Achieving the Fundamental Limit of Lossless Analog Compression via Polarization
Abstract
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.
Keywords
Cite
@article{arxiv.2312.06200,
title = {Achieving the Fundamental Limit of Lossless Analog Compression via Polarization},
author = {Shuai Yuan and Liuquan Yao and Yuan Li and Huazi Zhang and Jun Wang and Wen Tong and Zhiming Ma},
journal= {arXiv preprint arXiv:2312.06200},
year = {2024}
}
Comments
48 pages, 5 figures. This work was presented in part at the 2023 IEEE Global Communications Conference