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IEEE Communications Letters

Threshold-Controlled Residual Decoding for LDPC Codes via a Weight-Shared Neural Network

Hua Zhou, Likang Zhang

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.1109/lcomm.2026.3721615

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We investigate the application of machine learning techniques (in particular, deep neural networks, DNN) to improve the decoding algorithms of short quasi-cyclic low-density paritycheck (LDPC) codes adopted to the 5G standard. We note that straightforward application of general-purpose DNNs is not possible due to the curse of dimensionality problem – the training set size grows exponentially with the number of information bits. In our opinion, the only way to deal with this problem is to combine deep learning methods with existing decoding algorithms. We start with a Tanner-based neural network decoder with Min-Sum activation functions proposed by Nachmani et al. and extend it as follows. First, the quasi-cyclic nature of 5G LDPC codes allows us to use a single weight per circular matrix (circulant). We refer to this as weight sharing. This idea significantly reduces the training time, preserving the error-correcting performance. Second, we add residual connections to our NN architecture. Residual connections improve the performance and reduce the training time. We also present the results for the rate and length adaptation techniques. Rate adaptation allows multiple DNNs corresponding to different coding rates to run with a single set of trained weights. Length adaptation allows optimally reusing weights for multiple lifting size indices.
Recently, neural networks have improved MinSum message-passing decoders for low-density parity-check (LDPC) codes by multiplying or adding weights to the messages, where the weights are determined by a neural network. The neural network complexity to determine distinct weights for each edge is high, often limiting the application to relatively short LDPC codes. Furthermore, storing separate weights for every edge and every iteration can be a burden for hardware implementations. To reduce neural network complexity and storage requirements, this paper proposes a family of weight-sharing schemes that use the same weight for edges that have the same check node degree and/or variable node degree. Our simulation results show that node-degree-based weight-sharing can deliver the same performance requiring distinct weights for each node. This paper also combines these degree-specific neural weights with a reconstruction-computation-quantization (RCQ) decoder to produce a weighted RCQ (W-RCQ) decoder. The W-RCQ decoder with node-degree-based weight sharing has a reduced hardware requirement compared with the original RCQ decoder. As an additional contribution, this paper identifies and resolves a gradient explosion issue that can arise when training neural LDPC decoders.
For the Belief Propagation (BP) algorithm of low-density parity-check (LDPC) codes, existing deep learning methods have a limited performance improvement and it is difficult to train deep-level networks. In this paper, a model-driven quasi-residual network (Quasi-ResNet) BP decoding architecture is proposed for LDPC codes to further improve the performance of standard BP decoding. This method feeds the reliable messages calculated in current iteration into the next iteration based on the shortcut connection, and adjusts the weight of shortcut connection based on the error Back Propagation algorithm of neural network to determine the optimal genetic proportion of reliable messages. The decoding architecture is composed of a model-driven deep neural network (DNN) and shortcut connection. Simulation results show that the decoder can not only unfold more layers quickly compared with the DNN-based BP decoder, but also further improve the decoding performance.