Error-correcting code (ECC)


A code is a subset of a set or alphabet, with each element called a codeword. An error-correcting code consists of \(K\) codewords over an alphabet with \(N\) elements such that it is possible to recover the codewords from errors \(E\) from some error set \(\mathcal{E}\).


A code corrects errors associated with a noise channel if it is possible to recover any codeword after its coordinates have been changed after going through the channel. More technically, an error-correcting code \((u,\mathcal{E})\) is an encoder function \(u:[1\cdots K]\to[1\cdots N]\) with a set of correctable errors \(E:[1\cdots N]\to [1\cdots M]\) with the following property: there exists a decoder function \(d:[1\cdots M]\to [1\cdots K]\) such that for all \(E\in\cal{E}\) and states \(x\in[1\cdots K]\), \(d(E(e(x)))=x\).


The modern theory of error-correcting codes is rooted in the foundational work of C. Shannon [1], but error-correcting codes have been used prior to that work [2].



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Internal code ID: ecc

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Zoo Code ID: ecc

Cite as:
“Error-correcting code (ECC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.
@incollection{eczoo_ecc, title={Error-correcting code (ECC)}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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C. E. Shannon, “A Mathematical Theory of Communication”, Bell System Technical Journal 27, 379 (1948). DOI
A. Barg, “At the Dawn of the Theory of Codes”, The Mathematical Intelligencer 15, 20 (1993). DOI

Cite as:

“Error-correcting code (ECC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.