seeded bp decoding

To address the high latency and computational complexity of BP-OSD decoding for quantum LDPC codes, this paper proposes a lightweight fully parallel BP decoder. Methodologically, it eliminates external auxiliary algorithms and instead innovatively exploits oscillatory behavior in BP iterations to statistically identify unreliable bits; inspired by Chase decoding, it generates test patterns for efficient speculative post-processing—all operations are fully parallelized. Compared to BP-OSD, the proposed decoder significantly reduces latency and hardware complexity while achieving comparable or superior logical error rates across various bicyclic quantum LDPC codes. The key contribution is the first direct utilization of BP oscillation characteristics for reliability assessment and post-processing triggering—without incurring additional algorithmic overhead—thereby achieving high performance, low latency, and strong hardware efficiency.

This work addresses the challenge of efficiently decoding conventional BCH codes, whose dense parity-check matrices hinder high-performance iterative decoding in modern communication systems. The authors propose a quasi-belief propagation decoder that integrates prior knowledge—including channel noise variance, cyclic code structure, and parity redundancy—and, for the first time, extends extrinsic information transfer (EXIT) chart analysis to parameter optimization for high-density parity-check codes. Convergence is accelerated through novel message expansion and merging mechanisms, while mutual information evolution analysis enables efficient parallel decoding. Experimental results demonstrate that the proposed method significantly improves BCH code performance across various code rates and lengths, closely approaching that of LDPC codes with equivalent parameters, thereby confirming its generality and robustness.

Short-length LDPC codes suffer from poor convergence under belief propagation (BP) decoding, primarily due to a small number of error-prone variable nodes (VNs) that trigger decoding failure. Method: We propose a learnable multi-round BP (MRBP) decoding framework that unifies VN selection and channel error estimation—inspired by syndrome-based neural decoding. A lightweight neural network is designed to directly predict vulnerable VNs from the syndrome and node-wise reliability metrics, enabling end-to-end learning of targeted perturbations. Contribution/Results: Unlike existing MRBP methods relying on handcrafted heuristics, our approach significantly reduces the number of decoding iterations required to approach maximum-likelihood performance. On short codes (e.g., blocklengths N = 128–256), it improves decoding success probability by one to two orders of magnitude, without increasing per-iteration computational complexity.

Quantum low-density parity-check (QLDPC) codes suffer from degeneracy-induced stagnation and slow convergence under standard belief propagation (BP) decoding, preventing attainment of the theoretical distance bound. To address this, we propose Restarted Belief Propagation (RB), a novel BP-based decoder that integrates branch-and-bound optimization principles into the BP framework: it dynamically reinitializes node beliefs during iterations to actively escape degeneracy-driven local minima. RB preserves BP’s hardware efficiency—requiring no auxiliary codes or structural modifications. Experiments across diverse QLDPC code families demonstrate that RB achieves both the fastest convergence and highest error-correction accuracy among existing BP variants, yielding significantly lower logical error rates. Notably, RB is the first BP-style decoder to stably approach the code distance limit under generic settings. This work establishes RB as the state-of-the-art general-purpose BP decoder for practical quantum error correction.

Short-length LDPC codes under belief propagation (BP) decoding are prone to finite-length graph effects, often leading to erroneous or oscillatory decoding trajectories that limit performance. This work proposes a row-based enhancement (RBE) decoding method that introduces effective decoding diversity with minimal overhead by selectively amplifying outgoing messages from only a few parity-check rows, without modifying the parity-check matrix, scheduling strategy, or subcode structure. RBE represents the first efficient ensemble decoding approach based on partial row message enhancement, enabling flexible trade-offs between performance and complexity. On the 5G NR BG1 (144,96) code, a 32-member RBE ensemble reduces the BP-20 frame error rate from 1.6×10⁻² to 1.6×10⁻³ at Eb/N₀ = 4.0 dB, outperforming ensemble schemes of comparable size based on saturated min-sum and affine subcodes, while maintaining consistent gains across various code lengths, rates, and scheduling strategies.

This work addresses the high decoding complexity and suboptimal performance of conventional belief propagation (BP) decoding for BCH codes compared to LDPC codes. The authors propose a quasi-BP decoding framework that integrates code automorphism structures with an optimized redundant parity-check matrix and, for the first time, embeds a lightweight convolutional neural network into check nodes to replace the computationally intensive tanh and inverse-tanh operations. A triple-constraint loss function is designed to enforce non-negativity and order consistency in the outputs, enabling seamless concatenation with ordered statistics decoding. Experiments on three BCH codes demonstrate that the proposed method achieves performance within approximately 0.25 dB of the maximum-likelihood bound—comparable to LDPC codes of similar blocklength—while the neural-network-based variant incurs negligible performance loss, supporting efficient hardware implementation.

This work addresses the performance limitations of conventional belief propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes by introducing, for the first time, a classical multi-basis BP framework into the quantum domain. By decomposing the Tanner graph into acyclic subtrees, the method constructs multiple redundant parity-check representations to generate structured decoding diversity, enabling efficient list decoding through parallel BP executions. The approach retains linear time complexity and avoids superlinear post-processing overhead. Evaluated on [[144,12,12]] and [[288,12,18]] QLDPC codes, it significantly outperforms existing BP-based decoders, achieving up to 20% and 30% lower error rates compared to BPGD and BP-OSD, respectively, while requiring fewer total BP iterations.

This work addresses the limitations of conventional LDPC code design under iterative decoding—namely, combinatorial optimization difficulty, high computational cost, and complex parameter tuning—by proposing a deterministic gradient-based end-to-end optimization framework. The approach operates in a relaxed protograph space, modeling protograph elements as probabilities of being one, and introduces for the first time a differentiable density evolution (DE) model whose average performance is equivalent to that of the corresponding ensemble of binary protographs. Using DE-based bit error rate as the loss function enables efficient training without Monte Carlo estimation or line search. Combined with quantized DE and gradient optimization, the method significantly enhances design efficiency. Under min-sum decoding, the resulting long-block-length protographs outperform 5G LDPC codes of the same dimension and exhibit fast, reliable convergence.

This work addresses the degradation errors in iterative decoding of QLDPC codes caused by classical trapping sets and symmetric stabilizers. To mitigate this issue, the authors propose a multi-stage backtracking decoding framework that leverages internal dynamics from belief propagation decoders to construct a composite suspicious-node ranking metric. This metric identifies unreliable variable nodes whose initial log-likelihood ratios are then reset. The framework efficiently explores corrected configurations through beam search, enhanced with pruning strategies based on residual check weights and posterior reliability, and further augmented by ordered statistics decoding. Experimental results demonstrate that the proposed scheme significantly outperforms normalized min-sum decoding in terms of logical error rate and achieves performance comparable to belief propagation combined with tenth-order ordered statistics decoding.

Quantum LDPC codes suffer from degraded performance under belief propagation (BP) decoding due to short cycles and degeneracy in their Tanner graphs. This work proposes a general auxiliary node framework that introduces auxiliary variable and check nodes into the decoding graph of CSS quantum codes, thereby enhancing the design flexibility of the graphical structure. The framework unifies and extends existing techniques such as four-cycle elimination and subcode integration, enabling efficient BP decoding under circuit-level noise. The resulting graph-derived subcode-integrated decoder substantially reduces the logical error rate per decoding round and outperforms conventional BP decoding on four-cycle-free graphs.