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Message passing algorithms for non-linear nodes and data compression

S. Ciliberti·M. Mezard·R. Zecchina
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Abstract

The use of parity-check gates in information theory has proved to be very efficient. In particular, error correcting codes based on parity checks over low-density graphs show excellent performances. Another basic issue of information theory, namely data compression, can be addressed in a similar way by a kind of dual approach. The theoretical performance of such a Parity Source Coder can attain the optimal limit predicted by the general rate-distortion theory. However, in order to turn this approach into an efficient compression code (with fast encoding/decoding algorithms) one must depart from parity checks and use some general random gates. By taking advantage of analytical approaches from the statistical physics of disordered systems and SP-like message passing algorithms, we construct a compressor based on low-density non-linear gates with a very good theoretical and practical performance.

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S. Ciliberti, M. Mezard, R. Zecchina. 2005-08-30. Message passing algorithms for non-linear nodes and data compression. https://arxiv.org/abs/cond-mat/0508723

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