Soft-metric-based channel decoding for photon counting receivers

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 an 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 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 and bit error rate compared to binary symmetric channels. 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.