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IEEE International Symposium on Information Theory (ISIT)

Dynamic Dual-Window Decoding for SC-LDPC Codes with Wave Enhancement

Leyu Zhang, Yuqing Ren, Andreas Peter Burg

Published Jun 1, 2026• 0 citations
Publisher

Abstract

Windowed decoding (WD) based on the belief propagation (BP) algorithm, which slides along a code chain with fixed computational resources, is an efficient decoding scheme for spatially-coupled low-density parity-check (SC-LDPC) codes, particularly for long-length codes. However, due to the lack of decoding waves, WD suffers from a performance degradation compared to full BP decoding. In this paper, we propose a novel decoding schedule for WD, termed dual-WD, which enhances the decoding waves by dynamically merging and splitting two decoding windows that slide in opposite directions. Moreover, a sliding-step selection method based on partial syndrome checks is introduced to reduce decoding complexity. Simulation results demonstrate that the proposed dual-WD outperforms the conventional WD schemes under identical computational complexity constraints, thereby narrowing the performance gap between WD and full BP decoding.

DOI
10.1109/isit62367.2026.11654081

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Windowed decoding (WD) based on the belief propagation (BP) algorithm, which slides along a code chain with fixed computational resources, is an efficient decoding scheme for spatially-coupled low-density parity-check (SC-LDPC) codes, particularly for long-length codes. However, due to the lack of decoding waves, WD suffers from a performance degradation compared to full BP decoding. In this paper, we propose a novel decoding schedule for WD, termed dual-WD, which enhances the decoding waves by dynamically merging and splitting two decoding windows that slide in opposite directions. Moreover, a sliding-step selection method based on partial syndrome checks is introduced to reduce decoding complexity. Simulation results demonstrate that the proposed dual-WD outperforms the conventional WD schemes under identical computational complexity constraints, thereby narrowing the performance gap between WD and full BP decoding.
In this letter, we propose a reliability-based windowed decoding scheme for spatially coupled (SC) low-density parity-check (LDPC) codes. To mitigate the error propagation along the sliding windowed decoder of the SC LDPC codes, a partial message reservation method is proposed where only the reliable messages generated in the previous decoding window are reserved for the next decoding window. We also propose a partial syndrome check stopping rule for each decoding window, in which only the complete variable nodes are checked. Simulation results show that our proposed scheme significantly improves the error-floor performance compared to the sliding windowed decoder with the conventional weighted bit-flipping algorithm.
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 41%\mathbf{41\%}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.
In this paper, a bi-directional sliding window decoder is proposed for spatially coupled low-density parity-check (SC-LDPC) codes, which improves the decoding complexity and performance compared to the conventional sliding window decoding (SWD) by sharing messages at the overlapped part of forward and backward decoding windows. Moreover, by using proper scaling factors that determine the weight of each message at the overlapped part of two sliding windows, good local decoding effects can be efficiently spread out to both ends of SC-LDPC code during decoding process. Such effective message updates of the proposed bi-directional overlapped sliding window decoding (BO-SWD) improve error floor performance compared to the conventional SWD. The validity of BO-SWD is verified by simulation with various SC-LDPC ensembles.
This study investigates the Layered Sliding Window Decoding (LSWD) algorithm for Spatially Coupled Low-Density Parity-Check (SC LDPC) codes and proposes an enhanced decoding approach, the Improved Sliding Window Layered Decoding (ILSWD). While the LSWD algorithm reduces decoding latency and iteration counts compared to traditional Sliding Window Decoding (SWD), it does not significantly improve decoding performance. To address this, the ILSWD algorithm incorporates dynamic sliding window techniques, reorganizes decoding layers, and intro-duces suppression factors when errors enter the extended sliding window. Simulation results for 5G SC LDPC codes with single-sided coupling demonstrate that ILSWD achieves a 0.25 dB gain over LSWD at a specific bit error rate, alongside a notable improvement in decoding iteration rate. These findings highlight that ILSWD overcome the limitations of LSWD, offering a more efficient decoding solution with enhanced performance for SC LDPC codes in 5G applications.
In this work, we analyze efficient window shift schemes for windowed decoding of spatially coupled low-density parity-check (SC-LDPC) codes, which is known to yield close-to-optimal decoding results when compared to full belief propagation (BP) decoding. However, a drawback of windowed decoding is that either a significant amount of window updates are required leading to unnecessary high decoding complexity or the decoder suffers from sporadic burst-like error patterns, causing a decoder stall. To tackle this effect and, thus, to reduce the average decoding complexity, the basic idea is to enable adaptive window shifts based on a bit error rate (BER) prediction, which reduces the amount of unnecessary updates. As the decoder stall does not occur in analytical investigations such as the density evolution (DE), we examine different schemes on a fixed test-set and exhaustive monte-carlo simulations based on our graphic processing unit (GPU) simulation framework. As a result, we can reduce the average decoding complexity of the naive windowed decoder while improving the BER performance when compared to a non-adaptive windowed decoding scheme. Furthermore, we show that a foresightful stall prediction does not significantly outperform a retrospective stall detection which is much easier to implement in practice.
Spatially Coupled Low-Density Parity-Check (SCLDPC) codes are characterized by very long codeword lengths. For this reason, they are usually decoded with sliding window algorithms, which allow piecewise processing and decoding of the codeword symbols. In order to mitigate error propagation, it is possible to adapt strategies, such as non-uniform window sizes and node doping. In this paper, we propose a novel adaptive decoding schedule, which can be integrated with the aforementioned strategies. Numerical results confirm that the proposed approach can successfully detect error propagation events with more accuracy than conventional log-likelihood ratio-based approaches. Simulation results show that the error rate performance of time-invariant SC-LDPC codes significantly improves when the proposed strategies are adopted.