Single parity-check code

Description

An \([n,n-1,2]\) binary linear error-detecting code encoding an \(n\)-bit codeword into an \((n+1)\)-bit string. In this code, parity information of a codeword is sotred in an extra parity bit. If the Hamming weight of a codeword is odd, then its parity is 1. If the Hamming weight of a codeword is even, then its parity is 0. This code is inexpensive since it only requires an extra parity bit and a single parity check.

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 \(n\to\infty\). The code distance is 2.

Encoding

Concatenate the codeword with a parity bit which encodes the parity information of codeword.

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.

Parent

Cousin

Zoo code information

Internal code ID: single_parity_check

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Zoo Code ID: single_parity_check

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

Cite as:

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

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