Error Exponents of Low-Density Parity-Check Codes on the Binary Erasure   Channel
  We introduce a thermodynamic (large deviation) formalism for computing error exponents in error-correcting codes. Within this framework, we apply the heuristic cavity method from statistical mechanics to derive the average and typical error exponents of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) under maximum-likelihood decoding. 
Thierry Mora and Olivier Rivoire