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This paper investigates the application of bit-interleaved coded modulation and iterative decoding (BICM-ID) in orthogonal-frequency-division-multiplexing (OFDM) systems with signal space diversity (SSD) over frequency-selective Rayleigh-fading channels. Correlated fading over subcarriers is assumed. At first, a tight bound on the asymptotic error performance for the general case of precoding over all N subcarriers is derived and used to establish the best achievable asymptotic performance by SSD. It is then shown that precoding over subgroups of at least L subcarriers per group, where L is the number of channel taps, is sufficient to obtain this best asymptotic error performance, while significantly reducing the receiver complexity. The optimal joint subcarrier grouping and rotation matrix design is subsequently determined by solving the Vandermonde linear system. Illustrative examples show a good agreement between various analytical and simulation results