Score Based Error Correcting Code Decoder

2026-05-27

AI Summary

Soft-decision decoding remains challenging in terms of universality, efficiency, and the need for signal-to-noise ratio (SNR) estimation. This work proposes a novel framework that, for the first time, formulates error-correcting code decoding as a continuous-time denoising process via a score-matching-based neural probability flow ordinary differential equation (ODE). The approach trains directly on raw signed channel observations without requiring SNR conditioning and leverages ODE solvers to flexibly trade off decoding latency against accuracy. By incorporating parity-check constraints and employing Euler and DPM solvers, the method achieves the lowest bit error rate in 39 out of 42 code–SNR configurations, yielding an average SNR gain of 0.17 dB (up to 0.46 dB). Switching to the DPM solver further reduces decoding time by 8.86% on average (up to 12.82%) while preserving performance.

Abstract

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 0.17dB and a maximum gain of 0.46dB over the strongest competing baseline, we showed that swapping the solver from Euler to DPM preserves -ln(BER) while reducing end-to-end decoding time by 8.86% on average (up to 12.82%).

Problem

• error-correcting codes
• soft decoding
• decoding latency
• bit error rate
• noise robustness

Innovation

• score-based decoding
• neural ODE
• error-correcting codes
• soft decoding
• denoising