Description
LDPC code whose parity-check matrix is constructed by "spatially" coupling several copies of a regular LDPC parity-check matrix in chain-like fashion (or, more generally, in grid-like fashion) to yield a band matrix. A finite-length chain is then capped by imposing either open boundary conditions (yielding non-tail-biting SC-LDPC codes) or open boundary conditions (yielding tail-biting SC-LDPC codes); sometimes extra terminating vertices are added to the ends of the chain. Matrices corresponding to translationally invariant chains are called time-variant, and otherwise are called time-invariant. These codes can be constructed, e.g., using the lifting procedure or using edge-cutting vectors [6].
Protection
Rate
Spatial coupling of LDPC codes can increase the achievable rate against BEC, coming close to the capacity [1,4,9]. SC-LDPC codes achieve capacity of the binary memoryless symmetric (BMS) channel [10,11].
Parent
- Protograph LDPC code — SC-LDPC codes can be interpreted as protograph LDPC codes [12].
Cousins
- LDPC convolutional code (LDPC-CC) — Infinite-block versions of SC-LDPC are LDPC-CCs.
- Quantum spatially coupled (SC-QLDPC) code — SC-QLDPC code stabilizer-generator matrices have similar block form as the parity-check matrices of SC-LDPC codes.
References
- [1]
- A. Jimenez Felstrom and K. S. Zigangirov, “Time-varying periodic convolutional codes with low-density parity-check matrix”, IEEE Transactions on Information Theory 45, 2181 (1999) DOI
- [2]
- K. Engdahl, K. Sh. Zigangirov, “To the Theory of Low-Density Convolutional Codes. I”, Probl. Peredachi Inf., 35:4 (1999), 12–28; Problems Inform. Transmission, 35:4 (1999), 295–310
- [3]
- M. Lentmaier, D. V. Truhachev, and K. Sh. Zigangirov, Problems of Information Transmission 37, 288 (2001) DOI
- [4]
- S. Kudekar, T. J. Richardson, and R. L. Urbanke, “Threshold Saturation via Spatial Coupling: Why Convolutional LDPC Ensembles Perform So Well over the BEC”, IEEE Transactions on Information Theory 57, 803 (2011) DOI
- [5]
- S. Kudekar, T. Richardson, and R. L. Urbanke, “Spatially Coupled Ensembles Universally Achieve Capacity Under Belief Propagation”, IEEE Transactions on Information Theory 59, 7761 (2013) DOI
- [6]
- H. Esfahanizadeh, A. Hareedy, and L. Dolecek, “Finite-Length Construction of High Performance Spatially-Coupled Codes via Optimized Partitioning and Lifting”, IEEE Transactions on Communications 67, 3 (2019) DOI
- [7]
- N. ul Hassan, M. Lentmaier, and G. P. Fettweis, “Comparison of LDPC block and LDPC convolutional codes based on their decoding latency”, 2012 7th International Symposium on Turbo Codes and Iterative Information Processing (ISTC) (2012) DOI
- [8]
- D. J. Costello et al., “A Comparison of ARA- and Protograph-Based LDPC Block and Convolutional Codes”, 2007 Information Theory and Applications Workshop (2007) DOI
- [9]
- M. Lentmaier et al., “Terminated LDPC convolutional codes with thresholds close to capacity”, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005. (2005) arXiv:cs/0508030 DOI
- [10]
- S. Kudekar, T. Richardson, and R. Urbanke, “Spatially Coupled Ensembles Universally Achieve Capacity under Belief Propagation”, (2012) arXiv:1201.2999
- [11]
- S. Kumar et al., “Threshold Saturation for Spatially Coupled LDPC and LDGM Codes on BMS Channels”, IEEE Transactions on Information Theory 60, 7389 (2014) arXiv:1309.7543 DOI
- [12]
- A. Beemer et al., “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:
“Spatially coupled LDPC (SC-LDPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/sc_ldpc