Protograph LDPC code[13] 


Binary version of a \(q\)-ary protograph LDPC code. Its parity check matrix can be put into the form of a block matrix consisting of either a sum of permutation sub-matrices or the zero sub-matrix.


The minimum distance of protograph codes is bounded by a function of the number of commuting permutation-matrix blocks [4].


For reviews on protograph LDPC codes, see Ref. [5].





Thorpe, Jeremy. "Low-density parity-check (LDPC) codes constructed from protographs." IPN progress report 42.154 (2003): 42-154.
D. Divsalar et al., “Protograph based LDPC codes with minimum distance linearly growing with block size”, GLOBECOM ’05. IEEE Global Telecommunications Conference, 2005. (2005) DOI
D. Divsalar, S. Dolinar, and C. Jones, “Protograph LDPC Codes over Burst Erasure Channels”, MILCOM 2006 (2006) DOI
D. J. C. MacKay and M. C. Davey, “Evaluation of Gallager Codes for Short Block Length and High Rate Applications”, Codes, Systems, and Graphical Models 113 (2001) DOI
Y. Fang et al., “A Survey on Protograph LDPC Codes and Their Applications”, IEEE Communications Surveys & Tutorials 17, 1989 (2015) DOI
D. G. M. Mitchell, R. Smarandache, and D. J. Costello, “Quasi-cyclic LDPC codes based on pre-lifted protographs”, 2011 IEEE Information Theory Workshop (2011) DOI
D. Divsalar et al., “Constructing LDPC codes from simple loop-free encoding modules”, IEEE International Conference on Communications, 2005. ICC 2005. 2005 DOI
A. Beemer et al., “A Generalized Algebraic Approach to Optimizing SC-LDPC Codes”, (2017) arXiv:1710.03619
C. A. Kelley, “On codes designed via algebraic lifts of graphs”, 2008 46th Annual Allerton Conference on Communication, Control, and Computing (2008) DOI
C. A. Kelley and J. L. Walker, “LDPC codes from voltage graphs”, 2008 IEEE International Symposium on Information Theory (2008) DOI
L. W. Beineke et al., editors , Topics in Topological Graph Theory (Cambridge University Press, 2009) DOI
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Zoo Code ID: protograph_ldpc

Cite as:
“Protograph LDPC code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.
@incollection{eczoo_protograph_ldpc, title={Protograph LDPC code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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“Protograph LDPC code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.