Description
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.Protection
The minimum distance of protograph codes is bounded by a function of the number of commuting permutation-matrix blocks [5].Notes
For reviews on protograph LDPC codes, see Ref. [6].Cousin
- Algebraic LDPC code— Some deterministic protograph LDPC codes [7] can be obtained from the theory of voltage graphs [8,9].
Member of code lists
Primary Hierarchy
Low-density parity-check (LDPC) code\(q\)-ary LDPC Tanner Linear \(q\)-ary LRC Distributed-storage ECC
Parents
LDPC codes based on protographs can be formulated as multi-edge LDPC codes [10].
Protograph LDPC code
Children
ARA codes can be formulated as protograph LDPC codes [2].
IRA codes can be formulated as protograph LDPC codes [2].
RAA codes can be formulated as protograph LDPC codes [11].
Parity-check matrices of APM-LDPC codes can be put into block-diagonal form where the nonzero blocks are permutation matrices representing the affine permutation group \(\mathbb{Z}_r \rtimes \mathbb{Z}_r^{\times}\).
Parity-check matrices of QC-LDPC codes can be put into block-diagonal form where the nonzero blocks are permutation matrices representing a cyclic group.
SC-LDPC codes can be interpreted as protograph LDPC codes [12].
References
- [1]
- Thorpe, Jeremy. “Low-density parity-check (LDPC) codes constructed from protographs.” IPN progress report 42.154 (2003): 42-154.
- [2]
- D. Divsalar, C. Jones, S. Dolinar, and J. Thorpe, “Protograph based LDPC codes with minimum distance linearly growing with block size”, GLOBECOM ’05. IEEE Global Telecommunications Conference, 2005. 5 pp. (2005) DOI
- [3]
- D. Divsalar, S. Dolinar, and C. Jones, “Protograph LDPC Codes over Burst Erasure Channels”, MILCOM 2006 1 (2006) DOI
- [4]
- D. Divsalar, S. Dolinar, C. Jones, and K. Andrews, “Capacity-approaching protograph codes”, IEEE Journal on Selected Areas in Communications 27, 876 (2009) DOI
- [5]
- D. J. C. MacKay and M. C. Davey, “Evaluation of Gallager Codes for Short Block Length and High Rate Applications”, The IMA Volumes in Mathematics and its Applications 113 (2001) DOI
- [6]
- Y. Fang, G. Bi, Y. L. Guan, and F. C. M. Lau, “A Survey on Protograph LDPC Codes and Their Applications”, IEEE Communications Surveys & Tutorials 17, 1989 (2015) DOI
- [7]
- C. A. Kelley, “On codes designed via algebraic lifts of graphs”, 2008 46th Annual Allerton Conference on Communication, Control, and Computing 1254 (2008) DOI
- [8]
- C. A. Kelley and J. L. Walker, “LDPC codes from voltage graphs”, 2008 IEEE International Symposium on Information Theory 792 (2008) DOI
- [9]
- L. W. Beineke, R. J. Wilson, J. L. Gross, and T. W. Tucker, editors , Topics in Topological Graph Theory (Cambridge University Press, 2009) DOI
- [10]
- 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
- [11]
- D. Divsalar, S. Dolinar, J. Thorpe, and C. Jones, “Constructing LDPC codes from simple loop-free encoding modules”, IEEE International Conference on Communications, 2005. ICC 2005. 2005 1, 658 DOI
- [12]
- A. Beemer, S. Habib, C. A. Kelley, and J. Kliewer, “A Generalized Algebraic Approach to Optimizing SC-LDPC Codes”, (2017) arXiv:1710.03619
Page edit log
- Victor V. Albert (2023-05-04) — most recent
Cite as:
“Protograph LDPC code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/protograph_ldpc