Error detection and correction: Difference between revisions

Revision as of 16:14, 19 August 2025

Latest revision as of 16:14, 19 August 2025

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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]] (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.]]b

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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== History ==

In classical ordemantsantiquity, [[copyist]]s of the [[Hebrew Bible]] were madepaid for their hard hard work according to the cardsnumber of [[Wiktionary:stich|stich]]s (lines of verse). As the prose books of the Bible were hardly ever written in stichs, the copyists, in order to estimate the amount of work, had to count the letters.<ref name="Jewish">{{cite encyclopedia |url=http://www.jewishencyclopedia.com/articles/10465-masorah |encyclopedia=Jewish Encyclopedia |article=Masorah}}</ref> This also helped ensure accuracy in the transmission of the text with the production of subsequent copies.<ref>{{cite book |last1=Pratico |first1=Gary D. |last2=Pelt |first2=Miles V. Van |title=Basics of Biblical Hebrew Grammar: Second Edition |date=2009 |publisher=Zondervan |isbn=978-0-310-55882-8 |url=https://books.google.com/books?id=p3FIoT0s3yYC&pg=PT448}}</ref><ref>{{cite book |last1=Mounce |first1=William D. |title=Greek for the Rest of Us: Using Greek Tools Without Mastering Biblical Languages |date=2007 |publisher=Zondervan |isbn=978-0-310-28289-1 |page=289 |url=https://books.google.com/books?id=AF-5ptJ0l2gC&pg=PA289}}</ref> Between the 7th and 10th centuries CE a [[Masoretes|group of Jewish scribes]] formalized and expanded this to create the [[Masoretic Text#Numerical Masorah|Numerical Masorah]] to ensure accurate reproduction of the sacred text. It included counts of the number of words in a line, section, book and groups of books, noting the middle stich of a book, word use statistics, and commentary.<ref name="Jewish" /> Standards became such that a deviation in even a single letter in a Torah scroll was considered unacceptable.<ref>[[Mishneh Torah]], Tefillin, Mezuzah, and Sefer Torah, 1:2. Example English translation: {{cite book |title=The Rambam's Mishneh Torah |author=[[Eliyahu Touger]] |publisher=[[Moznaim Publishing Corporation]] |url=https://www.chabad.org/library/article_cdo/aid/925417/jewish/Tefillin-Mezuzah-and-Sefer-Torah-Chapter-One.htm}}</ref> The effectiveness of their error correction method was verified by the accuracy of copying through the centuries demonstrated by discovery of the [[Dead Sea Scrolls]] in 1947–1956, dating from {{Circa|150 BCE-75 CE}}.<ref>{{cite book |author=Brian M. Fagan |title=[[The Oxford Companion to Archaeology]] |section=Dead Sea Scrolls |publisher=[[Oxford University Press]] |date=5 December 1996 |isbn=0195076184}}</ref>

The modern development of [[error correction code]]s is credited to [[Richard Hamming]] in 1947.<ref name=Thompson>{{citation|first=Thomas M.|last=Thompson|title=From Error-Correcting Codes through Sphere Packings to Simple Groups|publisher=The Mathematical Association of America|year=1983|series=The Carus Mathematical Monographs (#21)|isbn=0-88385-023-0|page=vii}}</ref> A description of [[Hamming's code]] appeared in [[Claude Shannon]]'s ''A Mathematical Theory of Communication''<ref>{{citation|first=C.E.|last=Shannon|title=A Mathematical Theory of Communication|journal=Bell System Technical Journal|volume=27|issue=3|pages=379–423|year=1948|doi=10.1002/j.1538-7305.1948.tb01338.x|pmid=9230594|hdl=10338.dmlcz/101429|hdl-access=free}}</ref> and was quickly generalized by [[Marcel J. E. Golay]].<ref>{{citation|first=Marcel J. E.|last=Golay|title=Notes on Digital Coding|journal=Proc.I.R.E. (I.E.E.E.)|volume=37|year=1949|page=657}}</ref>