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. 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：本文基于极化框架研究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，在Hadamard变换下最大后验(MAP)估计的误差概率呈现极化现象。基于该发现，我们提出部分Hadamard压缩方案，并开发相应的模拟逐次消除(SC)解码器。该方案由确定性测量矩阵和非迭代重构算法组成，在空间复杂度和计算复杂度方面均具有优势。利用误差概率极化特性，我们证明该方法达到了Wu与Verdu提出的无损模拟压缩信息理论极限。