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The authors have derived a receiver model that provides an explicit relationship between the Q factor and the optical signal-to-noise ratio (OSNR) in optical fiber communication systems for arbitrary pulse shapes, realistic receiver filters, and arbitrarily polarized noise. It is shown how the system performance depends on both the degree of polarization of the noise and the angle between the Stokes' vectors of the signal and the noise. The results demonstrate that the relationship between the OSNR and the Q factor is not unique when the noise is partially polarized. This paper defines the enhancement factor and three other parameters that explicitly quantify the relative performance of different modulation formats in a receiver. The theoretical and experimental results show that the performance of the return-to-zero format is less sensitive to variations in the receiver characteristics than is the performance of the nonreturn-to-zero format. Finally, a validation of the formula is presented for computing the Q factor from the OSNR and the Stokes vectors of the signal and the noise by comparison with both experiments and Monte Carlo simulations.