Backward Error Correction Codes
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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 applications forward and backward error correction in computer science and telecommunication, error detection and correction or error control are error correction codes for non-volatile memories techniques that enable reliable delivery of digital data over unreliable communication channels. Many communication channels are subject to channel error correction codes ppt 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
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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 broadcasting (DVB) 7.4 Data storage quantum error correction codes 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 deterministic algorithm. If only error detection is required, a receiver ca
citations to reliable sources. Unsourced material may be challenged and removed. (August 2008) (Learn how and when to remove this template message) In information error correction code example theory and coding theory with applications in computer science and telecommunication,
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error detection and correction or error control are techniques that enable reliable delivery of digital data over
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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 https://en.wikipedia.org/wiki/Error_detection_and_correction detecting such errors, while error correction enables reconstruction of 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 https://en.wikipedia.org/wiki/Error_detection_and_correction Error-correcting code 6.3 Hybrid schemes 7 Applications 7.1 Internet 7.2 Deep-space telecommunications 7.3 Satellite 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
View all reference sources FREE REFERENCE ENTRIES A B C D E F G H I J K L M N O P Q R S T U V W http://www.encyclopedia.com/doc/1O11-backwarderrorcorrection.html X Y Z # Home Dictionaries, Thesauruses, Pictures, and Press Releases A http://www.tml.tkk.fi/Studies/Tik-110.300/1998/Essays/error_detection.html Dictionary of Computing January 2004 backward error correction Print this article Cite this article Tools A Dictionary of Computing | 2004 | 700+ words © A Dictionary of Computing 2004, originally published by Oxford University Press 2004. backward error correction (backward correction) Error correction that occurs in a channel through the error correction detection of errors by the receiver: the receiver responds to any errors in a block by requesting the transmitter to retransmit the affected block. Backward correction requires a return channel, by contrast with forward error correction.There are two ways in which the return channel can be used to indicate errors: positive acknowledgment and negative acknowledgment. With positive acknowledgment, the receiver returns confirmation of error correction code each block received correctly, and the transmitter is prepared to retransmit a block that is not acknowledged within an appropriate time. With negative acknowledgment, the receiver returns a request to retransmit any block received erroneously, and the transmitter is prepared to retransmit such a block (implying that the transmitter retains a copy of every block sent, indefinitely).Since the return channel itself may be prone to errors, and to limit the amount of storage necessary at the transmitter, the positive acknowledgment and retransmission (PAR) technique is generally preferred. See also error-detecting code. Cite this article Pick a style below, and copy the text for your bibliography. MLA Chicago APA JOHN DAINTITH. "backward error correction." A Dictionary of Computing. 2004. Encyclopedia.com. 1 Oct. 2016
control. There are different communications media with different quality of service (QOS). Consequently, there are several error detection and control schemes for different signal conditions. Some fundamental methods have existed for decades. In addition, there are also new methods that can take advantage of the nature of the signal type. These methods can be used to ensure reliable or adequate communications and faster data transfer rates which are used in today's innovative applications. 1. Error sources No errors can occur in the ideal transmission medium. However, none of the transmission media is ideal. The signal representing the data is always subject to various error sources. As the signal propagates along the transmission media its amplitude decreases. This phenomenon is called as the signal attenuation. The signal cannot be detected if it is too weak. In addition, as the length of the medium increases the waveform also changes during the transmission. This phenomenon is called as the delay distortion. The signal cannot be recognized if it is too distorted. Furthermore, the transmission media can also be a subject to interference resulting from other cables or signals caused by electromagnetic radiation. The medium itself may also cause constant white noise. All transmission errors increase as the length of the transmission medium inreases. [6] 2 Error bursts In practice, data communications systems are designed so that the transmission errors are within acceptable rate. Under normal circumstanced there are only few errors. However, it is possible that the signal conditions can be sometimes so weak that sometimes the signal cannot be received at all. It is also possible that sometimes the interference signal is stronger than the signal to be transmitted. Consequently, the data sent during the break is lost. The contiguous blocks of data corrupted by the error signal are called error bursts. The length and frequency of the error bursts depend on the quality of the data link which in turn depends on the transmission medium and the signal conditions. Therefore, the error detection and control should be able to handle as many errors that possible. However, the applications limit which error detection and control schemes are suitable. All applications benefit from the effeciency of the sheme to be used. In addition, some applications may require short codeword length or low latency whereas some other applications might prefer extremere low error rate, for example. 3 Error detection Error detection is a method that allows some sommunications erros to be detected. The data is encoded so that the encoded data contains