  This paper outlines a three-step procedure for determining the low bit error
rate performance curve of a wide class of LDPC codes of moderate length. The
traditional method to estimate code performance in the higher SNR region is to
use a sum of the contributions of the most dominant error events to the
probability of error. These dominant error events will be both code and decoder
dependent, consisting of low-weight codewords as well as non-codeword events if
ML decoding is not used. For even moderate length codes, it is not feasible to
find all of these dominant error events with a brute force search. The proposed
method provides a convenient way to evaluate very low bit error rate
performance of an LDPC code without requiring knowledge of the complete error
event weight spectrum or resorting to a Monte Carlo simulation. This new method
can be applied to various types of decoding such as the full belief propagation
version of the message passing algorithm or the commonly used min-sum
approximation to belief propagation. The proposed method allows one to
efficiently see error performance at bit error rates that were previously out
of reach of Monte Carlo methods. This result will provide a solid foundation
for the analysis and design of LDPC codes and decoders that are required to
provide a guaranteed very low bit error rate performance at certain SNRs.
