The training of neural encoders via deep learning necessitates a differentiable channel model due to the backpropagation algorithm. This requirement can be sidestepped by approximating either the channel distribution or its gradient through pilot signals in real-world scenarios. The initial approach draws upon the latest advancements in image generation, utilizing generative adversarial networks (GANs) or their enhanced variants to generate channel distributions. In this paper, we address this channel approximation challenge with diffusion models, which have demonstrated high sample quality in image generation. We offer an end-to-end channel coding framework underpinned by diffusion models and propose an efficient training algorithm. Our simulations with various channel models establish that our diffusion models learn the channel distribution accurately, thereby achieving near-optimal end-to-end symbol error rates (SERs). We also note a significant advantage of diffusion models: A robust generalization capability in high signal-to-noise ratio regions, in contrast to GAN variants that suffer from error floor. Furthermore, we examine the trade-off between sample quality and sampling speed, when an accelerated sampling algorithm is deployed, and investigate the effect of the noise scheduling on this trade-off. With an apt choice of noise scheduling, sampling time can be significantly reduced with a minor increase in SER.

翻译：通过深度学习训练神经编码器需要可微的信道模型，这是反向传播算法的必然要求。在实际场景中，可通过导频信号近似信道分布或其梯度来规避这一限制。初始方法借鉴图像生成领域的最新进展，利用生成对抗网络（GAN）或其改进变体生成信道分布。本文针对这一信道近似挑战，采用在图像生成中展现高样本质量的扩散模型。我们提出了一种基于扩散模型的端到端信道编码框架，并设计了一种高效的训练算法。通过多种信道模型的仿真实验表明，我们的扩散模型能够精确学习信道分布，从而实现近乎最优的端到端符号错误率（SER）。我们还注意到扩散模型的一个显著优势：在高信噪比区域具有强大的泛化能力，而GAN变体在此区域会出现错误平层。此外，我们研究了采用加速采样算法时样本质量与采样速度之间的权衡关系，并探讨了噪声调度对此权衡的影响。通过恰当选择噪声调度，可以在SER仅小幅增加的情况下显著缩短采样时间。