  We use higher dimensional bosonization and fermion decoration to construct
exactly soluble interacting fermion models to realize fermionic symmetry
protected trivial (SPT) orders (which are also known as symmetry protected
topological orders) in any dimensions and for generic fermion symmetries $G_f$,
which can be a non-trivial $Z_2^f$ extension (where $Z_2^f$ is the
fermion-number-parity symmetry). This generalizes the previous results from
group superconhomology of Gu and Wen (arXiv:1201.2648), where $G_f$ is assumed
to be a trivial $Z_2^f$ extension. We find that the SPT phases from fermion
decoration construction can be described in a compact way using higher groups.
