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In this paper, the authors design bit interleaved coded modulations including a partial algebraic precoder in order to transmit several spatial streams with full diversity over a transmit beamformed MIMO channel. The achievable diversity orders with the coded modulation are derived, and allow for efficiently choosing the system parameters for optimizing the performance. Additionnally, a very efficient low complexity soft output detector based on algebraic reduction is presented. With a low complexity at the receiver, the precoded BICM system allows achieving high performance at very high efficiencies, e.g., 12 bits per second per hertz.
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