i am looking for implementations and formulas for belief propagation detector for MIMO?
Please find attached the couple of articles catering exactly to your question.
This can help:
https://filebox.ece.vt.edu/~s14ece6504/projects/wechen5_gbp/index.html
Belief propagation is generally an estimation algorithm which can be used for detection too. Its application depends on the final decision rule.
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