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The analytical calculation of the bit error rate (BER) of digital optical receivers that employ avalanche photodiodes (APDs) is challenging due to 1) the stochastic nature of the avalanche photodiode's impulse-response function and 2) the presence of intersymbol interference (ISI). At ultrafast transmission rates, ISI becomes a dominant component of the BER, and its effect on the BER should be carefully addressed. One solution to this problem, termed the bit-pattern-dependent (PD) approach, is to first calculate the conditional BER given a specific bit pattern and then average over all possible bit patterns. Alternatively, a simplifying method, termed the bit-pattern-independent (PI) approach, has been commonly used whereby the average bit stream is used to calculate the distribution of the receiver output, which, in turn, is used to calculate the BER. However, when ISI is dominant, the PI approximation is inaccurate. Here, the two approaches are analytically compared by analyzing their asymptotic behavior and their bounds. Conditions are found to determine when the PI method overestimates the BER. The BER found using the PD method exponentially decays with the received optical power, whereas for the PI approach, the BER converges to a constant, which is unrealistic. For an InP-based APD receiver with a 100-nm multiplication layer, the PI method is found to be inaccurate for transmission rates beyond 20 Gb/s.

On the Use of Gaussian Approximation in Analyzing the Performance of Optical Receivers