Score Based Error Correcting Code Decoder

Error-correcting codes enable reliable communication, yet practical soft decoding remains challenging across code families and block lengths. We propose SB-ECC, a score-based decoder that casts decoding as continuous-time denoising. A neural denoiser defines a probability-flow ordinary differential equation (ODE) that iteratively updates the noisy channel observation toward a valid codeword, guided by parity constraints. The model is trained across noise levels without time/SNR conditioning, enabling inference without SNR estimation and supporting a direct latency--accuracy trade-off controlled by the ODE solver budget. We use the raw signed channel observation as input for learning a continuous denoising field. Across $42$ code/SNR settings, SB-ECC achieves the best BER in $39/42$ entries, with an average SNR gain of $0.17$\,dB and a maximum gain of $0.46$\,dB over the strongest competing baseline, we showed that swapping the solver from Euler to DPM preserves $-\ln(\mathrm{BER})$ while reducing end-to-end decoding time by $8.86\%$ on average (up to $12.82\%$).

Reliable communication and storage systems rely on error-correcting codes, which add structure to messages so receivers can recover the original data even after noise corrupts it. Decoding these codes accurately and quickly is difficult, especially across different code types and lengths. We introduce SB-ECC, a machine-learning decoder that treats decoding like gradually cleaning a noisy signal. Instead of first discarding part of the received information, our method uses the full signed signal and learns how to denoise it step by step toward a valid codeword while checking whether the code’s parity rules are satisfied. The decoder does not need to know the channel noise level in advance, and its computation can be adjusted at test time to balance speed and accuracy. Across a broad set of code and noise settings, SB-ECC improves bit-error performance over strong neural baselines in most cases. This suggests that score-based denoising can be a useful tool for building more reliable communication and storage systems, especially when flexible accuracy-latency trade-offs are important.