Learning About Syndrome Awareness and WMS Algorithm for Adaptive Neural Decoding for 6G LDPC Base Graph Enhancement

Abstract

6G wireless communication networks require low-latency, ultra-reliable error correction capabilities that adapt to dynamic channel scenarios and block lengths. This study presents a new adaptive neural decoding workflow for 5G-New Radio LDPC base graphs (BG1 and BG2). It combines a weighted Min-Sum (WMS) algorithm with syndrome-aware learning that uses parity-check feedback to guide neural decoding in two key ways: syndrome-based loss and syndrome-conditioned message updates. This approach overcomes the limitations of traditional min-sum (MS) and belief propagation (BP) decoders. To improve message updates among iterations based on real-time parity-check feedback, we first introduce trainable parameters for better training on the most challenging error patterns; a unique data pipeline collects "uncorrected" frame samples at low SNR and generates log-likelihood ratios (LLRs) under the Additive White Gaussian Noise (AWGN) channel and Rayleigh flat-fading channel. The training scheme has two stages: (1) an end-to-end supervised stage focused on minimizing both soft-BER and soft-FER loss across random noisy codewords, and (2) a boosting stage for learning residual corrections using mean-squared error on uncorrected frames. Performance is evaluated across various SNR levels, lifting factors, and code rates. Results show that BG1 outperforms BG2 in the AWGN channel by 1 dB and in the Rayleigh flat-fading channel by 2 dB. To balance reliability and decoding complexity, early convergence is achieved within 10 to 20 iterations. Additionally, lower rates and higher lifting factors produce sharper waterfalls and error floors below 10−7 and 10−8 for AWGN and Rayleigh, respectively. The proposed framework generalizes to different channel types and LDPC designs and offers a 0.3 dB waterfall gain compared to traditional neural Min–Sum decoders. These results demonstrate adaptable, high-performance error correction suitable for various wireless applications, highlighting the practicality of syndrome-aware WMS neural decoding for future 6G standards.