  We employ dimension-4 operators to improve the local vector and axial-vector
currents and calculate the nucleon isovector axial coupling $g^3_A$ with
overlap valence on $2+1$-flavor Domain Wall Fermion sea. Using the equality of
$g^3_A$ from the spatial and temporal components of the axial-vector current as
a normalization condition, we find that $g_A^3$ is increased by a few percent
towards the experimental value. The excited-state contamination has been taken
into account with three time separations between the source and sink. The
improved axial charges $g_A^{3}(24I)=1.22(4)$ and $g_A^{3}(32I)=1.21(3)$ are
obtained on a $24^3\times 64$ lattice at pion mass of 330 MeV and a $32^3\times
64$ lattice at pion mass 300 MeV are increased by $3.4\%$ and $1.7\%$ from
their unimproved values, respectively. We have also used clover fermion on the
same DWF configurations and find the same behavior for the local axial charge
as that of the overlap fermion.
