Polymer Expansions for Cycle LDPC Codes
  We prove that the Bethe expression for the conditional input-output entropy of cycle LDPC codes on binary symmetric channels above the MAP threshold is exact in the large block length limit. The analysis relies on methods from statistical physics. The finite size corrections to the Bethe expression are expressed through a polymer expansion which is controlled thanks to expander and counting arguments. 
Nicolas Macris and Marc Vuffray
cs.IT cond-mat.stat-mech math-ph math.IT math.MP