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Bit interleaved coded modulation with iterative decoding (BICM-ID) is a spectral efficiency coded modulation technique. This technique is therefore very attractive for many broadcasting services where transmission bandwidth is a primary concern. It has been shown that when signal constellation, interleaver and error-control code are fixed, signal mapping has a critical influence to the error performance of a BICM-ID system. Based on the technique of mutual information, good mappings of different 8-ary constellations are presented for BICM-ID systems over an additive white Gaussian noise (AWGN) channel. It is also shown that, compared to free Euclidean distances, mutual information is a more useful technique to find the good signal mappings for BICM-ID systems.