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Bit-interleaved coded modulation (BICM) has been adopted in many systems and standards for spectrally efficient coded transmission. The analytical evaluation of BICM performance parameters, in particular bit-error rate (BER), has received considerable attention in the recent past. In this paper, we derive BER approximations for BICM transmission over general fading channels impaired by Gaussian mixture noise (GMN). To this end, we build upon the saddlepoint approximation of the pairwise error probability (PEP) and a recently established approximation for the probability density function (PDF) of bit-wise reliability metrics for nonfading additive white Gaussian noise (AWGN) channels. We extend this PDF approximation to the case of GMN, and obtain closed-form expressions for its Laplace transform for fading GMN channels. The latter allows us to express the PEP and thus BER via the saddlepoint approximation. For the special case of fading AWGN channels the presented approximations are closed form, since the saddlepoint is well approximated by 1/2 for BICM decoding. Furthermore, we derive closed-form PEP expressions also for GMN channels in the high signal-to-noise ratio regime and establish the diversity and coding gain for BICM transmission over fading GMN channels. Selected numerical results for the BER of convolutional coded BICM highlight the usefulness of the proposed approximations and the differences between AWGN and GMN channels.