Margulis LDPC code[1] 

Description

Member of a class of LDPC codes deterministically constructed using a class of regular graphs with no short cycles. Related explicit LDPC constructions [2] utilize Ramanujan graphs [3,4].

Encoding

Efficient encoder improving over the original Gallager encoder [1].

Parents

References

[1]
G. A. Margulis, “Explicit constructions of graphs without short cycles and low density codes”, Combinatorica 2, 71 (1982) DOI
[2]
J. Rosenthal and P. O. Vontobel, “Constructions of regular and irregular LDPC codes using Ramanujan graphs and ideas from Margulis”, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252) DOI
[3]
A. Lubotzky, R. Phillips, and P. Sarnak, “Ramanujan graphs”, Combinatorica 8, 261 (1988) DOI
[4]
G. Davidoff, P. Sarnak, and A. Valette, Elementary Number Theory, Group Theory and Ramanujan Graphs (Cambridge University Press, 2001) DOI
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Zoo Code ID: margulis_ldpc

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

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/bits/tanner/regular_tanner/regular_ldpc/margulis_ldpc.yml.