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We design a bit-interleaved space-time coded modulation scheme using iterative decoding (BI-STCM-ID) combined with a new multidimensional mapping scheme invoking sphere-packing (SP) modulation, which we refer to as the space-time block-coded sphere-packed bit-interleaved coded modulation (STBC-SP-BICM) arrangement. The binary switching algorithm (BSA) is used to optimize the cost function employed for deriving different mapping strategies, which are designed with the aid of EXtrinsic Information Transfer (EXIT) charts for the sake of improving the convergence behavior of the system. The resultant system is amalgamated with a unity-rate code (URC) as a precoder to enhance the attainable iterative detection performance. An irregular URC (IrURC) is invoked to create an open EXIT tunnel at low signal-to-noise ratios (SNRs). The complexity of employing the multidimensional SP scheme is also addressed.