Conflict-Free Color-Clustered Sequential Belief-Propagation Decoding of Quantum LDPC Codes via Reinforcement Learning
Abstract
Belief-propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes is attractive due to its low complexity and low latency, but it is often limited by short cycles, degeneracy, and convergence failures. Reinforcement-learning-based sequential BP decoding (RL-S) improves BP by learning a syndrome-dependent variable-node (VN) update order, but its VN-by-VN schedule has limited within-iteration parallelism. In this paper, we propose a conflict-free color-clustered extension of RL-S. We construct a VN conflict graph in which two VNs are adjacent if they share an X-type or Z-type check, and color this graph so that same-color VNs have disjoint check neighborhoods. This also prevents VNs from the same Tanner 4- or 6-cycle from being updated simultaneously. During decoding, the trained VN-level Q-table selects a seed VN, and all remaining VNs with the same color are updated in parallel using the same pre-batch messages. For the [[288,12,18]] bivariate-bicycle code over the depolarizing channel, our proposed decoder achieves block-error-rate performance close to VN-level RL-S while reducing the scheduling decisions from 288 VNs to 11 color classes per BP iteration.
Related
- Low-Latency Belief-Propagation Decoding of Quantum LDPC Codes with Reinforcement-Learned Scheduling
- Learned Parallel Bit-Flipping Sequential Belief Propagation Decoding of Quantum LDPC Codes
- Dithered Belief Propagation for Real-Time Quantum Memory Decoding
- Logical Neural Belief Propagation for Linear-Complexity Decoding of Surface Codes
- Sequential Automorphism Ensemble Decoding with Early Stopping
BibTeX
@misc{moradi2026conflictfree,
title = {{Conflict-Free Color-Clustered Sequential Belief-Propagation Decoding of Quantum LDPC Codes via Reinforcement Learning}},
author = {Mohsen Moradi and Taejoon Kim and Remi A. Chou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20236},
eprint = {2609.20236},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20236},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Conflict-Free Color-Clustered Sequential Belief-Propagation Decoding of Quantum LDPC Codes via Reinforcement Learning
AU - Mohsen Moradi
AU - Taejoon Kim
AU - Remi A. Chou
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.20236
UR - https://arxiv.org/abs/2609.20236
AB - Belief-propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes is attractive due to its low complexity and low latency, but it is often limited by short cycles, degeneracy, and convergence failures. Reinforcement-learning-based sequential BP decoding (RL-S) improves BP by learning a syndrome-dependent variable-node (VN) update order, but its VN-by-VN schedule has limited within-iteration parallelism. In this paper, we propose a conflict-free color-clustered extension of RL-S. We construct a VN conflict graph in which two VNs are adjacent if they share an X-type or Z-type check, and color this graph so that same-color VNs have disjoint check neighborhoods. This also prevents VNs from the same Tanner 4- or 6-cycle from being updated simultaneously. During decoding, the trained VN-level Q-table selects a seed VN, and all remaining VNs with the same color are updated in parallel using the same pre-batch messages. For the [[288,12,18]] bivariate-bicycle code over the depolarizing channel, our proposed decoder achieves block-error-rate performance close to VN-level RL-S while reducing the scheduling decisions from 288 VNs to 11 color classes per BP iteration.
ER -