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A precoding design is proposed for multiple-input multiple-output (MIMO) systems utilizing nonbinary low-density parity check (NB-LDPC) codes and many-to-one mapping. When a high-order modulation scheme is used, many-to-one mapping converts a group of low-order Galois field (GF) coded symbols into one modulated MIMO symbol vector. In contrast, one-to-one mapping maps a high-order modulation symbol directly from one high-order GF coded symbol. With the help of an interleaver between the NB-LDPC encoder and the GF to MIMO symbol mapper, the many-to-one mapping enables turbo receiver and reduces the computational complexity by more than 95%. The proposed MIMO precoders enhance the error-rate performance of the many-to-one NB-LDPC MIMO system, especially in terms of reducing the error floor and improving the waterfall region. The proposed precoder design modifies the approach that suboptimally maximizes the minimal Euclidean distance between the received MIMO symbols. Simulation results show that the proposed precoders enhance the robustness of the precoder design and reduce the inner and outer iterations of the turbo receiver. [ABSTRACT FROM PUBLISHER]