4.2 Data rate vs. background level

Using Eq. (9), a bound on the highest data rate possible while operating at a given BER and $(M,\bar n_s,\bar n_b,T_s,T_d,$   detector$)$ was calculated. As $\bar n_b \rightarrow 0$, the data rate tends to the maximum dictated by $M$, $T_s$, and $T_d$: $\log_2M/(MT_s+T_d)$. Fig. 4 shows the maximum attainable data rate for a various $M$ and a range of $n_b$, and with fixed $\bar n_s$, $T_s$, $T_d$, and detector. Also shown is the RS coding performance when $M=256$.

Figure 4: Capacity of $M$-PPM on an optical channel, with $M\in \{2,64,256,2048,4096\}$, $P_b = 10^{-6}$, $\bar n_s=100$, $T_s=31.25$ ns, $T_d = 432000$ ns, and the SLiK APD detector.