Gallager error-correcting codes for binary asymmetric channels
Izaak Neri, N S Skantzos, D Bollé · Journal of Statistical Mechanics Theory and Experiment · 2008
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 endogenous property and complexity, characterizing solutions of recursive equations of distributions for cavity fields.