Failure analysis of two-bit flipping decoding algorithms

We consider a class of bit flipping algorithms for low-density parity-check codes over the binary symmetric channel in which one additional bit at a variable and check nodes is employed. For these two-bit flipping algorithms, we give and illustrate through examples a recursive procedure for finding all uncorrectable error patters and corresponding induced subgraphs, referred as a trapping set profile. This procedure is used to select a small collection of good algorithms that in a decoding diversity approach, run in parallel or serial, outperform Gallager A/B, min-sum and sum product algorithm in the error floor region.