Score Based Error Correcting Code Decoder

Abstract

Error-correcting codes enable reliable communication, yet practical soft decoding remains challenging across code families and block lengths. We propose \textbf{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 $ 0.21$\,dB and a maximum gain of $0.44$\,dB over the strongest prior method. Additionally, 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 $12.82\%$).