  In the derivation of Holographic Dark Energy (HDE), the area law of the black
hole entropy assumes a crucial role. However, the entropy-area relation can be
modified including some quantum effects, motivated from the Loop Quantum
Gravity (LQG), string theory and black hole physics. In this paper, we study
the cosmological implications of the interacting logarithmic entropy-corrected
HDE (LECHDE) model in the framework of Brans-Dicke (BD) cosmology. As system's
infrared (IR) cut-off, we choose the average radius of Ricci scalar curvature,
i.e. $R^{-1/2}$. We obtain the Equation of State (EoS) parameter $\omega_D$,
the deceleration parameter $q$ and the evolution of energy density parameter
$\Omega'_D$ of our model in a non-flat universe. Moreover, we study the
limiting cases corresponding to our model without corrections and to the
Einstein's gravity.
