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A unified bit-based probabilistic data association (B-PDA) detection approach is proposed for multiple-input-multiple-output (MIMO) systems employing high-order rectangular quadrature amplitude modulation (QAM). The new approach transforms the symbol detection process of QAM to a bit-based process by introducing a unified matrix representation (UMR) of QAM. Both linear natural and nonlinear binary reflected Gray bit-to-symbol mappings are considered. With the aid of simulation results, we demonstrate that the linear-natural-mapping-based B-PDA approach typically attained an improved detection performance [measured in terms of both bit error ratio (BER) and symbol error ratio (SER)] in comparison with the conventional symbol-based probabilistic data association (PDA)-aided MIMO detector, despite its dramatically reduced computational complexity. The only exception is that, at low SNRs, the linear-natural-mapping-based B-PDA is slightly inferior in terms of its BER to the conventional symbol-based PDA using binary reflected Gray mapping. Furthermore, the simulation results show that the linear-natural-mapping-based B-PDA MIMO detector may approach the best-case performance provided by the nonlinear binary reflected Gray-mapping-based B-PDA MIMO detector under ideal conditions. Additionally, the implementation of the B-PDA MIMO detector is shown to be much simpler in the case of the linear natural mapping. Based on these two points, we conclude that, in the context of the uncoded B-PDA MIMO detector, it is preferable to use the linear natural bit-to-symbol mapping, rather than the nonlinear Gray mapping.