  Low-density parity-check (LPDC) decoders assume the channel estate
information (CSI) is known and they have the true a posteriori probability
(APP) for each transmitted bit. But in most cases of interest, the CSI needs to
be estimated with the help of a short training sequence and the LDPC decoder
has to decode the received word using faulty APP estimates. In this paper, we
study the uncertainty in the CSI estimate and how it affects the bit error rate
(BER) output by the LDPC decoder. To improve these APP estimates, we propose a
Bayesian equalizer that takes into consideration not only the uncertainty due
to the noise in the channel, but also the uncertainty in the CSI estimate,
reducing the BER after the LDPC decoder.
