3.2.2 PPM signaling on the noiseless photon counting channel

When no background photons are absorbed, $\bar n_b = 0$, and the capacity simplifies to [McE81]

$$C = {(1 - e^{-\eta \bar n_s}) \log_2 M \over \eta \bar n_s (MT_s + T_d)} ,$$ (7)

where $\eta \bar n_s$ is the average number of absorbed photons per pulse. This can provide an easy bound for the noisy photon counting channel. As $\bar n_b \rightarrow 0$, the capacity will approach this noiseless case.