  A class of two-bit bit flipping algorithms for decoding low-density
parity-check codes over the binary symmetric channel was proposed in [1].
Initial results showed that decoders which employ a group of these algorithms
operating in parallel can offer low error floor decoding for high-speed
applications. As the number of two-bit bit flipping algorithms is large,
designing such a decoder is not a trivial task. In this paper, we describe a
procedure to select collections of algorithms that work well together. This
procedure relies on a recursive process which enumerates error configurations
that are uncorrectable by a given algorithm. The error configurations
uncorrectable by a given algorithm form its trapping set profile. Based on
their trapping set profiles, algorithms are selected so that in parallel, they
can correct a fixed number of errors with high probability.
