The Benefit of Thresholding in LP Decoding of LDPC Codes
  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. 
Jon Feldman, Ralf Koetter, Pascal O. Vontobel