Informed Dynamic Scheduling for QLDPC Codes

Tzu-Hsuan Huang; Yeong-Luh Ueng

doi:10.22331/q-2026-01-16-1967

Informed Dynamic Scheduling for QLDPC Codes

¹Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan
²Department of Electrical Engineering & Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan

Published:	2026-01-16, volume 10, page 1967
Editor:	Narayanan Rengaswamy
Eprint:	arXiv:2410.01197v2
Doi:	https://doi.org/10.22331/q-2026-01-16-1967
Citation:	Quantum 10, 1967 (2026).

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Abstract

Recent research has shown that syndrome-based belief propagation using layered scheduling (sLBP) can not only accelerate the convergence rate but also improve the error rate performance by breaking the quantum trapping sets for quantum low-density parity-check (QLDPC) codes, showcasing a result distinct from classical error correction codes. In this paper, we consider edge-wise informed dynamic scheduling (IDS) for QLDPC codes based on syndrome-based residual belief propagation (sRBP). However, the construction of QLDPC codes and the identical prior intrinsic information assignment will result in an equal residual in many edges, causing a performance limitation for sRBP. Two heuristic strategies, including edge pool design and error pre-correction, are introduced to tackle this obstacle and quantum trapping sets. Then, a novel sRBP equipped with a predict-and-reduce-error mechanism (PRE-sRBP) is proposed, which can provide over one order of performance gain on the considered bicycle codes and symmetric hypergraph (HP) code under similar iterations compared to sLBP.

► BibTeX data

@article{Huang2026informeddynamic,
  doi = {10.22331/q-2026-01-16-1967},
  url = {https://doi.org/10.22331/q-2026-01-16-1967},
  title = {Informed {D}ynamic {S}cheduling for {QLDPC} {C}odes},
  author = {Huang, Tzu-Hsuan and Ueng, Yeong-Luh},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {1967},
  month = jan,
  year = {2026}
}

► References

[1] Nikolas P. Breuckmann and Jens Niklas Eberhardt. ``Quantum low-density parity-check codes''. PRX Quantum 2, 040101 (2021).
https://doi.org/10.1103/PRXQuantum.2.040101

[2] Maxime A. Tremblay, Nicolas Delfosse, and Michael E. Beverland. ``Constant-overhead quantum error correction with thin planar connectivity''. Phys. Rev. Lett. 129, 050504 (2022).
https://doi.org/10.1103/PhysRevLett.129.050504

[3] Sergey Bravyi, Andrew W. Cross, Dmitri Maslov Jay M. Gambetta, Patrick Rall, and Theodore J. Yoder. ``High-threshold and low-overhead fault-tolerant quantum memory''. Nature 627, 778 (2024).
https://doi.org/10.1038/s41586-024-07107-7

[4] Michael A. Nielsen and Isaac L. Chuang. ``Quantum computation and quantum information''. Cambridge University Press. (2009). 10th Anniversary edition.
https://doi.org/10.1017/cbo9780511976667

[5] A.R. Calderbank, E.M. Rains, P.M. Shor, and N.J.A. Sloane. ``Quantum error correction via codes over GF(4)''. IEEE Transactions on Information Theory 44, 1369 (1998).
https://doi.org/10.1109/18.681315

[6] D.J.C. MacKay, G. Mitchison, and P.L. McFadden. ``Sparse-graph codes for quantum error correction''. IEEE Transactions on Information Theory 50, 2315–2330 (2004).
https://doi.org/10.1109/TIT.2004.834737

[7] David Poulin and Yeojin Chung. ``On the iterative decoding of sparse quantum codes''. Quant. Inf. Comput. 8, 0987–1000 (2008).
https://doi.org/10.26421/QIC8.10-8

[8] Nithin Raveendran and Bane Vasić. ``Trapping sets of quantum LDPC codes''. Quantum 5 (2021).
https://doi.org/10.22331/q-2021-10-14-562

[9] Pavel Panteleev and Gleb Kalachev. ``Degenerate quantum LDPC codes with good finite length performance''. Quantum 5, 585 (2021).
https://doi.org/10.22331/q-2021-11-22-585

[10] Joschka Roffe, David R. White, Simon Burton, and Earl Campbell. ``Decoding across the quantum low-density parity-check code landscape''. Phys. Rev. Res. 2, 043423 (2020).
https://doi.org/10.1103/PhysRevResearch.2.043423

[11] Javier Valls, Francisco Garcia-Herrero, Nithin Raveendran, and Bane Vasić. ``Syndrome-based min-sum vs OSD-0 decoders: FPGA implementation and analysis for quantum ldpc codes''. IEEE Access 9, 138734–138743 (2021).
https://doi.org/10.1109/ACCESS.2021.3118544

[12] Andres I. Vila Casado, Miguel Griot, and Richard Wesel. ``Improving LDPC decoders via informed dynamic scheduling''. In Information Theory Workshop. Pages 208–213. (2007).
https://doi.org/10.1109/ITW.2007.4313075

[13] Gal Elidan, Ian McGraw, and Daphne Koller. ``Residual belief propagation: Informed scheduling for asynchronous message passing'' (2012). arXiv:1206.6837.
arXiv:1206.6837

[14] A. I. V. Casado, M. Griot, and R. D. Wesel. ``Informed dynamic scheduling for belief-propagation decoding of LDPC codes''. In 2007 IEEE International Conference on Communications. Pages 932–937. (2007).
https://doi.org/10.1109/ICC.2007.158

[15] Andres I. Vila Casado, Miguel Griot, and Richard D. Wesel. ``LDPC decoders with informed dynamic scheduling''. IEEE Transactions on Communications 58, 3470–3479 (2010).
https://doi.org/10.1109/TCOMM.2010.101910.070303

[16] Tofar C.-Y. Chang, Pin-Han Wang, Jian-Jia Weng, I-Hsiang Lee, and Yu T. Su. ``Belief-propagation decoding of LDPC codes with variable node–centric dynamic schedules''. IEEE Transactions on Communications 69, 5014–5027 (2021).
https://doi.org/10.1109/TCOMM.2021.3078776

[17] Jean-Pierre Tillich and Gilles Zémor. ``Quantum ldpc codes with positive rate and minimum distance proportional to the square root of the blocklength''. IEEE Transactions on Information Theory 60, 1193–1202 (2014).
https://doi.org/10.1109/TIT.2013.2292061

[18] Daniel Eric Gottesman. ``Stabilizer codes and quantum error correction''. PhD thesis. California Institute of Technology. (1997).
https://doi.org/10.7907/rzr7-dt72

[19] Richard Cleve. ``Quantum stabilizer codes and classical linear codes''. Phys. Rev. A 55, 4054–4059 (1997).
https://doi.org/10.1103/PhysRevA.55.4054

[20] A. R. Calderbank and Peter W. Shor. ``Good quantum error-correcting codes exist''. Phys. Rev. A 54, 1098–1105 (1996).
https://doi.org/10.1103/PhysRevA.54.1098

[21] A. M. Steane. ``Error correcting codes in quantum theory''. Phys. Rev. Lett. 77, 793–797 (1996).
https://doi.org/10.1103/PhysRevLett.77.793

[22] Emanuel Knill and Raymond Laflamme. ``Theory of quantum error-correcting codes''. Phys. Rev. A 55, 900–911 (1997).
https://doi.org/10.1103/PhysRevA.55.900

[23] F.R. Kschischang, B.J. Frey, and H.-A. Loeliger. ``Factor graphs and the sum-product algorithm''. IEEE Transactions on Information Theory 47, 498–519 (2001).
https://doi.org/10.1109/18.910572

[24] D. J. C. MacKay. ``Information theory, inference and learning algorithms''. Cambridge University Press. (2003).

[25] Ching-Yi Lai and Kao-Yueh Kuo. ``Log-domain decoding of quantum LDPC codes over binary finite fields''. IEEE Transactions on Quantum Engineering 2, 1–15 (2021).
https://doi.org/10.1109/TQE.2021.3113936

[26] Tom Richardson. ``Error floors of LDPC codes''. Proc. annual Allerton conference on commun. control and computing (2003).

[27] D.E. Hocevar. ``A reduced complexity decoder architecture via layered decoding of LDPC codes''. In IEEE Workshop onSignal Processing Systems, 2004. SIPS 2004. Pages 107–112. (2004).
https://doi.org/10.1109/SIPS.2004.1363033

[28] Juntan Zhang and M.P.C. Fossorier. ``Shuffled iterative decoding''. IEEE Transactions on Communications 53, 209–213 (2005).
https://doi.org/10.1109/TCOMM.2004.841982

[29] J. Chen and M.P.C. Fossorier. ``Density evolution for two improved BP-based decoding algorithms of LDPC codes''. IEEE Communications Letters 6, 208–210 (2002).
https://doi.org/10.1109/4234.1001666

[30] 3GPP. ``5G; NR; multiplexing and channel coding (release 15) 38.212''. document Technical specification (TS) (2018).

[31] Xingcheng Liu, Zhenzhu Zhou, Ru Cui, and Erwu Liu. ``Informed decoding algorithms of LDPC codes based on dynamic selection strategy''. IEEE Transactions on Communications 64, 1357–1366 (2016).
https://doi.org/10.1109/TCOMM.2016.2527642

[32] Xingcheng Liu, Chunlei Fan, and Xuechen Chen. ``Dynamic scheduling decoding of LDPC codes based on Tabu search''. IEEE Transactions on Communications 65, 4612–4621 (2017).
https://doi.org/10.1109/TCOMM.2017.2732950

[33] Xingcheng Liu, Li'e Zi, Dong Yang, and Zhongfeng Wang. ``Improved decoding algorithms of LDPC codes based on reliability metrics of variable nodes''. IEEE Access (2019).
https://doi.org/10.1109/ACCESS.2019.2904173

[34] R. Gallager. ``Low-density parity-check codes''. IRE Transactions on Information Theory 8, 21–28 (1962).
https://doi.org/10.1109/TIT.1962.1057683

[35] Tzu-Hsuan Huang. ``PRE-sRBP''. https://github.com/quantumrbp/srbp.git (2026).
https://github.com/quantumrbp/srbp.git

[36] Nedeljko Varnica, Marc P. C. Fossorier, and Aleksandar Kavcic. ``Augmented belief propagation decoding of low-density parity check codes''. IEEE Transactions on Communications 55, 1308–1317 (2007).
https://doi.org/10.1109/TCOMM.2007.900611

[37] D. Chase. ``Class of algorithms for decoding block codes with channel measurement information''. IEEE Transactions on Information Theory 18, 170–182 (1972).
https://doi.org/10.1109/TIT.1972.1054746

[38] Joschka Roffe. ``LDPC: Python tools for low density parity check codes''. https://pypi.org/project/ldpc/ (2022).
https://pypi.org/project/ldpc/

[39] Tzu-Hsuan Huang and Yeong-Luh Ueng. ``A binary BP decoding using posterior adjustment for quantum LDPC codes''. In ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Pages 9001–9005. (2024).
https://doi.org/10.1109/ICASSP48485.2024.10446153

[40] H. Yao, W. A. Laban, C. Hager, A. G. i Amat, and H. D. Pfister. ``Belief propagation decoding of quantum LDPC codes with guided decimation'' (2023). arXiv:2312.10950.
arXiv:2312.10950

[41] Julien Du Crest, Francisco Garcia-Herrero, Mehdi Mhalla, Valentin Savin, and Javier Valls. ``Layered decoding of quantum ldpc codes''. In 2023 12th International Symposium on Topics in Coding (ISTC). Pages 1–5. (2023).
https://doi.org/10.1109/ISTC57237.2023.10273477

[42] Adam Holmes, Mohammad Reza Jokar, Ghasem Pasandi, Yongshan Ding, Massoud Pedram, and Frederic T. Chong. ``Nisq+: Boosting quantum computing power by approximating quantum error correction''. In 2020 ACM/IEEE 47th Annual International Symposium on Computer Architecture (ISCA). Pages 556–569. (2020).
https://doi.org/10.1109/ISCA45697.2020.00053

[43] Kao-Yueh Kuo and Ching-Yi Lai. ``Refined belief propagation decoding of sparse-graph quantum codes''. IEEE Journal on Selected Areas in Information Theory 1, 487–498 (2020).
https://doi.org/10.1109/JSAIT.2020.3011758

Cited by

[1] Dimitris Chytas, Nithin Raveendran, and Bane Vasic, "Enhanced Min-Sum Decoding of Quantum Codes Using Previous Iteration Dynamics", arXiv:2501.05021, (2025).

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