5 Conclusions

This report considered an X2000 2nd delivery laser and detector, representing the current technology available. Capacity was reported in terms of BER vs. background level, code rate vs. background level, and data rate vs. background level. Optimization of the PPM order and APD gain were also discussed.

Results indicate that for 256-PPM and rate 7/8 coding, RS codes can handle all but the last 3.5 dB of the background levels that capacity promises can be handled while operating at a BER of $10^{-6}$.

The optimal value of PPM order depends greatly on the background light. For nighttime reception, the optimal PPM order was found to be $M=2036$, while for daytime reception, $M=18$. With mismatched PPM order, the capacity reduces by more than a factor of two, which suggests that multiple-order PPM systems should be used if feasible.

Future advances in lasers and detectors have not been considered in this report. Evaluating capacity for these advancements would provide very useful information regarding the limits at which the optical channel can operate. This work is straightforward but as of yet undone.

The report also gives a framework that can be used for evaluating the sensitivity of the capacity to each parameter. Holding all parameters fixed but one, it is possible to show the sensitivity of capacity to each parameter. This would provide valuable feedback to laser and detector developers and to system designers, who could then expend effort in the areas leading to the biggest system gains. For the APD, this would include a study of the affects of the quantum efficiency, thermal noise levels, dark currents, and so forth; for the lasers, this would include the repetition rate and the pulse power. Also, note that in this report we mostly kept $\bar n_s$ fixed at 100 photons per pulse. It is important to know how the capacity changes for varying $\bar n_s$.

Also unknown is the capacity loss due to the hard PPM symbol demodulator. Removing it and providing soft slot statistics directly to the decoder would improve capacity, and a study to quantify this gain would be an important advancement in our understanding of the optical channel.

Acknowledgements: The author thanks Meera Srinivasan for providing the C program to bound the symbol error using the APD, Juan Ceniceros for providing many FOCAS link tables, Gerry Ortiz for providing X2000 2nd delivery laser and detector parameters, and Bob McEliece for helpful discussions regarding the units of capacity and optimization of the PPM order.