  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 greater than what previous methods can
manage, and reduces the bitrate 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.
