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arXiv · 2512.01389

Syndrome-Flow Consistency Model Achieves One-step Denoising Error Correction Codes

Haoyu Lei·Chin Wa Lau·Kaiwen Zhou·Nian Guo·Farzan Farnia
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Abstract

Error Correction Codes (ECC) are fundamental to reliable digital communication, yet designing neural decoders that are both accurate and computationally efficient remains challenging. Recent denoising diffusion decoders achieve state-of-the-art performance, but their iterative sampling limits practicality in low-latency settings. To bridge this gap, consistency models (CMs) offer a potential path to high-fidelity one-step decoding. However, applying CMs to ECC presents a significant challenge: the discrete nature of error correction means the decoding trajectory is highly non-smooth, making it incompatible with a simple continuous timestep parameterization. To address this, we re-parameterize the reverse Probability Flow Ordinary Differential Equation (PF-ODE) by soft-syndrome condition, providing a smooth trajectory of signal corruption. Building on this, we propose the Error Correction Syndrome-Flow Consistency Model (ECCFM), a model-agnostic framework designed specifically for ECC task, ensuring the model learns a smooth trajectory from any noisy signal directly to the original codeword in a single step. Across multiple benchmarks, ECCFM attains lower bit-error-rate (BER) and frame-error-rate (FER) than transformer-based decoders, while delivering inference speeds 30x to 100x faster than iterative denoising diffusion decoders.

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Haoyu Lei, Chin Wa Lau, Kaiwen Zhou, Nian Guo, Farzan Farnia. 2026-02-17. Syndrome-Flow Consistency Model Achieves One-step Denoising Error Correction Codes. https://arxiv.org/abs/2512.01389

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