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Thouless-Anderson-Palmer Approach for Lossy Compression

Tatsuto Murayama
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Abstract

We study an ill-posed linear inverse problem, where a binary sequence will be reproduced using a sparce matrix. According to the previous study, this model can theoretically provide an optimal compression scheme for an arbitrary distortion level, though the encoding procedure remains an NP-complete problem. In this paper, we focus on the consistency condition for a dynamics model of Markov-type to derive an iterative algorithm, following the steps of Thouless-Anderson-Palmer's. Numerical results show that the algorithm can empirically saturate the theoretical limit for the sparse construction of our codes, which also is very close to the rate-distortion function.

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Tatsuto Murayama. 2003-12-29. Thouless-Anderson-Palmer Approach for Lossy Compression. https://doi.org/10.1103/physreve.69.035105

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