  The fusion barrier distribution has provided a nice representation for the
channel coupling effects on heavy-ion fusion reactions at energies around the
Coulomb barrier. Here we discuss how one can extract the same representation
using the so called sum-of-differences (SOD) method with quasi-elastic
scattering cross sections. In contrast to the conventional quasi-elastic
barrier distribution, the SOD barrier distribution has an advantage in that it
can be applied both to non-symmetric and symmetric systems. It is also the case
that the correspondence to the fusion barrier distribution is much better than
the quasi-elastic barrier distribution. We demonstrate its usefulness by
studying $^{16}$O+$^{144}$Sm, $^{58}$Ni+$^{58}$Ni, and $^{12}$C+$^{12}$C
systems.
