Channel simulation algorithms can efficiently encode random samples from a prescribed target distribution $Q$ and find applications in machine learning-based lossy data compression. However, algorithms that encode exact samples usually have random runtime, limiting their applicability when a consistent encoding time is desirable. Thus, this paper considers approximate schemes with a fixed runtime instead. First, we strengthen a result of Agustsson and Theis and show that there is a class of pairs of target distribution $Q$ and coding distribution $P$, for which the runtime of any approximate scheme scales at least super-polynomially in $D_\infty[Q \Vert P]$. We then show, by contrast, that if we have access to an unnormalised Radon-Nikodym derivative $r \propto dQ/dP$ and knowledge of $D_{KL}[Q \Vert P]$, we can exploit global-bound, depth-limited A* coding to ensure $\mathrm{TV}[Q \Vert P] \leq \epsilon$ and maintain optimal coding performance with a sample complexity of only $\exp_2\big((D_{KL}[Q \Vert P] + o(1)) \big/ \epsilon\big)$.

翻译：信道模拟算法能够高效编码来自指定目标分布$Q$的随机样本，并在基于机器学习的损耗数据压缩中具有应用。然而，编码精确样本的算法通常具有随机运行时间，这在需要一致编码时间时限制了其适用性。因此，本文转而考虑具有固定运行时间的近似方案。首先，我们强化了Agustsson和Theis的结果，证明存在一类目标分布$Q$与编码分布$P$的组合，使得任何近似方案的运行时间至少以$D_\infty[Q \Vert P]$的超多项式规模增长。随后，我们通过对比证明：若可访问未归一化的Radon-Nikodym导数$r \propto dQ/dP$并已知$D_{KL}[Q \Vert P]$，则可通过利用全局界限的深度受限A*编码，在仅需$\exp_2\big((D_{KL}[Q \Vert P] + o(1)) \big/ \epsilon\big)$的样本复杂度下，确保$\mathrm{TV}[Q \Vert P] \leq \epsilon$并维持最优编码性能。