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Hee-Youl Kwak

Publications and source records attributed to Hee-Youl Kwak.

16 recordsLinked to original sources
arXiv2026

Logical Neural Belief Propagation for Linear-Complexity Decoding of Surface Codes

Quantum error correction (QEC) requires accurate and efficient decoders, yet belief propagation (BP), despite its linear decoding complexity, often provides insufficient logical accuracy on surface codes. We propose Logical Neural Belief Propagation (L-NBP), a BP-based neural decoder that redirects the decoding objective from physical-level to logical-level decoding. L-NBP uses a neural BP (NBP) module to produce posterior beliefs, which a logical classifier transforms into a continuous-valued soft syndrome for logical-operator prediction. Trained end-to-end by backpropagation, the NBP module learns soft syndromes that are favorable for logical classification. On surface codes, L-NBP matches or outperforms BP with ordered-statistics decoding (BP-OSD) and minimum-weight perfect matching (MWPM) while retaining the linear complexity of BP, and achieves a threshold of $17.5\%$ under depolarizing noise. Under circuit-level noise, L-NBP matches the accuracy of BP-OSD on the distance-$9$ surface code while requiring only $0.2\%$ of its complexity.

quant-ph↗
arXiv2026

WeaveMark: Robust and Scalable Multi-bit LLM Watermarking via Coded Payload Spreading

Multi-bit watermarking for large language models (LLMs) enables content source tracing by embedding user-identifiable messages into generated text. Existing methods face a fundamental trade-off among extraction accuracy, text quality, and payload capacity. We propose WeaveMark, a robust and scalable multi-bit LLM watermarking scheme based on coded payload spreading. WeaveMark shifts this trade-off frontier by improving payload capacity through multi-bit-per-token spreading, improving extraction accuracy through soft-decision error-correcting code, and preserving text quality through unbiased multilayer reweighting. It further introduces dedicated zero-bit layers for reliable watermark presence detection. Experiments show large gains, especially for long messages and edited text. WeaveMark achieves 89.8% match rate for 32-bit messages at 200 tokens, compared with 20.8% for BiMark. Under 10% substitution attacks on 16-bit messages at 200 tokens, it maintains 86.0% versus 30.7%, while preserving text quality. Our code is available at https://github.com/qkrrkd90-source/WeaveMark.

cs.CR↗
arXiv2026

Design of Outage-Limit-Approaching Protograph LDPC Codes via Generalized Rootchecks

This paper presents a new protograph-based LDPC code design framework that simultaneously achieves full diversity over block-fading channels (BFCs) and near-capacity performance over additive white Gaussian noise channels. By leveraging a Boolean approximation-based analysis-Diversity Evolution-we derive structural constraints with generalized rootchecks that guarantee full diversity. Building on these constraints, we propose a diversity-aligned protograph template tailored for the two-block BFC (M=2) that ensures full diversity under iterative belief propagation decoding. Furthermore, a genetic algorithm guided by density evolution is employed to optimize the protograph edges within this family for improved coding gain. The resulting codes, termed DA-GRP-LDPC codes, simultaneously achieve full diversity and enhanced coding gain, reaching a 0.8 dB gap to the outage limit for the two-block BFC at a block length of 16,896. This demonstrates that the proposed framework effectively bridges the gap between diversity optimality in non-ergodic channels and high coding gain in ergodic channels.

cs.IT↗
arXiv2026

Spectral-Aligned Pruning for Universal Error-Correcting Code Transformers

Universal channel decoders based on transformers-such as the Foundation Error Correction Code Transformer (FECCT)-achieve competitive decoding performance across diverse code families with a single shared backbone, optionally followed by code-specific finetuning. However, the high computational complexity and large parameter footprint of FECCT present substantial obstacles to practical deployment. To address these challenges, we investigate structured pruning for FECCT and propose Spectral-Aligned Pruning (SAP), a structure-aware framework that enables cross-code reuse of structured pruning masks by leveraging the spectrum of the corresponding bipartite graph. SAP is grounded in classical graph analysis of codes: the two algebraically largest adjacency eigenvalues provide compact spectral proxies for degree scale, expansion ratio, and minimum-distance lower bounds. These quantities are directly relevant to decoding performance: degree scale reflects how densely codeword bits and parity checks are connected; expansion ratio influences how information propagates across the bipartite graph; and minimum distance characterizes codeword separation. Based on this connection, SAP uses these two leading eigenvalues as a lightweight code signature for pruning-mask retrieval. Empirically, this two-dimensional signature yields stable library selection equivalent to higher-dimensional spectral signatures in our evaluation. After pruning, SAP performs per-code recovery via parameter-efficient low-rank adaptation (LoRA), enabling a shared pruned backbone while storing only small code-specific adapter parameters. Experiments across diverse codes show that SAP achieves decoding performance comparable to dedicated per-code pruning, while enabling substantial reductions in computational cost and model memory footprint through kernel-level structured pruning.

cs.IT↗
arXiv2026

Evolutionary BP+OSD Decoding for Low-Latency Quantum Error Correction

Quantum error correction (QEC) for fault-tolerant quantum computing requires a balanced decoding solution that offers high performance, low complexity, and low latency. However, the de facto standard, belief propagation (BP) combined with ordered statistics decoding (OSD), suffers from excessive iterations in the BP stage and high complexity in the OSD stage. To address these challenges, we propose an evolutionary BP (EBP) decoder optimized via a differential evolution (DE) algorithm. By leveraging the gradient-free nature of DE, we enable end-to-end optimization of the EBP+OSD structure to maximize overall performance. In addition, a multi-objective selection rule is introduced to suppress frequent OSD activation, significantly reducing complexity overhead. Experimental results on surface codes and quantum low-density parity-check (QLDPC) codes demonstrate that EBP plus OSD simultaneously achieves superior decoding performance and substantially lower complexity compared to conventional BP plus OSD, particularly in stringent low-latency regimes.

quant-ph↗
arXiv2026

Qubit-centric Transformer for Surface Code Decoding

For reliable large-scale quantum computation, quantum error correction (QEC) is essential to protect logical information distributed across multiple physical qubits. Taking advantage of recent advances in deep learning, neural network-based decoders have emerged as a promising approach to improve the reliability of QEC. We propose the qubit-centric transformer (QCT), a novel and universal QEC decoder based on a transformer architecture with a qubit-centric attention mechanism. Our decoder transforms input syndromes from the stabilizer domain into qubit-centric tokens via a specialized embedding strategy. These qubit-centric tokens are processed through attention layers to effectively identify the underlying logical error. Furthermore, we introduce a graph-based masking method that incorporates the topological structure of quantum codes, enforcing attention toward relevant qubit interactions. Across various code distances for surface codes, QCT achieves state-of-the-art decoding performance, significantly outperforming existing neural decoders and the belief propagation (BP) with ordered statistics decoding (OSD) baseline. Notably, QCT achieves a high threshold of 18.1% under depolarizing noise, which closely approaches the theoretical bound of 18.9% and surpasses both the BP+OSD and the minimum-weight perfect matching (MWPM) thresholds. This qubit-centric approach provides a scalable and robust framework for surface code decoding, advancing the path toward fault-tolerant quantum computing.

quant-ph↗
arXiv2026

5G LDPC Codes as Root LDPC Codes via Diversity Alignment

This paper studies the diversity of protographbased quasi-cyclic low-density parity-check (QC-LDPC) codes over nonergodic block-fading channels under iterative beliefpropagation decoding. We introduce diversity evolution (DivE), a Boolean-function-based analysis method that tracks how the fading dependence of belief-propagation messages evolves across decoding iterations. Under a Boolean approximation of block fading, DivE derives a Boolean fading function for each variable node (VN) output (i.e., the a-posteriori reliability after iterative decoding), from which the VN diversity order can be directly determined. Building on this insight, we develop a greedy blockmapping search that assigns protograph VNs to fading blocks so that all information VNs achieve full diversity, while including the minimum additional parity VNs when full diversity is infeasible at the nominal rate. Numerical results on the 5G New Radio LDPC codes show that the proposed search finds block mappings that guarantee full diversity for all information bits without modifying the base-graph structure, yielding a markedly steeper high-SNR slope and lower BLER than random mappings.

cs.IT↗
arXiv2026

Neural Window Decoder for SC-LDPC Codes

In this paper, we propose a neural window decoder (NWD) for spatially coupled low-density parity-check (SC-LDPC) codes. The proposed NWD retains the conventional window decoder (WD) process but incorporates trainable neural weights. To train the weights of NWD, we introduce two novel training strategies. First, we restrict the loss function to target variable nodes (VNs) of the window, which prunes the neural network and accordingly enhances training efficiency. Second, we employ the active learning technique with a normalized loss term to prevent the training process from biasing toward specific training regions. Next, we develop a systematic method to derive non-uniform schedules for the NWD based on the training results. We introduce trainable damping factors that reflect the relative importance of check node (CN) updates. By skipping updates with less importance, we can omit $\mathbf{41\%}$ of CN updates without performance degradation compared to the conventional WD. Lastly, we address the error propagation problem inherent in SC-LDPC codes by deploying a complementary weight set, which is activated when an error is detected in the previous window. This adaptive decoding strategy effectively mitigates error propagation without requiring modifications to the code and decoder structures.

cs.LG↗
arXiv2025

Lowering the Error Floor of Error Correction Code Transformer

With the success of transformer architectures across diverse applications, the error correction code transformer (ECCT) has gained significant attention for its superior decoding performance. In spite of its advantages, the error floor problem in ECCT decoding remains unexplored. We present the first investigation into this issue, revealing that ECCT encounters error floors, limiting its effectiveness in practical settings. To address this error floor problem, we adopt a hybrid decoding framework that integrates ECCT with conventional hard decision decoders. Unlike prior hybrid decoding schemes, our key contribution lies in proposing a novel loss function that explicitly takes into account the interaction between ECCT and hard decision decoders during training. The proposed loss function guides ECCT to focus on residual errors that are not corrected by the hard decision stages, effectively lowering the error floor. Simulation results confirm that the hybrid decoder trained with the proposed loss function achieves substantial performance gains over standard ECCT in both the waterfall and the error floor regions.

cs.IT↗
arXiv2025

Cross-Attention Message-Passing Transformers for Code-Agnostic Decoding in 6G Networks

Channel coding for 6G networks is expected to support a wide range of requirements arising from heterogeneous communication scenarios. These demands challenge traditional code-specific decoders, which lack the flexibility and scalability required for next-generation systems. To tackle this problem, we propose an AI-native foundation model for unified and code-agnostic decoding based on the transformer architecture. We first introduce a cross-attention message-passing transformer (CrossMPT). CrossMPT employs two masked cross-attention blocks that iteratively update two distinct input representations-magnitude and syndrome vectors-allowing the model to effectively learn the decoding problem. Notably, our CrossMPT has achieved state-of-the-art decoding performance among single neural decoders. Building on this, we develop foundation CrossMPT (FCrossMPT) by making the architecture invariant to code length, rate, and class, allowing a single trained model to decode a broad range of codes without retraining. To further enhance decoding performance, particularly for short blocklength codes, we propose CrossMPT ensemble decoder (CrossED), an ensemble decoder composed of multiple parallel CrossMPT blocks employing different parity-check matrices. This architecture can also serve as a foundation model, showing strong generalization across diverse code types. Overall, the proposed AI-native code-agnostic decoder offers flexibility, scalability, and high performance, presenting a promising direction to channel coding for 6G networks.

cs.IT↗
arXiv2024

Boosted Neural Decoders: Achieving Extreme Reliability of LDPC Codes for 6G Networks

Ensuring extremely high reliability in channel coding is essential for 6G networks. The next-generation of ultra-reliable and low-latency communications (xURLLC) scenario within 6G networks requires frame error rate (FER) below $10^{-9}$. However, low-density parity-check (LDPC) codes, the standard in 5G new radio (NR), encounter a challenge known as the error floor phenomenon, which hinders to achieve such low rates. To tackle this problem, we introduce an innovative solution: boosted neural min-sum (NMS) decoder. This decoder operates identically to conventional NMS decoders, but is trained by novel training methods including: i) boosting learning with uncorrected vectors, ii) block-wise training schedule to address the vanishing gradient issue, iii) dynamic weight sharing to minimize the number of trainable weights, iv) transfer learning to reduce the required sample count, and v) data augmentation to expedite the sampling process. Leveraging these training strategies, the boosted NMS decoder achieves the state-of-the art performance in reducing the error floor as well as superior waterfall performance. Remarkably, we fulfill the 6G xURLLC requirement for 5G LDPC codes without a severe error floor. Additionally, the boosted NMS decoder, once its weights are trained, can perform decoding without additional modules, making it highly practical for immediate application. The source code is available at https://github.com/ghy1228/LDPC_Error_Floor.

cs.IT↗
arXiv2024

CrossMPT: Cross-attention Message-Passing Transformer for Error Correcting Codes

Error correcting codes (ECCs) are indispensable for reliable transmission in communication systems. The recent advancements in deep learning have catalyzed the exploration of ECC decoders based on neural networks. Among these, transformer-based neural decoders have achieved state-of-the-art decoding performance. In this paper, we propose a novel Cross-attention Message-Passing Transformer (CrossMPT), which shares key operational principles with conventional message-passing decoders. While conventional transformer-based decoders employ self-attention mechanism without distinguishing between the types of input vectors (i.e., magnitude and syndrome vectors), CrossMPT updates the two types of input vectors separately and iteratively using two masked cross-attention blocks. The mask matrices are determined by the code's parity-check matrix, which explicitly captures the irrelevant relationship between two input vectors. Our experimental results show that CrossMPT significantly outperforms existing neural network-based decoders for various code classes. Notably, CrossMPT achieves this decoding performance improvement, while significantly reducing the memory usage, complexity, inference time, and training time.

cs.LG↗
arXiv2023

Boosting Learning for LDPC Codes to Improve the Error-Floor Performance

Low-density parity-check (LDPC) codes have been successfully commercialized in communication systems due to their strong error correction capabilities and simple decoding process. However, the error-floor phenomenon of LDPC codes, in which the error rate stops decreasing rapidly at a certain level, presents challenges for achieving extremely low error rates and deploying LDPC codes in scenarios demanding ultra-high reliability. In this work, we propose training methods for neural min-sum (NMS) decoders to eliminate the error-floor effect. First, by leveraging the boosting learning technique of ensemble networks, we divide the decoding network into two neural decoders and train the post decoder to be specialized for uncorrected words that the first decoder fails to correct. Secondly, to address the vanishing gradient issue in training, we introduce a block-wise training schedule that locally trains a block of weights while retraining the preceding block. Lastly, we show that assigning different weights to unsatisfied check nodes effectively lowers the error-floor with a minimal number of weights. By applying these training methods to standard LDPC codes, we achieve the best error-floor performance compared to other decoding methods. The proposed NMS decoder, optimized solely through novel training methods without additional modules, can be integrated into existing LDPC decoders without incurring extra hardware costs. The source code is available at https://github.com/ghy1228/LDPC_Error_Floor .

cs.IT↗
arXiv2023

How to Mask in Error Correction Code Transformer: Systematic and Double Masking

In communication and storage systems, error correction codes (ECCs) are pivotal in ensuring data reliability. As deep learning's applicability has broadened across diverse domains, there is a growing research focus on neural network-based decoders that outperform traditional decoding algorithms. Among these neural decoders, Error Correction Code Transformer (ECCT) has achieved the state-of-the-art performance, outperforming other methods by large margins. To further enhance the performance of ECCT, we propose two novel methods. First, leveraging the systematic encoding technique of ECCs, we introduce a new masking matrix for ECCT, aiming to improve the performance and reduce the computational complexity. Second, we propose a novel transformer architecture of ECCT called a double-masked ECCT. This architecture employs two different mask matrices in a parallel manner to learn more diverse features of the relationship between codeword bits in the masked self-attention blocks. Extensive simulation results show that the proposed double-masked ECCT outperforms the conventional ECCT, achieving the state-of-the-art decoding performance with significant margins.

cs.LG↗
arXiv2023

Iterative Soft Decoding Algorithm for DNA Storage Using Quality Score and Redecoding

Ever since deoxyribonucleic acid (DNA) was considered as a next-generation data-storage medium, lots of research efforts have been made to correct errors occurred during the synthesis, storage, and sequencing processes using error correcting codes (ECCs). Previous works on recovering the data from the sequenced DNA pool with errors have utilized hard decoding algorithms based on a majority decision rule. To improve the correction capability of ECCs and robustness of the DNA storage system, we propose a new iterative soft decoding algorithm, where soft information is obtained from FASTQ files and channel statistics. In particular, we propose a new formula for log-likelihood ratio (LLR) calculation using quality scores (Q-scores) and a redecoding method which may be suitable for the error correction and detection in the DNA sequencing area. Based on the widely adopted encoding scheme of the fountain code structure proposed by Erlich et al., we use three different sets of sequenced data to show consistency for the performance evaluation. The proposed soft decoding algorithm gives 2.3% ~ 7.0% improvement of the reading number reduction compared to the state-of-the-art decoding method and it is shown that it can deal with erroneous sequenced oligo reads with insertion and deletion errors.

cs.IT↗
arXiv2022

Construction of Protograph-Based Partially Doped Generalized LDPC Codes

A generalized low-density parity-check (GLDPC) code is a class of codes, where single parity check nodes in a conventional low-density parity-check (LDPC) code are replaced by linear codes with higher parity check constraints. In this paper, we introduce a new method of constructing GLDPC codes by inserting the generalized check nodes for partial doping. While the conventional protograph GLDPC code dopes the protograph check nodes by replacing them with the generalized check nodes, a new GLDPC code is constructed by adding the generalized check nodes and partially doping the selected variable nodes to possess higher degrees of freedom, called a partially doped GLDPC (PD-GLDPC) code. The proposed PD-GLDPC codes can make it possible to do more accurate extrinsic information transfer (EXIT) analysis and the doping granularity can become finer in terms of the protograph than the conventional GLDPC code. We also propose the constraint for the typical minimum distance of PD-GLDPC codes and prove that the PD-GLDPC codes satisfying this condition have the linear minimum distance growth property. Furthermore, we obtain the threshold optimized protograph for both regular and irregular ensembles of the proposed PD-GLDPC codes over the binary erasure channel (BEC). Specifically, we propose the construction algorithms for both regular and irregular protograph-based PD-GLDPC codes that enable the construction of GLDPC codes with higher rates than the conventional ones. The block error rate performance of the proposed PD-GLDPC code shows that it has a reasonably good waterfall performance with low error floor and outperforms other LDPC codes for the same code rate, code length, and degree distribution.

cs.IT↗