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A power and bandwidth-efficient bit-interleaved coded modulation (BICM) with orthogonal frequency-division multiplexing (OFDM) and iterative decoding (BI-COFDM-ID) using combined multidimensional mapping and subcarrier grouping is proposed for broadband transmission in a frequency-selective fading environment. A tight bound on the asymptotic error performance is developed, which shows that subcarrier mapping and grouping have independent impacts on the overall error performance, and hence, they can be independently optimized. Specifically, it is demonstrated that the optimal subcarrier mapping is similar to the optimal multidimensional mapping for bit-interleaved coded modulation with iterative decoding (BICM-ID) in frequency-flat Rayleigh fading environment, whereas the optimal subcarrier grouping is the same with that of OFDM with linear constellation preceding (LCP). Furthermore, analytical and simulation results show that the proposed system with the combined optimal subcarrier mapping and grouping can achieve the full channel diversity without using LCP and provide significant coding gains as compared to the previously studied BI-COFDM-ID with the same power, bandwidth, and receiver complexity.