2.2.1 Bits per photon or bits per channel use

A channel capacity of $C$ bits per channel use can be restated as $C / \bar n_s$ bits per signal photon, $C / M$ bits per PPM slot (neglecting the dead time), and $C/(MT_s + T_d)$ bits per second. The capacity in bits per photon or bits per channel use is not bounded for noiseless PPM, if perfect timing is assumed [PPR81]. (Other practical constraints bound it [McE81,Les83].) Intuitively, the reason is that by choosing increasing values of $M$ and keeping the slot duration fixed, the statistics governing the number of photons detected in the signal slot remain the same, but the number of bits per symbol increases as $\log_2 M$. Thus, the capacity in bits per photon (or bits per channel use) increases as $\log_2 M$, an unbounded number as $M$ increases.

This unbounded capacity in bits/photon is not particularly useful, however, because it necessitates a low data rate and wasted power. Lasers on a spacecraft can have power allocated to them on a continual basis, at least within the intervals of time set aside for transmission to earth. This power is used primarily to charge the laser after it has fired a pulse. If the laser waits an extensive period of time between pulse firings, that power is being wasted. From an information theoretical standpoint, the waste can be quantified by the lost entropy of the signal. The information content of a set of signaling slots (ones) and nonsignaling slots (zeroes) decreases as their probabilities are made more disparate. An increasing $M$ means that the information content per slot (or per unit time) is decreasing, because $M-1$ out of $M$ of the slots contain zeroes.