Error correction code: Difference between revisions

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In [[computing]], [[telecommunication]], [[information theory]], and [[coding theory]], an '''error correction code,''' sometimes '''error correcting code,''' ('''ECC''') is used for [[error control|controlling errors]] in data over unreliable or noisy [[communication channel]]s.<ref>{{cite book |author-last1=Glover |author-first1=Neal |author-last2=Dudley |author-first2=Trent |title=Practical Error Correction Design For Engineers |edition=Revision 1.1, 2nd |publisher=[[Cirrus Logic]] |___location=CO, USA |date=1990 |isbn=0-927239-00-0 |id={{ISBN|978-0-927239-00-4}}}}</ref><ref name="Hamming">{{cite journal |author-last=Hamming |author-first=R. W. |title=Error Detecting and Error Correcting Codes |journal=[[Bell System Technical Journal]] |volume=29 |issue=2 |pages=147–160 |publisher=[[AT&T]] |___location=USA |date=April 1950 |url=httpshttp://signallakewww3.alcatel-lucent.com/innovationbstj/hammingvol29-1950/articles/bstj29-2-147.pdf |doi=10.1002/j.1538-7305.1950.tb00463.x |access-date=244 December 2012 }}{{Dead link|date=August 2019 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> The central idea is the sender encodes the message with a [[Redundancy (information theory)|redundant]] in the form of an ECC. The American mathematician [[Richard Hamming]] pioneered this field in the 1940s and invented the first error-correcting code in 1950: the [[Hamming (7,4) code]].<ref name="Hamming"/>

The redundancy allows the receiver to detect a limited number of errors that may occur anywhere in the message, and often to correct these errors without retransmission. ECC gives the receiver the ability to correct errors without needing a [[reverse channel]] to request retransmission of data, but at the cost of a fixed, higher forward channel bandwidth. ECC is therefore applied in situations where retransmissions are costly or impossible, such as one-way communication links and when transmitting to multiple receivers in [[multicast]]. For example, in the case of a satellite orbiting around [[Uranus]], a retransmission because of decoding errors can create a delay of 5 hours. ECC information is usually added to [[mass storage]] devices to enable recovery of corrupted data, is widely used in [[modem]]s, and is used on systems where the primary memory is [[ECC memory]].