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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 code|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>
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All error-detection and correction schemes add some [[Redundancy (information theory)|redundancy]] (i.e., some extra data) to a message, which receivers can use to check consistency of the delivered message and to recover data that has been determined to be corrupted. Error detection and correction schemes can be either [[systematic code|systematic]] or non-systematic. In a systematic scheme, the transmitter sends the original (error-free) data and attaches a fixed number of ''check bits'' (or ''parity data''), which are derived from the data bits by some encoding algorithm. If error detection is required, a receiver can simply apply the same algorithm to the received data bits and compare its output with the received check bits; if the values do not match, an error has occurred at some point during the transmission. If error correction is required, a receiver can apply the decoding algorithm to the received data bits and the received check bits to recover the original error-free data. In a system that uses a non-systematic code, the original message is transformed into an encoded message carrying the same information and that has at least as many bits as the original message.
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If the channel characteristics cannot be determined, or are highly variable, an error-detection scheme may be combined with a system for retransmissions of erroneous data. This is known as [[automatic repeat request]] (ARQ), and is most notably used in the Internet. An alternate approach for error control is [[hybrid automatic repeat request]] (HARQ), which is a combination of ARQ and error-correction coding.
== Types of error correction ==
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