Learning to Decode Linear Codes with Generalized Belief Propagation Network

Samira Malek

cs.AINov 4, 2026

Learning to Decode Linear Codes with Generalized Belief Propagation Network

Authors: Samira Malek

Organizations: Pennsylvania State University

Abstract

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.

Figures & tables

Fig. 1: Tanner graph with variable nodes $\{v_{i}\}_{i=1}^{5}$ and check nodes $\{c_{i}\}_{i=1}^{4}$ .

Fig. 2: Architecture of one GBPNet iteration for the Tanner graph in Fig. 1 , comprising three cascaded variable sublayers with five fully connected blocks, followed by a learned element-wise scaling operation layer, message recombination, and a check-node update.

Codes	Parameter	BP			Hyp BP [ 8 ]			ECCT [ 5 ]			CrossMPT [ 4 ]			GBPNet
Codes	Parameter	4	5	6	4	5	6	4	5	6	4	5	6	4	5	6
BCH	(63,36)	4.03	5.42	7.26	4.29	5.91	8.01	4.86	6.65	9.10	5.03	6.91	9.37	6.10	7.87	10.21
BCH	(63,51)	4.50	5.82	7.42	4.80	6.44	8.58	5.66	7.89	11.01	5.78	8.08	11.41	6.42	8.78	12.03
Polar	(64,32)	4.26	5.38	6.50	4.59	6.10	7.69	6.99	9.44	12.32	7.50	9.97	13.31	8.24	10.42	13.85
	(64,48)	4.74	5.94	7.42	4.92	6.44	8.39	6.36	8.46	11.09	6.51	8.70	11.31	7.43	9.36	11.94
	(128,96)	4.61	5.79	7.08	4.94	6.76	9.09	6.31	9.12	12.47	7.15	10.15	13.13	7.96	10.97	13.89

TABLE I: Quantitative comparison of GBPNet at SNRs of

4

5

, and

6

dB. Results are reported as

-\ln(\mathrm{BER})

(larger is better).

Fig. 3: Decoding performance comparison for BCH(127, 64), demonstrating that GBPNet outperforms conventional BP even with regular training, highlighting the effectiveness of its architecture, while high-SNR and progressive training provide further improvements.

Fig. 4: BER comparison of different state-of-the-art decoding methods on the MacKay (96,48) code. The figure also shows the effect of using multiple variable-node sublayers, with GBPNet results for $K=1,2,3$ .

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Neural decoding maps brain activity or error-correction syndromes to stimuli, behavior, language, or corrective actions.

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Forward error correction is essential for reliable communication over noisy channels. Attention-based model-free neural decoders have shown strong performance for short codes, but their scalability to longer codes is limited by the quadratic memory and computational cost of attention. In this paper, we introduce the Mamba message-passing decoder (MMPD), an attention-free syndrome-based neural decoder for binary linear codes. MMPD retains the Tanner-graph structure of a message-passing decoder by performing local pairwise aggregation along variable-check edges. To enable efficient long-range information propagation, these local updates are combined with bidirectional Mamba state-space blocks. By avoiding dense attention matrices, MMPD scales more favorably for long codes in both memory and computation. Experiments on the (1056, 880) LDPC code show that MMPD achieves a 0.45 dB gain over the state-of-the-art CrossMPT decoder at a specified target bit error rate, while reducing memory consumption by a factor of 1.5. This reduction factor increases substantially for longer codes, demonstrating the applicability of MMPD to scalable neural decoding of practical long codes.

Abstract

Neural Decoding

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