  Compared to the linear MIMO detectors, the Belief Propagation (BP) detector
has shown greater capabilities in achieving near optimal performance and better
nature to iteratively cooperate with channel decoders. Aiming at real
applications, recent works mainly fall into the category of reducing the
complexity by simplified calculations, at the expense of performance sacrifice.
However, the complexity is still unsatisfactory with exponentially increasing
complexity or required exponentiation operations. Furthermore, due to the
inherent loopy structure, the existing BP detectors persistently encounter
error floor in high signal-to-noise ratio (SNR) region, which becomes even
worse with calculation approximation. This work aims at a revised BP detector,
named {Belief-selective Propagation (BsP)} detector by selectively utilizing
the \emph{trusted} incoming messages with sufficiently large \textit{a priori}
probabilities for updates. Two proposed strategies: symbol-based truncation
(ST) and edge-based simplification (ES) squeeze the complexity (orders lower
than the Original-BP), while greatly relieving the error floor issue over a
wide range of antenna and modulation combinations. For the $16$-QAM $8 \times
4$ MIMO system, the $\mathcal{B}(1,1)$ {BsP} detector achieves more than
$4$\,dB performance gain (@$\text{BER}=10^{-4}$) with roughly $4$ orders lower
complexity than the Original-BP detector. Trade-off between performance and
complexity towards different application requirement can be conveniently
obtained by configuring the ST and ES parameters.
