Error correcting codes are a fundamental component of communication systems, enabling reliable data transmission over noisy channels. Recently, neural decoders have demonstrated notable performance gains over classical iterative algorithms. In this paper, we propose a Generalized Belief Propagation Network (GBPNet) that preserves message-passing symmetry while enhancing the decoder's learning capability. The architecture uses cascaded variable-node updates and learned element-wise message scaling while retaining the Tanner graph structure. We also introduce two training strategies, progressive training and high-SNR training, that improve decoding accuracy. Experimental results on several linear codes show that GBPNet achieves lower bit error rates than conventional belief propagation and the evaluated state-of-the-art neural decoders.

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