Dealing with low-weight errors that lead BP OSD to fail
Abstract
Belief Propagation combined with Ordered Statistics Decoding (BP OSD) is an open-source decoding tool used widely within the community due to its versatility and ease of application to Quantum Low Density Parity Check (QLDPC) codes. However, the degeneracy of quantum codes has been observed to degrade the performance of BP OSD, particularly leading to error floors for low physical error rates. Here, we investigate the low-weight error configurations responsible for such failures in Bivariate Bicycle codes. We show that, at code capacity, BP OSD fails on errors whose weight is significantly smaller than d/2, arising from global symmetries of the decoding graph that prevent the convergence of parallel BP. Furthermore, our analysis reveals new pitfalls that can arise when analysing the performance of BP OSD in the rare events regime, such as loss of ergodicity in splitting methods and numerical instabilities in the decoder. We show how to mitigate these failure mechanisms by modifying the BP update rules and the decoder implementation, leading to substantial improvement in logical error rate.
Related
- Why 2D Models Fail to Capture Flow Properties in 3D Heterogeneous Media: A Connectivity Perspective
- Fail-closed conformal multiresolution error control for conservative three-dimensional dose remapping in synthetic phantoms
- ECDSA.Fail: Open Autoresearch for Optimizing Elliptic-Curve Point Addition in Shor's Algorithm
- Removal-angular-spectrum-guided targeted notch matching for suppressing MSF errors in oblique-incidence MJP
- Transfer-function-guided suppression of grinding-induced mid-spatial-frequency errors on single-crystal silicon
BibTeX
@misc{fregona2026dealing,
title = {{Dealing with low-weight errors that lead BP OSD to fail}},
author = {Giacomo Fregona and Matthias C. Löbl and Benjamin J. Brown and Michael J. Kastoryano and Stefano Paesani},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30305},
eprint = {2610.30305},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30305},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dealing with low-weight errors that lead BP OSD to fail
AU - Giacomo Fregona
AU - Matthias C. Löbl
AU - Benjamin J. Brown
AU - Michael J. Kastoryano
AU - Stefano Paesani
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30305
UR - https://arxiv.org/abs/2610.30305
AB - Belief Propagation combined with Ordered Statistics Decoding (BP OSD) is an open-source decoding tool used widely within the community due to its versatility and ease of application to Quantum Low Density Parity Check (QLDPC) codes. However, the degeneracy of quantum codes has been observed to degrade the performance of BP OSD, particularly leading to error floors for low physical error rates. Here, we investigate the low-weight error configurations responsible for such failures in Bivariate Bicycle codes. We show that, at code capacity, BP OSD fails on errors whose weight is significantly smaller than d/2, arising from global symmetries of the decoding graph that prevent the convergence of parallel BP. Furthermore, our analysis reveals new pitfalls that can arise when analysing the performance of BP OSD in the rare events regime, such as loss of ergodicity in splitting methods and numerical instabilities in the decoder. We show how to mitigate these failure mechanisms by modifying the BP update rules and the decoder implementation, leading to substantial improvement in logical error rate.
ER -