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International Conference on Wireless Communications and Signal Processing (WCSP)

Efficient Shuffled Sliding Window Decoding of SC-LDPC Codes

Qin Du, Lisha Luo, Xuan He

Published Oct 23, 2025• 0 citations
Publisher

Abstract

Spatially coupled low-density parity-check (SCLDPC) codes provide excellent performance and low latency under sliding window decoding (SWD). To achieve a low-power and low-complexity SC-LDPC decoder, we propose a variant of SWD called size-$\lambda$monotonic double-ended queue SWD ($\lambda$MDQSWD), where$\lambda$refers to the storage complexity of the update at a check node (CN). Our$\lambda$MDQ-SWD employs the shuffled schedule in SWD and uses the MDQ structure to implement the CN update. Moreover, it considers using only the minimum magnitude from target symbols for the CN update to avoid redundant computations. Simulation results show that, although under$\lambda=2$, the proposed algorithm achieves comparable error correction performance to the state-of-the-art algorithms. Moreover, a detailed hardware implementation for the CN update is designed. Analysis using the 90 nm CMOS technology library shows that, compared to the state-of-the-art algorithms, the$\lambda$MDQ-SWD with$\lambda=2$reduces the area and increases the clock frequency of CN update by 63.7 % and 107.6 %, respectively.

DOI
10.1109/wcsp68525.2025.1010573

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Spatially coupled low-density parity-check (SC-LDPC) codes can achieve capacity approaching performance with a small message recovery latency due to the sliding window decoding (SWD). Using a partial Tanner graph, the SWD performs iterative message passing until the average error probability Peof the target symbols falls below a threshold or the maximum iteration number is reached. However, Pedoes not decrease monotonically as iteration progresses. This implies the symbol likelihoods that were yielded when the decoding terminates may not be optimal for making decisions. Therefore, this paper proposes an improved SWD (ISWD) for SC-LDPC codes. The proposal monitors the achievable minimum of Peand stores its associated likelihoods, so that when the decoding terminates the target symbols will be estimated based on the stored likelihoods. Our research shows the ISWD is able to enhance the decoding performance, especially in the waterfall region. It exhibits an asymptotic convergence to the SWD performance. A complexity reducing variant of the ISWD is also proposed to facilitate the decoding but at the cost of error-correction performance.
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.
In this paper, we investigate the problem of decoder error propagation for spatially coupled low-density parity-check (SC-LDPC) codes with sliding window decoding (SWD). This problem typically manifests itself at signal-to-noise ratios (SNRs) close to capacity under low-latency operating conditions. In this case, infrequent but severe decoder error propagation can sometimes occur. To help understand the error propagation problem in SWD of SC-LDPC codes, a multi-state Markov model is developed to describe decoder behavior and to analyze the error performance of spatially coupled LDPC codes under these conditions. We then present two approaches -check node (CN) doping and variable node (VN) doping -to combating decoder error propagation and improving decoder performance. Next we describe how the performance can be further improved by employing an adaptive approach that depends on the availability of a noiseless binary feedback channel. To illustrate the effectiveness of the doping techniques, we analyze the error performance of CN doping and VN doping using the multi-state decoder model. We then present computer simulation results showing that CN and VN doping significantly improve the performance in the operating range of interest at a cost of a small rate loss and that adaptive doping further improves the performance. We also show that the rate loss is always less than that resulting from encoder termination and can be further reduced by doping only a fraction of the VNs at each doping position in the code graph with only a minor impact on performance. Finally, we show how the encoding problem for VN doping can be greatly simplified by doping only systematic bits, with little or no performance loss.
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.
Sliding window decoding has been employed as the decoding scheme of quasi-cyclic spatially-coupled low-density parity-check (QC-SC-LDPC) codes, with the decoding latency and complexity independent of the coupling length but proportional to the window size. The window size was empirically chosen at least three times the constraint length in previous works, which results in the preference of QC-SC-LDPC codes with small constraint length, to reduce the decoding latency and complexity in practical systems. However, the code design freedom and the decoder throughput are limited for these QC-SC-LDPC codes. In this paper, the optimal window size under the constraint of practical decoding complexity is analyzed employing multi-edge-type density evolution (MET-DE). It can be verified from the MET-DE analytical result that the optimal window size could achieve less than twice the constraint length for several edge spreading patterns, which largely loose this restriction in practical code design. Furthermore, it could be observed that besides the constraint length, the specific structure of the edge spreading pattern could affect the optimal window size as well, and thus the MET-DE analytical method for the optimal window size could effectively guide the design of QC-SC-LDPC codes in practical systems. Then an improved sliding window decoding scheme is proposed, including the optimal choice of window size and a parity-check based early termination scheme. Finally, the performance and robustness of the proposed sliding window decoding scheme for QC-SC-LDPC codes are demonstrated via simulation, with the decoding complexity at most twice as that of the conventional LDPC coded schemes.
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.