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Generalized Gallager code[1]

Description

A LDPC code that generalizes the Gallager codes using the Tanner construction. While Gallager-code parity-check matrices consist of repetition-code submatrices that are randomly permuted, generalized Gallager-code matrices instead use more general binary linear component codes.

Member of code lists

Primary Hierarchy

Classical Domain
Binary Kingdom
Binary codeECC
Binary group-orbit codeECC
Linear binary codeLinear \(q\)-ary Linear code over \(\mathbb{Z}_q\) ECC
Regular binary Tanner codeTanner Linear \(q\)-ary ECC
Parents
Regular binary Tanner code
Generalized Gallager code
Children
Gallager (GL) code

References

[1]
J. Boutros, O. Pothier, and G. Zemor, “Generalized low density (Tanner) codes”, 1999 IEEE International Conference on Communications (Cat. No. 99CH36311) 441 DOI
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Zoo Code ID: generalized_gallager

Cite as:
“Generalized Gallager code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/generalized_gallager, arXiv:2606.11484
BibTeX:
@incollection{eczoo_generalized_gallager,
title={Generalized Gallager code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/generalized_gallager}
}
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Permanent link:
https://errorcorrectionzoo.org/c/generalized_gallager

Cite as:

“Generalized Gallager code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/generalized_gallager, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/tanner/regular_tanner/generalized_gallager.yml.