Calculation and measurement of the probability of error in a binary optical communication channel provided by a polarization-modulated laser beam

A calculation is given of the total probability of an error $P_{\text{er}}$ in an optical communication channel in which the signal is in the form of a polarization-modulated laser beam. A general expression is derived for $P_{\text{er}}$ and it is used to obtain an equation for $P_{\text{er}}$ for an intensity-modulated laser beam. Measurements of $P_{\text{er}}$ under polarization- and intensity-modulation conditions are reported. It is shown that the threshold value corresponding to the minimum total error under polarization-modulation conditions is constant and equal to zero irrespective of the intensity of the laser and background radiation, whereas the optimal threshold under intensity-modulation conditions generally fluctuates. It is also shown that under the polarization-modulation conditions the intensity of the laser beam ensuring a given probability of total error is $\sqrt2$ times lower than the corresponding value under intensity-modulation conditions.