Relative entropy coding (REC) algorithms encode a random sample following a target distribution $Q$, using a coding distribution $P$ shared between the sender and receiver. Sadly, general REC algorithms suffer from prohibitive encoding times, at least on the order of $2^{D_{\text{KL}}[Q||P]}$, and faster algorithms are limited to very specific settings. This work addresses this issue by introducing a REC scheme utilizing space partitioning to reduce runtime in practical scenarios. We provide theoretical analyses of our method and demonstrate its effectiveness with both toy examples and practical applications. Notably, our method successfully handles REC tasks with $D_{\text{KL}}[Q||P]$ about three times what previous methods can manage and reduces the compression rate by approximately 5-15\% in VAE-based lossless compression on MNIST and INR-based lossy compression on CIFAR-10 compared to previous methods, significantly improving the practicality of REC for neural compression.

翻译：相对熵编码算法利用发送方和接收方共享的编码分布$P$，对遵循目标分布$Q$的随机样本进行编码。然而，通用相对熵编码算法存在编码时间过长的缺陷（至少达到$2^{D_{\text{KL}}[Q||P]}$量级），而快速算法仅适用于极为特定的场景。本文通过引入一种利用空间划分降低实际场景运行时长的相对熵编码方案来解决该问题。我们对该方法进行了理论分析，并通过玩具示例与实际应用验证其有效性。值得注意的是，我们的方法成功处理了$D_{\text{KL}}[Q||P]$约为先前方法三倍的相对熵编码任务，并在基于VAE的MNIST无损压缩和基于INR的CIFAR-10有损压缩中，将压缩率较先前方法降低约5-15%，显著提升了相对熵编码在神经压缩领域的实用性。