We consider error correction capability of column-weight-three LDPC codes under different decoding algorithms. It is known that while the minimum distance of the codes in the 3-left-regular ensemble of LDPC codes grown linearly with the codelength, the error correction capability grows only logarithmically with the codelength under the Gallager A algorithm. In this talk, we consider a two bit decoder and derive sufficient conditions to correct any k errors. We also consider the Linear Programming (LP) decoder and derive sufficient conditions to correct any k errors.