An analytical method is presented for deriving the BER of optical OOK systems using soft decision Viterbi decoding. An APD and photon counter are employed as a detector, and the background optical noise and dark current noise of the APD are taken into account in the analysis. We employ two kinds of the soft decision boundary, which are the optimum boundary maximizing the cutoff rate R0 and the equal spacing boundary. For the symbol metric quantization methods both the optimum metric of the logarithm of the soft decision probability and the linear increment metric are utilized. Since the optical channel is not symmetric, we derive the tight upper-bound of the BER conditioned on the data sequence with the aid of the generating function of the employed code. Then averaging the conditional BER by the data sequence, we obtain the average BER. Numerical results of the BER are given for hard decision and 4-level soft decision comparing with the no coding case, and show the significance of the coding gain. Effects of the soft decision boundary and metric quantization method are also examined from the view points of both the BER and the cutoff rate R0. It is shown that, the linear increment metric system is easily realized, but the BER degrades rapidly with the scintillation. Therefore the boundary spacing should be changed according to the signal level in the linear increment metric case. Furthermore some computer simulations are made to confirm the validity of the analysis.

An optical On-Off Keyed (OOK) pulse is often stretched in dispersive channels, thus producing intersymbol interference (ISI) and degrading the performance. In this paper, error probability is presented for a convolutionally encoded optical OOK channels with ISI. Both ISI-matched and ISI-mismatched decoders are taken into account in the error probability analysis. The encoded optical OOK signal is received by Avalanche Photo Diode (APD) and the number of APD output photo-electrons is counted for soft decision Viterbi decoding. Error probability is derived for a 3-bit and an ideal soft decision schemes in ISI-mismatched decoder and for an ideal soft decision scheme in ISI-matched decoder. Numerical results demonstrate the effects of mismatching or 3-bit soft decision scheme. Some computer simulations are carried out to confirm the validity of the analysis.