Error-correcting codes with feedback: Difference between revisions

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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.<ref name="standard">See {{Harvnb|Deppe|2007}} and {{Harvnb|Hill|1995}}.</ref>

The main scenario imagined is the following. Suppose that Alice wishes to send a value ''x'' to Bob, but the communication channel between Alice and Bob is imperfect, and can introduce errors. An error-correcting code is a way of [[coding theory|encoding]] ''x'' as a message where Bob willswill successfully understand the value ''x'' even if the message Alice sends and the message Bob receives are not exactly the same. In an error-correcting code with feedback, the channel is two-way, where Bob can send feedback to Alice about the message he received.

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In an error-correcting code with '''noiselessnoiselesddf feedback''', the feedback the sender receives is always free of errors. In an error-correcting code with 'a''noisy feedback''', errors can occur in the feedback as well as in the message.

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An error-correcting code withwdwith noiseless feedback is equivalent to an adaptive [[search]]ing strategy with errors.<ref name="standard" />

In 1956 [[Claude Shannon]] introduced the 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 minimimum number of randomly chosen questions to determine the answer. In 1964 [[Elwyn Berlekamp]] considered in his dissertation error correcting codes with noiseless feedback.<ref>{{Harvnb|Deppe|2007}}.</ref>