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The moment-generating function (MGF) of the received photoelectric current is evaluated for a linear optical communication system consisting of distributed amplified spontaneous emission (ASE), polarization-mode dispersion (PMD), and polarization dependent loss (PDL). Using this function, optical performance characterization based on the bit error rate (BER), Q-factor, and signal-to-noise ratio (SNR), can be evaluated. As an example of the applicability to binary differential phase-shift keying (DPSK) systems with defined PDL, the BER results predicted by linked model and lumped model are compared. Our results indicate that the difference can be orders of magnitude when the PDL is larger than 2.5 dB. Additionally, random PDL induced statistical feature of the BER is entirely different for these two models. Finally, relations between the statistical variations of other performance parameters ( Q-factor and SNR) and link model parameters (input signal polarization, average PDL value, and link number K) are also investigated.