On the Error Correction of Regular LDPC Codes Using the Flipping Algorithm

The iterative bit flipping algorithm is applied 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 a linear (in the block length) number of worst case errors. In this paper, this result is extended to the case where the left degree is at least four. For the case where the left degree is larger than four, an improvement, compared to existing results, of several orders of magnitude is obtained on the fraction of worst case errors that can be corrected. It is also shown how the results can be further improved when random errors produced by the channel (as opposed to worst case errors) are considered.