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Topic: Error correction

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	Error correction and detection - Wikipedia, the free encyclopedia
		Error correction and detection schemes find use in implementations of reliable data transfer over noisy transmission links, data storage media (including dynamic RAM, compact discs), and other applications where the integrity of data is important.
		While the use of error correction and detection schemes are not limited only to sender-receiver systems, in discussing a particular scheme, it will be advantageous for us to use the terminology of a "sender" and a "receiver" for simplicity.
		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.
	en.wikipedia.org /wiki/Error-correction (1864 words)

	Reed-Solomon error correction - Wikipedia, the free encyclopedia
		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.
		In the same sense that one can correct a curve by interpolating past a gap, a Reed-Solomon code can bridge a series of errors in a block of data to recover the coefficients of the polynomial that drew the original curve.
		A Reed-Solomon code is twice as powerful at erasure correction than at error correction, and any combination of errors and erasures can be corrected as long as the equation 2E + S ≤ (n−k) is satisfied, where E is the number of errors and S is the number of erasures in the block.
	en.wikipedia.org /wiki/Reed-Solomon_error_correction (1114 words)

	Error Correction Codes
		There's an error correction code that separates the bits holding the original value (data bits) from the error correction bits (check bits), and the difference between the calculated and actual error correction bits is the position of the bit that's wrong.
		Error correction codes are a way to represent a set of symbols so that if any 1 bit of the representation is accidentally flipped, you can still tell which symbol it was.
		The finished code, 011101011000101, is sent to the remote side, which recomputes the error code bits from the symbol bits, and compares that to the error code bits actually received.
	burtleburtle.net /bob/math/errorcor.html (905 words)

	Error-correction - Wikipedia
		In computer science and information theory, error-correction consists of methods to detect and 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 that data.
		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.
		Error-correction in practice is complicated by the fact that errors might occur in bursts rather than at random.
	www.web-dictionary.org /encyclopedia/er/Error_correction.html (281 words)

	Biological vs. quantum error correction mechanisms
		Error correction mechanisms are common in biology and widely thought of as endemic to that realm to the exclusion of the quantum.
		We would conclude that the error correction mechanisms found in biological organisms are pre-dated by their occurrence in quantum sources and the maintenance of error correction mechanisms in the machinery below the biological even permits them to function and to exist.
		We would say that error correction mechanisms cannot be used as an example of a life feature that shows a level of organization not found in the physical.
	www.mightymall.com /1st3seconds/errorcm.html (842 words)

	Interventions: Error Correction & Word Drill Techniques (Site not responding. Last check: 2007-11-07)
		When the student commits a reading error (e.g., substitution, omission, 5-second hesitation), immediately pronounce the correct word for the student, have the student repeat the word correctly, and then direct the student to continue reading.
		When the student commits a reading error (e.g., substitution, omission, 5-second hesitation), immediately pronounce the correct word for the student and have the student repeat the word correctly.
		This cue is given directly after a reading error and alerts the student to the fact that she or she has misread the word.
	www.interventioncentral.org /htmdocs/interventions/rdngfluency/errcorrect.shtml (960 words)

	ECC Technologies, Inc. ECC FAQs
		Error correction is needed to ensure the accuracy and integrity of data and, in some cases, to create fault-tolerance (where components can fail with no loss of performance or data).
		Error correction is currently being used to make high capacity storage devices such as magnetic and optical disk and tape reliable.
		Error correction can be used to extend the battery life of portable computers and other battery-powered electronic devices by allowing a significant decrease in the DRAM refresh rate.
	members.aol.com /mnecctek/faqs.html (1761 words)

	Error correction (Site not responding. Last check: 2007-11-07)
		Error correction detects and corrects corruption during transmission.
		Error correction is normally configured correctly by Windows 2000 when you install a modem.
		Forced EC Requires that the modems use the V.42 error correction method or terminate the connection when V.42 cannot be used.
	www.microsoft.com /windows/windows2000/en/advanced/help/sag_MODEconcepts_115.htm (206 words)

	EE4253 Hamming Code
		Correction of such errors requires more information, since the position of the bad bit must be identified if it is to be corrected.
		It may now be observed that if an error occurs in any of the seven bits, that error will affect different combinations of the three parity bits depending on the bit position.
		The ability to correct single bit errors comes at a cost which is less than sending the entire message twice.
	www.ee.unb.ca /tervo/ee4253/hamming.htm (1094 words)

	Brainstorms: Error Correction Runs Deep
		In addition to looking at the ‘source’ or cause of error correction, it is also interesting to look at the result or effect of error correction on the processes of evolutionary change.
		If as you seem to suggest error correction is part of GSH and if error correction reduces evolution then it seems that it's not Darwinian mechanisms but GSH that suffers from problems explaining the facts of evolution.
		For example, the "need" of error correction, the multitude of ways that "errors" are avoided, the limited applicability of the parity code concept to mutifunctional RNAs (along with the myriad ways by which the parity is broken) all point to a pretty different mode of design, an entirely different "personality".
	www.iscid.org /boards/ubb-get_topic-f-6-t-000170.html (2054 words)

	Forward error correction - Wikipedia, the free encyclopedia
		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.
		This has been standard practice in satellite and deep space communications since Voyager 2 first used the technique in its 1986 encounter with Uranus.
		The most recent (early 1990s) development in error correction is turbo coding, a scheme that combines two or more relatively simple convolutional codes and an interleaver to produce a block code that can perform to within a fraction of a decibel of the Shannon limit.
	www.wikipedia.org /wiki/Forward_error_correction (547 words)

	CQC Intro's : Quantum Error Correction (Site not responding. Last check: 2007-11-07)
		During the correction procedure, the entanglement between the system and its environment is transferred to an entanglement between the measuring apparatus and the environment.
		First, completely general error processes can be corrected, including relaxation and entanglement with the environment, and to do this it is sufficient merely to be able to correct for spin flips (sigma_x Pauli spin operator) and sign flips (sigma_z Pauli spin operator) [2,3,4,5].
		Third, the probability of failure of the quantum error correction falls exponentially with the redundancy, in the limit of large redundancy, as long as the error rate is below a given level [4,5].
	www.qubit.org /oldsite/intros/QEC.html (1300 words)

	Realization of quantum error correction : Nature
		Finally, the primary qubit state is corrected on the basis of the ancillae measurement outcome.
		We verify error correction by comparing the corrected final state to the uncorrected state and to the initial state.
		In principle, the approach enables a quantum state to be maintained by means of repeated error correction, an important step towards scalable fault-tolerant quantum computation using trapped ions.
	www.nature.com /nature/journal/v432/n7017/abs/nature03074.html;jsessionid=EC9F18407FD26E0A587AB6C545F64551 (305 words)

	Hamming Codes
		Forward Error Correction (FEC), the ability of receiving station to correct a transmission error, can increase the throughput of a data link operating in a noisy environment.
		The transmitting station must append information to the data in the form of error correction bits, but the increase in frame length may be modest relative to the cost of re transmission.
		The number of parity or error check bits required is given by the Hamming rule, and is a function of the number of bits of information transmitted.
	www2.rad.com /networks/1994/err_con/hamming.htm (777 words)

	Error Nuker: Find and fix Windows registry problems
		Error Nuker is a powerful utility that will scan the Windows Registry to identify errors and ways to optimize the performance of the Windows Registry.
		Error Nuker is different — its number one priority is safety.
		After the scan is complete, Error Nuker will show you a full list of errors with details, broken down by types and let you fix individual invalid entries or all invalid entries of a certain type.
	www.ErrorNuker.com (560 words)

	Diagnostic Error Codes
		This may be due to an internal error or to a failed connection which did not allow the interrupt command to be sent to the drive properly.
		This error is most likely an internal malfunction of the drive and not related to the condition of the cables etc. Retest and replace the drive if the error repeats.
		An error was reported by the drive during the Write command (to cause the auto-relocation) or the Read Verify command (to verify the relocation happened).
	support.wdc.com /techinfo/general/errorcodes.asp (1794 words)

	BBC \| British Council teaching English - Methodology - Error Correction 1 (Site not responding. Last check: 2007-11-07)
		When it comes to error correction we are dealing with one individual's reaction to a student's piece of writing or utterance.
		To be sure about the type of error produced by a student we need to know where the student's interlanguage is (the language used by a student in the process of learning a second language).
		Correct errors by writing the correct forms in their place.
	www.teachingenglish.org.uk /think/methodology/error_correct.shtml (914 words)

	The Ubiquitous Reed-Solomon Codes
		Careful engineering can reduce the error rate to what may sound like a negligible level--the industry standard for hard disk drives is 1 in 10 billion--but given the volume of information processing done these days, that "negligible" level is an invitation to daily disaster.
		If, for example, you anticipate no more than one error to occur in transmission, then repeating each bit three times and using "majority vote" at the receiving end will guarantee that the message is heard correctly (e.g., 111 000 011 111 will be correctly heard as 1011).
		And just as the eye can recognize and correct for a couple of "bad" points in what is otherwise clearly a smooth parabola, the Reed-Solomon code can spot incorrect values of P and still recover the original message.
	www.siam.org /siamnews/mtc/mtc193.htm (1356 words)

	ERROR CORRECTION
		Errors within each category have common characteristics and are correctable in the same fashion.
		Errors discovered through the reconciliation process must be promptly corrected in the agency's accounting records and/or in STARS as appropriate.
		If an error is detected in STARS, the correction will normally require that the agency prepare and submit to the Comptroller General's Office both: (a) a transaction reversal of the incorrect transaction, and (b) a corrected transaction.
	www.cg.state.sc.us /info/error/detect.htm (805 words)

	Error detection coding (Site not responding. Last check: 2007-11-07)
		Error detection coding is designed to permit the detection of errors.
		Once detected, the receiver may ask for a re-transmission of the erroneous bits, or it may simply inform the recipient that the transmission was corrupted.
		As can be seen, the addition of a parity bit has reduced the uncorrected error rate by three orders of magnitude.
	www-dept.cs.ucl.ac.uk /staff/S.Bhatti/D51-notes/node32.html (662 words)

	Learn more about Reed-Solomon error correction in the online encyclopedia. (Site not responding. Last check: 2007-11-07)
		The Reed-Solomon error correction is an error-correcting code which encodes blocks of n-bit symbols.
		Reed-Solomon codes are unusual in that they correct bursts of errors with very little additional data.
		Also they permit a designer to trade-off computational power to get more data per block, or an ability to correct larger groups of errors.
	www.onlineencyclopedia.org /r/re/reed_solomon_error_correction.html (382 words)

	Technical Reference Infobase: Error Correction (Site not responding. Last check: 2007-11-07)
		Error correction is the method by which modems verify that the information sent to them has been undamaged during the transfer.
		Though error correction may slow down data transfer on noisy lines, it does provide greater reliability.
		As with data compression protocols, for an error correction protocol to be used, it must be supported by both modems in the connection.
	www.modems.com /glossary/glos3.html (109 words)

	Memory Error Detection and Correction
		Since memory errors are rare if the system is operating correctly, the vast majority of errors will be single-bit errors, and will be detected.
		Unfortunately, while parity allows for the detection of single bit errors, it does not provide a means of determining which bit is in error, which would be necessary to correct the error.
		If the syndrome is non-zero, it can be used to index a table to determine which bits are in error, or that the error is uncorrectable.
	www.brouhaha.com /~eric/computers/ecc.html (1160 words)

	Modem Error Correction Protocols (Site not responding. Last check: 2007-11-07)
		Error correction is the ability of the modem to make a transmission be resent if it detects that there might be an error.
		V-Series: This is a Hayes proprietary error correction protocol that has become extinct.
		CSP (CompuCom Speed Protocol): is an error correction and data compression protocol available on CompuCom DIS modems.
	home.fuse.net /Walts_Place/modemerrorcorrection.htm (166 words)

	Audio Compact Disk - Writing and Reading the data (Site not responding. Last check: 2007-11-07)
		Error detection and correction codes are fundamental to the operation of any digital storage system.
		In practice some errors are so large that they cannot be corrected by the error-detection and correction algorithms.
		Unless these errors are handled by some other means, they can result in audible clicks in the audio output.
	www.ee.washington.edu /conselec/CE/kuhn/cdaudio2/95x7.htm (2671 words)

	A Fundamental Introduction to the Compact Disc Player
		There is then an error inherent in the quantization process regardless of the ideality of the rest of the system.
		However, quantization error becomes quite significant when a low-level signal approaches the level of the LSB, then the quantizing error actually becomes the signal, and therefore is an audible component of the output.
		As stated previously, the primary job of the noise shaper is to alter the frequency spectrum of the error signals so as to move most of the quantization error out of the audible frequency range.
	www.tc.umn.edu /~erick205/Papers/paper.html (5473 words)

	3 ERROR CORRECTION TECHNIQUES
		Most of the tasks being supported require the selection of a single correct interpretation of user input (one exception to this is search engines, which may have multiple correct responses).
		The interface designer should use information about the probability of correctness and the overhead for correcting a mistaken choice of default to decide when it is appropriate to choose a default.
		Certain modes of input are known to be less error prone than others (compare typing to handwriting recognition), and there are times when it is appropriate to make use of this fact.
	www.cc.gatech.edu /fce/errata/publications/survey/node10.html (1332 words)

	Quantum Error Correction
		As a result of this observation, the problem of finding good ways of correcting all errors up to a maximum weight reduces to that of constructing codes with sufficiently high minimum distance.
		An important consequence of invariance under a change of basis of error operators is that the set of errors correctable by a particular code and decoding procedure is linearly closed.
		We explain the condition for correctability by using the subsystems interpretation of decoding procedures.
	www.eskimo.com /~knill/qip/ecprhtml/node18.html (610 words)

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