基于极格的带边信息的普适高斯Quantization
Universal Gaussian Quantization with Side Information using Polar Lattices
摘要：
我们考虑高斯观测的边信息的通用量化，其中边信息是发送方观测的噪声版本，噪声方差未知的发送方。在本文中，我们提出了一个普遍的速率最佳和实用的量化方案的所有值的未知噪声方差。我们的方案使用了以前工作中的极格子，并基于底层辅助设备的结构分解进行，这样即使在一轮恢复失败时，各方也会同意一个比前一个更接近的共同“参考点”。我们还提出了有限块长度分析显示失真的次指数收敛和速率的指数收敛。我们的计划的整体复杂性是$O(N^2\log^2 N)$的任何目标失真和固定速率大于率失真界。
英文摘要：
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.
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