Message-Passing Algorithms for Non-Linear Nodes and Data Compression

The use of parity-check gates in information theory has proved to be very effi cient. In particular, error correcting codes based on parity checks over lowdensity 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 effi cient 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. Copyright © 2006 S. Karger AG, Basel Published online: August 25, 2006 DOI: 10.1159/000094188 Fax +41 61 306 12 34 E-Mail [email protected]