On guaranteed error correction capability of GLDPC codes

In this paper, it is shown that generalized LDPC codes can correct a linear fraction of errors under the parallel bit flipping algorithm when the underlying Tanner graph is a good expander. A lower bound on the size of variable node sets which have required expansion is established as a function of the column weight of the code, the girth of the Tanner graph and the error correction capability of the sub-code. It is also shown that the bound on the required expansion cannot be improved when the column weight is even by studying a class of trapping sets. An upper bound on the guaranteed error correction capability is found by investigating the size of smallest possible trapping sets.