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We propose using a soft-input decoder for the decoding of internally convolutional coded Poisson noise-dominated fiber-optic code-division multiple-access (CDMA) communication systems using optical orthogonal codes. We first compute the coded symbol log-likelihoods at the output of the Poisson noise-dominated channel, which is then used by a soft-input maximum-likelihood decoder, for a fiber-optic CDMA system assuming both on-off keying and binary pulse position modulation schemes. Furthermore, we develop a discrete soft-output channel model for a Poisson noise-dominated channel, with which we evaluate the upper bound on the bit error probability of the internally coded Poisson noise-dominated fiber-optic CDMA system using a soft-input decoder. It is shown that the soft-input decoder significantly outperforms the hard-input decoder. Furthermore, the performance of the soft-input decoder is also evaluated in the presence of different values of dark current.