Achieving the Fundamental Limit of Lossless Analog Compression via Polarization
CoRR(2023)
摘要
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.
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