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Created page with "In mathematics, computer science, telecommunication, information theory, and searching theory, '''error-correcting codes with feedback''' refers to error..."

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In [[mathematics]], [[computer science]], [[telecommunication]], [[information theory]], and [[searching theory]], '''error-correcting codes with feedback''' refers to [[error correcting codes]] designed to work in the presence of feedback from the receiver to the sender.

== Problem ==

Alice (the sender) wishes to send a value ''x'' to Bob (the receiver). The communication channel between Alice and Bob is imperfect, and can introduce errors.

== Solution ==
An error-correcting code is a way of [[coding theory|encoding]] ''x'' as a message such that Bob will successfully understand the value ''x'' as intended by Alice, even if the message Alice sends and the message Bob receives differ. In an error-correcting code with feedback, the channel is [[Two-way communication|two-way]]: Bob can send feedback to Alice about the message he received.

== Noisy feedback ==
In an error-correcting code without '''noisy feedback''', the feedback received by the sender is always free of errors. In an error-correcting code with '''noisy feedback''', errors can occur in the feedback, as well as in the message.

An error-correcting code with '''noiseless feedback''' is equivalent to an [[Adaptive algorithm|adaptive]] [[search algorithm|search]] strategy with errors.

== History ==
In 1956, [[Claude Shannon]] introduced the [[Discrete signal|discrete]] [[memoryless]] channel with noiseless feedback. In 1961, [[Alfréd Rényi]] introduced the [[Bar-Kochba game]] (also known as [[Twenty questions]]), with a given percentage of wrong answers, and calculated the minimum number of randomly chosen questions to determine the answer.

In his 1964 dissertation, [[Elwyn Berlekamp]] considered error correcting codes with noiseless feedback. In Berlekamp's scenario, the receiver chose a subset of possible messages and asked the sender whether the given message was in this subset, a 'yes' or 'no' answer. Based on this answer, the receiver then chose a new subset and repeated the process. The game is further complicated due to noise; some of the answers will be wrong.

==Sources==
* .
* .

==Source==

[http://wikipedia.org/ http://wikipedia.org/]
[[Category:Error-correcting codes]]
==See Also on BitcoinWiki==
* [[Attrace]]
* [[Asura Coin]]
* [[Cloudbric]]
* [[Bitbose]]
* [[ZeroBank]]

Error-correcting codes with feedback - Revision history

Admin: Created page with "In mathematics, computer science, telecommunication, information theory, and searching theory, '''error-correcting codes with feedback''' refers to error..."