We consider universal quantization with side information for Gaussian observations, where the side information is a noisy version of the sender's observation with noise variance unknown to the sender. In this paper, we propose a universally rate optimal and practical quantization scheme for all values of unknown noise variance. Our scheme uses Polar lattices from prior work, and proceeds based on a structural decomposition of the underlying auxiliaries so that even when recovery fails in a round, the parties agree on a common "reference point" that is closer than the previous one. We also present the finite blocklength analysis showing an sub-exponential convergence for distortion and exponential convergence for rate. The overall complexity of our scheme is $O(N^2\log^2 N)$ for any target distortion and fixed rate larger than the rate-distortion bound.

翻译：我们考虑带边信息的高斯观测通用量化问题，其中边信息是发送端观测值的含噪版本，且噪声方差对发送端未知。本文针对所有未知噪声方差值，提出了一种通用速率最优且实用的量化方案。该方案基于先前工作中的极坐标格点，通过对底层辅助变量进行结构分解来运作：即使某轮恢复失败，双方仍能就一个比先前更接近的公共"参考点"达成一致。我们还给出了有限码长分析，表明畸变呈次指数收敛，速率呈指数收敛。对于任意目标畸变和大于率畸变界的固定速率，本方案的整体复杂度为$O(N^2\log^2 N)$。