On the dynamics of the error floor behavior in regular LDPC codes

It is shown that dominant trapping sets of regular LDPC codes, so called absorption sets, undergo a two-phase dynamic behavior in the iterative message-passing (MP) decoding algorithm. Using a linear dynamic model for the iteration behavior of these sets, it is shown that they undergo an initial geometric growth phase which stabilizes in a final bit-flipping behavior where the algorithm reaches a fixed point. This analysis is shown to lead to very accurate numerical calculations of the error floor bit error rates down to error rates that are inaccessible by simulation. The topology of the dominant absorption sets of an example code, the IEEE 802.3 an (2048, 1723) regular LDPC code, is identified and tabulated using topological relationships in combination with search algorithms.