list of error-correcting codes 16 Codeword confusion 17 Merge? 18 Fire codes Software patents[edit] I have heard that some methods for FEC are covered by software patents. Does anyone know if this is (still) the case? If so, it should probably be mentioned in the article. Haakon 13:06, 17 Jan 2005 (UTC) Weird[edit] From the article: The original information may or may not appear in the encoded output; codes that include the unmodified input in the output are systematic, while those that do not are nonsystematic.. Ehm, if the original information did not appear in the encoded output, then what sense should such an encoded output make? We couldn't reconstruct the original information back from the encoded output... or do you mean "the original information may not appear in plain text in the encoded output"? Yes, exactly -- the original sequence of bits always occurs in the output of a systematic encoder, but the original sequence of bits almost never occurs in the output of a nonsystematic decoder (although, of course, the information can still be extracted). Please improve the article to make this easier to under
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