Error detection and correction: Difference between revisions

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{{More citations needed|article|date=August 2008}}

[[File:Reed–Solomon error correction Mona Lisa LroLrLasercomFig4.jpg|thumb|To clean up transmission errors introduced by Earth's atmosphere (left), Goddard scientists applied [[Reed-Solomon_error_correction|Reed–Solomon error correction]] (right), which is commonly used in CDs and DVDs. Typical errors include missing pixels (white) and false signals (black). The white stripe indicates a brief period when transmission was interrupted.]]

In [[information theory]] and [[coding theory]] with applications in [[computer science]] and [[telecommunications]], '''error detection and correction''' ('''EDAC''') or '''error control''' are techniques that enable [[reliable delivery]] of [[digital data]] over unreliable [[communication channel]]s. 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 detecting such errors, while error correction enables reconstruction of the original data in many cases.

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=== Internet ===

In a typical [[TCP/IP]] stack, error control is performed at multiple levels:

* Each [[Ethernet frame]] uses [[Cyclic redundancy check|CRC-32]] error detection. Frames with detected errors are discarded by the receiver hardware.

* The [[IPv4]] header contains a [[IPv4 header checksum|checksum]] protecting the contents of the header. [[Network packet|Packets]] with incorrect checksums are dropped within the network or at the receiver.

* The checksum was omitted from the [[IPv6]] header in order to minimize processing costs in [[network routing]] and because current [[link layer]] technology is assumed to provide sufficient error detection (see also RFC 3819).

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=== Data storage ===

Error detection and correction codes are often used to improve the reliability of data storage media.<ref>{{Cite book|last1=Kurtas|first1=Erozan M.|url=https://books.google.com/books?id=Vx_NBQAAQBAJ&q=Error+detection+and+correction+codes+are+often+used+to+improve+the+reliability+of+data+storage+media&pg=PR5|title=Advanced Error Control Techniques for Data Storage Systems|last2=Vasic|first2=Bane|date=2018-10-03|publisher=CRC Press|isbn=978-1-4200-3649-7|language=en}}{{Dead link|date=March 2020 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> A parity track capable of detecting single-bit errors was present on the first [[magnetic tape data storage]] in 1951. The [[optimal rectangular code]] used in [[group coded recording]] tapes not only detects but also corrects single-bit errors. Some [[file format]]s, particularly [[archive formats]], include a checksum (most often [[CRC32]CRC-32]) to detect corruption and truncation and can employ redundancy or [[parity file]]s to recover portions of corrupted data. [[Cross-interleaved Reed–Solomon coding|Reed-Solomon codes]] are used in [[compact disc]]s to correct errors caused by scratches.

Modern hard drives use Reed–Solomon codes to detect and correct minor errors in sector reads, and to recover corrupted data from failing sectors and store that data in the spare sectors.<ref>{{cite web |archive-url=https://web.archive.org/web/20080202143103/http://www.myharddrivedied.com/presentations_whitepaper.html |archive-date=2008-02-02 |url=http://www.myharddrivedied.com/presentations_whitepaper.html |title=My Hard Drive Died |author=Scott A. Moulton}}</ref> [[RAID]] systems use a variety of error correction techniques to recover data when a hard drive completely fails. Filesystems such as [[ZFS]] or [[Btrfs]], as well as some [[RAID]] implementations, support [[data scrubbing]] and resilvering, which allows bad blocks to be detected and (hopefully) recovered before they are used.<ref>{{Cite book|last1=Qiao|first1=Zhi|last2=Fu|first2=Song|last3=Chen|first3=Hsing-Bung|last4=Settlemyer|first4=Bradley|title=2019 IEEE International Conference on Cluster Computing (CLUSTER) |chapter=Building Reliable High-Performance Storage Systems: An Empirical and Analytical Study |date=2019|pages=1–10|doi=10.1109/CLUSTER.2019.8891006|isbn=978-1-7281-4734-5|s2cid=207951690}}</ref> The recovered data may be re-written to exactly the same physical ___location, to spare blocks elsewhere on the same piece of hardware, or the data may be rewritten onto replacement hardware.

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| author = Jeff Layton | magazine = [[Linux Magazine]]

}}</ref><ref>{{cite web

| url = httphttps://bluesmoke.sourceforge.net/

| title = EDAC Project

| access-date = 2014-08-12