  We address photon-number-assisted, polarization- based, binary communication
systems equipped with photon counting receivers. In these channels information
is encoded in the value of polarization phase-shift but the carrier has and
additional degree of freedom, i.e. its photon distribution, which may be
exploited to implement binary input-multiple output (BIMO) channels also in the
presence of a phase-diffusion noise affecting the polarization. Here we analyze
the performances of these channels, which approach capacity by means of
iteratively decoded error correcting codes. In this paper we use soft-metric-
based low density parity check (LDPC) codes for this purpose. In order to take
full advantage of all the information available at the output of a photon
counting receiver, soft information is generated in the form of log-likelihood
ratios, leading to improved frame error rate (FER) and bit error rate (BER)
compared to binary symmetric channels (BSC). We evaluate the classical capacity
of the considered BIMO channel and show the potential gains that may be
provided by photon counting detectors in realistic implementations.
