4.6 Comparison of simulation to upper bound of uncoded APD-detected PPM

Most numerical results in this report required the determining the probability of uncoded PPM symbol detection error. Two approaches were taken- simulation and bounding. Using the method given in [DS88] to simulate the statistical properties of the APD, a channel was simulated for 100,000 256-PPM symbols. The probability of uncoded symbol error is shown in Fig. 10, and is compared to the upper bound used in Eq. (5) used to derive the remainder of the numerical results in the report. Since the upper bound is tighter than the union bound, it necessarily converges to the true value. We see this happening, if slowly, in Fig. 10.

Figure 10: Probability of uncoded 256-PPM symbol error on an optical channel with $\bar n_s=100$, $T_s=31.25$ns, and the SLiK APD detector.