  In this paper, we calculate the inclusive rate of $W^{+} W^{-}$ pair
production through leptonic decay channels $W^+W^- \to l^+\nu_l + l^{\prime -}
\nu_{l'}$ in the $k_t$-factorization framework. We also consider the exclusive
$W^{+} W^{-}$ pair production through the one-loop induced $gg \to H \to
W^+W^-$ channel that is important for the study of new physics beyond the
Standard Model. The results are compared with predictions from the Herwig 7
event generator in the collinear factorization framework and with the
experimental data from the ATLAS and the CMS collaborations. It will be shown
that our predictions for the $W^+W^-$ boson pair production signals are in
agreement with the experimental data as well as the collinear results.
