Parity-check code

Description

Also known as a sum-zero or even-weight code. An \([n,n-1,2]\) linear binary code whose codewords consist of the message string appended with a parity-check bit such that the parity (i.e., sum over all coordinates of each codeword) is zero. If the Hamming weight of a message is odd (even), then the parity bit is one (zero). This code requires only one extra bit of overhead and is therefore inexpensive.

Protection

This code cannot protect information, it can only detect 1-bit error.

Rate

The code rate is \(\frac{n}{n+1}\to 1\) as \(n\to\infty\).

Decoding

If the receiver finds that the parity information of a codeword disagrees with the parity bit, then the receiver will discard the information and request a resend.

Realizations

Can be realized on almost every communication device. Parity-check codes are some of the earlier error-correcting codes ([1], Ch. 27).

Parents

Cousins

References

[1]
Encyclopedia of Computer Science and Technology, Second Edition Volume I (CRC Press, 2017). DOI
[2]
T. R. Oenning and Jaekyun Moon, “A low-density generator matrix interpretation of parallel concatenated single bit parity codes”, IEEE Transactions on Magnetics 37, 737 (2001). DOI
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Zoo code information

Internal code ID: parity_check

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Zoo Code ID: parity_check

Cite as:
“Parity-check code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/parity_check
BibTeX:
@incollection{eczoo_parity_check, title={Parity-check code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/parity_check} }
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Permanent link:
https://errorcorrectionzoo.org/c/parity_check

Cite as:

“Parity-check code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/parity_check

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/bits/easy/parity_check.yml.