Low-density generator-matrix (LDGM) code 

Description

Binary linear code with a sparse generator matrix. Alternatively, a member of an infinite family of \([n,k,d]\) codes for which the number of nonzero entries in each row and column of the generator matrix are both bounded by a constant as \(n\to\infty\). The dual of an LDGM code has a sparse parity-check matrix and is called an LDPC code.

Rate

Certain LDGM codes come close to achieving Shannon capacity [1].

Parents

Child

Cousins

References

[1]
J. Garcia-Frias and Wei Zhong, “Approaching Shannon performance by iterative decoding of linear codes with low-density generator matrix”, IEEE Communications Letters 7, 266 (2003) DOI
[2]
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
[3]
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: ldgm

Cite as:
“Low-density generator-matrix (LDGM) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/ldgm
BibTeX:
@incollection{eczoo_ldgm, title={Low-density generator-matrix (LDGM) code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/ldgm} }
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Cite as:

“Low-density generator-matrix (LDGM) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/ldgm

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