  The coupled dark energy model provides a possible approach to mitigate the
coincidence problem of cosmological standard model. Here, the coupling term is
assumed as $\bar{Q}=3H\xi_x\bar{\rho}_x$, which is related to the interaction
rate and energy density of dark energy. We derive the background and
perturbation evolution equations for several coupled models. Then, we test
these models by currently available cosmic observations which include cosmic
microwave background radiation from Planck 2015, baryon acoustic oscillation,
type Ia supernovae, $f\sigma_8(z)$ data points from redshift-space distortions,
and weak gravitational lensing. The constraint results tell us there is no
evidence of interaction at 2$\sigma$ level, it is very hard to distinguish
different coupled models from other ones.
