On the guaranteed error correction capability of LDPC codes
  We investigate the relation between the girth and the guaranteed error correction capability of $\gamma$-left regular LDPC codes when decoded using the bit flipping (serial and parallel) algorithms. A lower bound on the number of variable nodes which expand by a factor of at least $3 \gamma/4$ is found based on the Moore bound. An upper bound on the guaranteed correction capability is established by studying the sizes of smallest possible trapping sets. 
Shashi Kiran Chilappagari, Dung Viet Nguyen, Bane Vasic, Michael   Marcellin