Neural Normalized MinSum (N-NMS) decoding delivers better frame error rate (FER) performance on linear block codes than conventional normalized MinSum (NMS) by assigning dynamic multiplicative weights to each check-to-variable message in each iteration. Previous N-NMS efforts have primarily investigated short-length block codes (N < 1000), because the number of N-NMS parameters to be trained is proportional to the number of edges in the parity check matrix and the number of iterations, which imposes am impractical memory requirement when Pytorch or Tensorflow is used for training. This paper provides efficient approaches to training parameters of N-NMS that support N-NMS for longer block lengths. Specifically, this paper introduces a family of neural 2-dimensional normalized (N-2D-NMS) decoders with with various reduced parameter sets and shows how performance varies with the parameter set selected. The N-2D-NMS decoders share weights with respect to check node and/or variable node degree. Simulation results justify this approach, showing that the trained weights of N-NMS have a strong correlation to the check node degree, variable node degree, and iteration number. Further simulation results on the (3096,1032) protograph-based raptor-like (PBRL) code show that N-2D-NMS decoder can achieve the same FER as N-NMS with significantly fewer parameters required. The N-2D-NMS decoder for a (16200,7200) DVBS-2 standard LDPC code shows a lower error floor than belief propagation. Finally, a hybrid decoding structure combining a feedforward structure with a recurrent structure is proposed in this paper. The hybrid structure shows similar decoding performance to full feedforward structure, but requires significantly fewer parameters.

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.

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