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.

翻译：纠错码是可靠数字通信的基础，然而设计既准确又计算高效的神经解码器仍具挑战。近期去噪扩散解码器取得了最先进的性能，但其迭代采样过程限制了在低延迟场景下的实用性。为弥合这一差距，一致性模型为高保真一步解码提供了潜在路径。然而，将一致性模型应用于纠错码面临重大挑战：纠错过程的离散特性意味着解码轨迹高度非平滑，使其无法兼容简单的连续时间步参数化。为解决此问题，我们通过软症状条件对反向概率流常微分方程进行重新参数化，从而提供平滑的信号损坏轨迹。在此基础上，我们提出纠错症状流一致性模型——一个专为纠错任务设计的模型无关框架，确保模型能够学习从任意含噪信号直接到原始码字的平滑轨迹，并实现单步解码。在多个基准测试中，ECCFM获得了比基于Transformer的解码器更低的误比特率和误帧率，同时推理速度比迭代去噪扩散解码器快30至100倍。