Channel simulation is an alternative to quantization and entropy coding for performing lossy source coding. Recently, channel simulation has gained significant traction in both the machine learning and information theory communities, as it integrates better with machine learning-based data compression algorithms and has better rate-distortion-perception properties than quantization. As the practical importance of channel simulation increases, it is vital to understand its fundamental limitations. Recently, Sriramu and Wagner provided an almost complete characterisation of the redundancy of channel simulation algorithms. In this paper, we complete this characterisation. First, we significantly extend a result of Li and El Gamal, and show that the redundancy of any instance of a channel simulation problem is lower bounded by the channel simulation divergence. Second, we give two proofs that the asymptotic redundancy of simulating iid non-singular channels is lower-bounded by $1/2$: one using a direct approach based on the asymptotic expansion of the channel simulation divergence and one using large deviations theory.

翻译：信道模拟是执行有损信源编码的一种替代量化与熵编码的方法。近年来，信道模拟在机器学习和信息论领域均获得了显著关注，因为它能更好地与基于机器学习的数据压缩算法相结合，并且相比量化具有更优的速率‑失真‑感知特性。随着信道模拟在实际应用中的重要性日益提升，理解其基本局限性至关重要。近期，Sriramu与Wagner几乎完整刻画了信道模拟算法的冗余度特征。本文中，我们完成了这一刻画。首先，我们显著扩展了Li与El Gamal的结果，证明任何信道模拟问题实例的冗余度均以信道模拟散度为下界。其次，我们给出了两种证明，表明独立同分布非奇异信道模拟的渐近冗余度下界为$1/2$：一种基于信道模拟散度渐近展开的直接方法，另一种则利用大偏差理论。