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Iterative decoding of bit-interleaved coded modulation (BICM) is analyzed. The interleaver of a BICM system is shown to provide not only time diversity gain as a channel interleaver, but also interleaving gain as a code interleaver. Our performance analysis of BICM assumes a uniform interleaver, and it is shown that the interleaving gain can be achieved at high SNR. The design rules on the symbol mapper are derived and a new symbol mapper design, called the maximum squared Euclidean weight (MSEW) symbol mapper, is presented for both 8-PSK and 16-QAM. Extensions to other signal constellations is straight forward. Simulation results confirm our analysis and show that BICM with MSEW symbol mapping achieves near Shannon limit performance.