Strong generative models can accurately learn channel distributions. This could save recurring costs for physical measurements of the channel. Moreover, the resulting differentiable channel model supports training neural encoders by enabling gradient-based optimization. The initial approach in the literature draws upon the modern 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 (DMs), which have demonstrated high sample quality and mode coverage in image generation. In addition to testing the generative performance of the channel distributions, we use an end-to-end (E2E) coded-modulation framework underpinned by DMs and propose an efficient training algorithm. Our simulations with various channel models show that a DM can accurately learn channel distributions, enabling an E2E framework to achieve near-optimal symbol error rates (SERs). Furthermore, we examine the trade-off between mode coverage and sampling speed through skipped sampling using sliced Wasserstein distance (SWD) and the E2E SER. We investigate the effect of noise scheduling on this trade-off, demonstrating that with an appropriate choice of parameters and techniques, sampling time can be significantly reduced with a minor increase in SWD and SER. Finally, we show that the DM can generate a correlated fading channel, whereas a strong GAN variant fails to learn the covariance. This paper highlights the potential benefits of using DMs for learning channel distributions, which could be further investigated for various channels and advanced techniques of DMs.

翻译：强大的生成模型能够精确学习信道分布。这可以节省信道物理测量的重复成本。此外，所得可微分信道模型通过支持基于梯度的优化，可用于训练神经编码器。文献中的初始方法借鉴了图像生成领域的最新进展，利用生成对抗网络（GANs）或其增强变体来生成信道分布。本文中，我们使用扩散模型（DMs）来解决这一信道逼近挑战，该模型在图像生成中已展现出高样本质量和良好的模态覆盖。除了测试信道分布的生成性能外，我们采用了一个以DMs为基础的端到端（E2E）编码调制框架，并提出了一种高效的训练算法。我们在多种信道模型下的仿真表明，DM能够精确学习信道分布，使E2E框架实现接近最优的符号错误率（SERs）。此外，我们通过跳跃采样，利用切片Wasserstein距离（SWD）和E2E SER，研究了模态覆盖与采样速度之间的权衡。我们探讨了噪声调度对此权衡的影响，证明通过选择合适的参数和技术，可以在SWD和SER轻微增加的情况下显著减少采样时间。最后，我们展示了DM能够生成相关衰落信道，而一种强大的GAN变体则无法学习协方差。本文强调了使用DMs学习信道分布的潜在优势，未来可针对各种信道和DMs的先进技术进行进一步研究。