  The present work is based on the holographic dark energy model with Hubble
horizon as the infrared cut-off. The interaction rate between dark energy and
dark matter has been reconstructed for three different parameterizations of the
deceleration parameter. Observational constraints on the model parameters have
been obtained by maximum likelihood analysis using the observational Hubble
parameter data (OHD), type Ia supernovab data (SNe), baryon acoustic
oscillation data (BAO) and the distance prior of cosmic microwave background
(CMB) namely the CMB shift parameter data (CMBShift). The interaction rate
obtained in the present work remains always positive and increases with
expansion. It is very similar to the result obtained in previous findings where
the interaction rate has been reconstructed for a parametrization of the dark
energy equation of state. Tighter constraints on the interaction rate have been
obtained in the present work as it is based on larger data sets. The nature of
the dark energy equation of state parameter has also been studied for the
present models. Though the reconstruction is done from different
parametrizations, the overall nature of the interaction rate is very similar in
all the cases. Different information criteria and the Bayesian evidence, which
have been invoked in the context of model selection, show that the these models
are at close proximity of each other.
