In this paper, we study the lossless analog compression for i.i.d. nonsingular signals via the polarization-based framework. We prove that for nonsingular source, the error probability of maximum a posteriori (MAP) estimation polarizes under the Hadamard transform, which extends the polarization phenomenon to analog domain. Building on this insight, we propose partial Hadamard compression and develop the corresponding analog successive cancellation (SC) decoder. The proposed scheme consists of deterministic measurement matrices and non-iterative reconstruction algorithm, providing benefits in both space and computational complexity. Using the polarization of error probability, we prove that our approach achieves the information-theoretical limit for lossless analog compression developed by Wu and Verdu.

翻译：本文研究基于极化框架对独立同分布非奇异信号的无损模拟压缩问题。我们证明，对于非奇异信源，最大后验概率估计的误差概率在哈达玛变换下呈现极化现象，从而将极化现象扩展至模拟域。基于此发现，我们提出部分哈达玛压缩方案，并开发相应的模拟逐次消除译码器。该方案由确定性测量矩阵与非迭代重建算法构成，在空间复杂度与计算复杂度方面均具有优势。通过误差概率的极化性质，我们证明该方法达到了Wu与Verdu提出的无损模拟压缩信息论极限。