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IEEE Journal on Selected Areas in Information Theory

Error Propagation Mitigation in Sliding Window Decoding of Spatially Coupled LDPC Codes

Min Zhu, David G. M. Mitchell, Michael Lentmaier, Daniel J. Costello

Published Jan 1, 2023• 11 citations
Publisher

Abstract

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.

DOI
10.1109/jsait.2023.3312656

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arXiv:1805.02902•IEEE Communications Letters•May 11, 2018•21 citations
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.
Due to their capacity achieving performance with sliding window decoding (SWD), spatially coupled LDPC (SC-LDPC) codes are emerging as candidates for next generation channel coding applications. In this paper we present a general model of SWD of SC-LDPC codes and develop an analysis that allows us to estimate error probability performance under decoder error propagation conditions that can occur when low latency operation is desired. We also show how the model parameters can be estimated and indicate how the model can be used to predict the performance of code doping techniques used to mitigate the effects of decoder error propagation.
In this paper, we study the problem of error propagation in sliding window decoding (SWD) of spatially coupled LDPC (SC-LDPC) codes. A general decoder model that accounts for error propagation is proposed and analyzed, and the decoded block error rate (BLER) is calculated using the model. In order to improve the BLER performance under decoder error propagation conditions, adaptive variable node (VN) doping is proposed, assuming a noiseless binary feedback channel is available. Example calculations using the proposed model, as well as numerical simulation results, are used to show that adaptive VN doping improves the BLER performance compared to the periodic VN doping and to the undoped case.
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.
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.
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 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.