Gallager error correcting codes for binary asymmetric channels

Abstract

We derive critical noise levels for Gallager codes on asymmetric channels as a function of the input bias and the temperature. Using a statistical mechanics approach we study the space of codewords and the entropy in the various decoding regimes. We further discuss the relation of the convergence of the message passing algorithm with the endogeny property and complexity, characterizing solutions of recursive equations of distributions for cavity fields.

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• Parallel dynamics of disordered Ising spin systems on finitely connected directed random graphs with arbitrary degree distributions
• The phase diagram of Lévy spin glasses
• Decoding communities in networks
• Code optimization, frozen glassy phase and improved decoding algorithms for low-density parity-check codes
• Statistical mechanics of LDPC codes on channels with memory
• Error correcting code using tree-like multilayer perceptron