Single parity-check (SPC) code 

Also known as Sum-zero code, Zero-sum code, Even-weight code.

Description

An \([n,n-1,2]\) linear binary code whose codewords consist of the message string appended with a parity-check bit or parity 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.Wagner's rule yields a procedure that is linear in \(n\) [1] (see [2; Sec. 29.7.2] for a description).

Realizations

Can be realized on almost every communication device. SPCs are some of the earliest error-correcting codes ([3], Ch. 27).

Parents

Cousins

References

[1]
R. Silverman and M. Balser, “Coding for constant-data-rate systems”, Transactions of the IRE Professional Group on Information Theory 4, 50 (1954) DOI
[2]
A. Lapidoth, A Foundation in Digital Communication (Cambridge University Press, 2017) DOI
[3]
Encyclopedia of Computer Science and Technology, Second Edition Volume I (CRC Press, 2017) DOI
[4]
M. Ergen, “Basics of Cellular Communication”, Mobile Broadband 19 (2008) DOI
[5]
P. Boyvalenkov, D. Danev, "Linear programming bounds." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
[6]
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
[7]
T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.
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Zoo Code ID: parity_check

Cite as:
“Single parity-check (SPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/parity_check
BibTeX:
@incollection{eczoo_parity_check, title={Single parity-check (SPC) 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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Cite as:

“Single parity-check (SPC) 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/edit/main/codes/classical/bits/easy/parity_check.yml.