  Consider data transmission over a binary-input additive white Gaussian noise
channel using a binary low-density parity-check code. We ask the following
question: Given a decoder that takes log-likelihood ratios as input, does it
help to modify the log-likelihood ratios before decoding? If we use an optimal
decoder then it is clear that modifying the log-likelihoods cannot possibly
help the decoder's performance, and so the answer is "no." However, for a
suboptimal decoder like the linear programming decoder, the answer might be
"yes": In this paper we prove that for certain interesting classes of
low-density parity-check codes and large enough SNRs, it is advantageous to
truncate the log-likelihood ratios before passing them to the linear
programming decoder.
