  The coupling between dark sectors provides a possible approach to mitigate
the coincidence problem of cosmological standard model. In this paper, dark
energy is treated as a fluid with a constant equation of state, whose coupling
with dark matter is proportional the Hubble parameter and energy density of
dark energy, that is, $\bar{Q}=3\xi_x\bar{H}\bar{\rho}_x$. Particularly, we
consider the Hubble expansion rate to be perturbed in the perturbation
evolutions of dark sectors. Using jointing data sets which include cosmic
microwave background radiation, baryon acoustic oscillation, type Ia
supernovae, and redshift-space distortions, we perform a full Monte Carlo
Markov Chain likelihood analysis for the coupled model. The results show that
the mean value with errors of interaction rate is:
$\xi_x=0.00305_{-0.00305-0.00305-0.00305}^{+0.000645+0.00511+0.00854}$ for
$Q^{\mu}_A\parallel u^{\mu}_c$;
$\xi_x=0.00317_{-0.00317-0.00317-0.00317}^{+0.000628+0.00547+0.00929}$ for
$Q^{\mu}_A\parallel u^{\mu}_x$, which means that the recently cosmic
observations favored small interaction rate which is up to the order of
$10^{-3}$. Moreover, in contrast to the coupled model with unperturbed
expansion rate, we find perturbed Hubble expansion rate could bring about
negligible impact on the model parameter space.
