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A generalised performance bounding technique for BICM systems is presented. We show that, in the Rayleigh fading channel, it is possible to estimate accurately the error performance of coded BICM systems employing large signal constellations, by using only the error performance of a BPSK system employing the same code in the same channel. Our method generalizes the work of G. Caire et al. (see IEEE Trans. on Information Theory, vol.44, no.3, p.927-46, 1998) to all SNR values and is independent of the channel coding scheme and the code rate. The work here implies that, in the Rayleigh fading channel, analytical bounds for any coding scheme derived for the BPSK system can be easily applied to BICM systems with larger signal constellations. Simulation results are presented for the Rayleigh fading channel to verify the analysis.