Neural Window Decoder for SC-LDPC Codes

TL;DR

The paper addresses decoding SC-LDPC codes with a Neural Window Decoder (NWD) that preserves the window decoding flow while introducing trainable weights. It introduces three core ideas: target-specific training to prune weights and accelerate convergence; neural non-uniform scheduling via trainable damping factors and a schedule-importance metric to selectively skip CN updates; and an adaptive NWD that uses an EP-resilient weight set when prior-window errors are detected to mitigate error propagation. The results show substantial complexity reductions (up to ~41% fewer CN updates) with little or no loss in performance, plus notable BLER/FER improvements and competitive performance relative to BP for long chains. The approach is hardware-friendly, scalable to long SC-LDPC codes, and requires only loading trained weights into an existing WD-based decoder, making it practical for real-world deployment.

Abstract

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.

Figures (14)

• Figure 1: (a) A protograph of the $(3,6)$-regular SC-LDPC code with $w=2$ and $L=4$ constructed by the edge-spreading technique (b) window decoding with window size $W=6$ and target size $T=1$. The dotted box indicates the window at the third stage, where the VNs in the first $T$ positions in the window serve as target VNs (dark-filled nodes), and the previous target VNs transmit their decision LLRs (arrows).
• Figure 2: Examples of the non-uniform decoding schedules of a $(3,6)-$regular SC-LDPC code with $W=8, \overline{\ell}=16$ using (a) soft BER based method and (b) pragmatic method Hassan2017. CN updates are only performed in the schedules with bold colors.
• Figure 3: A code within a window with $W=3$ and $\overline{\ell}=2$ is mapped to the neural network for training the NWD. The dashed lines in the network represent the edges that are included for all-inclusive training but are pruned for target-specific training.
• Figure 4: Ratio between the numbers of trainable weights for target-specific training and all-inclusive training. A smaller ratio indicates a greater complexity reduction effect achieved by target-specific training.
• Figure 5: Evolution of BLER over training epochs for NWD with different target sizes $T$.