  Recently, we introduced a new class of finite alphabet iterative decoders
(FAIDs) for low-density parity-check (LDPC) codes. These decoders are capable
of surpassing belief propagation in the error floor region on the Binary
Symmetric channel with much lower complexity. In this paper, we introduce a a
novel scheme to further increase the guaranteed error correction capability
from what is achievable by a FAID on column-weight-three LDPC codes. The
proposed scheme uses a plurality of FAIDs which collectively correct more error
patterns than a single FAID on a given code. The collection of FAIDs utilized
by the scheme is judiciously chosen to ensure that individual decoders have
different decoding dynamics and correct different error patterns. Consequently,
they can collectively correct a diverse set of error patterns, which is
referred to as decoder diversity. We provide a systematic method to generate
the set of FAIDs for decoder diversity on a given code based on the knowledge
of the most harmful trapping sets present in the code. Using the well-known
column-weight-three $(155,64)$ Tanner code with $d_{min}$ = 20 as an example,
we describe the method in detail and show that the guaranteed error correction
capability can be significantly increased with decoder diversity.
