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Multi-edge LDPC code[1]

Description

Irregular LDPC code whose construction generalizes those of the original examples of irregular LDPC as well as RA codes.

Realizations

Quantum key distribution [2–4].

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
Low-density parity-check (LDPC) code\(q\)-ary LDPC Tanner Linear \(q\)-ary LRC Distributed-storage ECC
Parents
Low-density parity-check (LDPC) code
Multi-edge LDPC code
Children
Irregular LDPC code
The multi-edge code construction generalizes generalizes several of the original examples of irregular LDPC codes. Irregular LDPC codes can be formulated as multi-edge LDPC codes [1; Sec. XI].
Protograph LDPC code
LDPC codes based on protographs can be formulated as multi-edge LDPC codes [5].
Hsu-Anastasopoulos LDPC (HA-LDPC) code
HA-LDPC codes can be formulated as multi-edge LDPC codes [6].
MacKay-Neal LDPC (MN-LDPC) code
MN-LDPC codes can be formulated as multi-edge LDPC codes [6].

References

[1]
Richardson, Tom, and Rüdiger Urbanke. "Multi-edge type LDPC codes." Workshop honoring Prof. Bob McEliece on his 60th birthday, California Institute of Technology, Pasadena, California. 2002.
[2]
M. Milicevic, C. Feng, L. M. Zhang, and P. G. Gulak, “Quasi-cyclic multi-edge LDPC codes for long-distance quantum cryptography”, npj Quantum Information 4, (2018) arXiv:1702.07740 DOI
[3]
H. Mani, T. Gehring, P. Grabenweger, B. Ömer, C. Pacher, and U. L. Andersen, “Multiedge-type low-density parity-check codes for continuous-variable quantum key distribution”, Physical Review A 103, (2021) DOI
[4]
A. A. E. Hajomer, I. Derkach, R. Filip, U. L. Andersen, V. C. Usenko, and T. Gehring, “Continuous-variable quantum passive optical network”, Light: Science & Applications 13, (2024) arXiv:2402.16044 DOI
[5]
D. G. M. Mitchell, R. Smarandache, and D. J. Costello, “Quasi-cyclic LDPC codes based on pre-lifted protographs”, 2011 IEEE Information Theory Workshop 350 (2011) DOI
[6]
K. KASAI and K. SAKANIWA, “Spatially-Coupled MacKay-Neal Codes and Hsu-Anastasopoulos Codes”, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E94-A, 2161 (2011) arXiv:1102.4612 DOI
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Zoo Code ID: multi_edge_ldpc

Cite as:
“Multi-edge LDPC code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/multi_edge_ldpc
BibTeX:
@incollection{eczoo_multi_edge_ldpc, title={Multi-edge LDPC code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/multi_edge_ldpc} }
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Permanent link:
https://errorcorrectionzoo.org/c/multi_edge_ldpc

Cite as:

“Multi-edge LDPC code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/multi_edge_ldpc

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