Error Control Coding Theory
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citations to reliable sources. Unsourced material may be challenged and removed. (August 2008) (Learn how and when to
Error Detection And Correction
remove this template message) In information theory and coding theory error detection and correction in computer networks with applications in computer science and telecommunication, error detection and correction or error control are
Error Control Coding In Digital Communication
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 error detection and correction using hamming code example 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. 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 crc error detection 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 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.
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 in
Error Detection And Correction In Data Link Layer
computer science and telecommunication, error detection and correction or error control are techniques checksum error detection example that enable reliable delivery of digital data over unreliable communication channels. Many communication channels are subject to channel noise,
Error Correction
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 https://en.wikipedia.org/wiki/Error_detection_and_correction 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 7.5 Error-correcting memory https://en.wikipedia.org/wiki/Error_detection_and_correction 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 can simply apply the same a
random bit errors during data transmission. Error coding is a method of detecting and correcting these errors to ensure information is transferred intact from its source to its destination. Error coding is used for fault tolerant computing in computer memory, https://users.ece.cmu.edu/~koopman/des_s99/coding/ magnetic and optical data storage media, satellite and deep space communications, network communications, cellular telephone networks, and almost any other form of digital data communication. Error coding uses mathematical formulas to encode data bits at the source into longer bit words for transmission. The "code word" can then be decoded at the destination to retrieve the information. The extra bits in the code word provide redundancy that, according to error detection the coding scheme used, will allow the destination to use the decoding process to determine if the communication medium introduced errors and in some cases correct them so that the data need not be retransmitted. Different error coding schemes are chosen depending on the types of errors expected, the communication medium's expected error rate, and whether or not data retransmission is possible. Faster processors and better communications technology make more error detection and complex coding schemes, with better error detecting and correcting capabilities, possible for smaller embedded systems, allowing for more robust communications. However, tradeoffs between bandwidth and coding overhead, coding complexity and allowable coding delay between transmission, must be considered for each application. Contents: Introduction Key Concepts Shannon's Theorem Tradeoffs Available tools, techniques, and metrics Liner Block Codes CRCCodes Convolutional Codes Relationship to other topics Conclusions Annotated Reference List Introduction Error coding is a method of providing reliable digital data transmission and storage when the communication medium used has an unacceptable bit error rate (BER) and a low signal-to-noise ratio (SNR). Error coding is used in many digital applications like computer memory, magnetic and optical data storage media, satellite and deep space communications, network communications, and cellular telephone networks. Rather than transmitting digital data in a raw bit for bit form, the data is encoded with extra bits at the source. The longer "code word" is then transmitted, and the receiver can decode it to retrieve the desired information. The extra bits transform the data into a valid code word in the coding scheme. The space of valid code words is smaller than the space of possible bit strings of that length, therefore the destination can recognize invalid code word
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