On the Block Error Probability of LP Decoding of LDPC Codes
  In his thesis, Wiberg showed the existence of thresholds for families of regular low-density parity-check codes under min-sum algorithm decoding. He also derived analytic bounds on these thresholds. In this paper, we formulate similar results for linear programming decoding of regular low-density parity-check codes. 
Ralf Koetter and Pascal O. Vontobel