  We introduce a two-stage decimation process to improve the performance of
neural belief propagation (NBP), recently introduced by Nachmani et al., for
short low-density parity-check (LDPC) codes. In the first stage, we build a
list by iterating between a conventional NBP decoder and guessing the least
reliable bit. The second stage iterates between a conventional NBP decoder and
learned decimation, where we use a neural network to decide the decimation
value for each bit. For a (128,64) LDPC code, the proposed NBP with decimation
outperforms NBP decoding by 0.75 dB and performs within 1 dB from
maximum-likelihood decoding at a block error rate of $10^{-4}$.
