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This paper discusses the iterative decoding of a serial concatenation of a short constraint length convolutional code and coded PPM through a bit interleaver. To reduce the complexity of iterative decoding, we propose to compute and store only a subset of the channel likelihoods. We show that this can be done while suffering a negligible loss in performance. The complexity of implementing the forward-backward algorithm is also reduced when partial likelihoods are retained and when optical links are used to support deep space communication at high data rates.