On the error correction of regular LDPC codes using the flipping algorithm

We apply the iterative bit flipping algorithm to the standard regular low-density parity-check (LDPC) code ensemble. In the past it was shown, for a typical code in the ensemble with left degree at least five and block length sufficiently large, that this algorithm can correct all error patterns with some linear (in the block length) number of errors. We extend this result to the case where the left degree is at least four. For the case where the left degree is larger than four, we obtain an improvement of several orders of magnitude compared to the existing results on the fraction of worst case errors that can be corrected. We also show how our results can be improved when we consider random errors (as opposed to worst case errors) produced by the channel.