  Finite alphabet iterative decoders (FAID) with multilevel messages that can
surpass BP in the error floor region for LDPC codes on the BSC were previously
proposed. In this paper, we propose decimation-enhanced decoders. The technique
of decimation which is incorporated into the message update rule, involves
fixing certain bits of the code to a particular value. Under appropriately
chosen rules, decimation can significantly reduce the number of iterations
required to correct a fixed number of errors, while maintaining the good
performance of the original decoder in the error floor region. At the same
time, the algorithm is much more amenable to analysis. We shall provide a
simple decimation scheme for a particularly good 7-level FAID for column-weight
three codes on the BSC, that helps to correct a fixed number of errors in fewer
iterations, and provide insights into the analysis of the decoder. We shall
also examine the conditions under which the decimation-enhanced 7-level FAID
performs at least as good as the 7-level FAID.
