  In this paper, we are concerned with global existence and optimal decay rates
of solutions for the three-dimensional compressible Hall-MHD equations. First,
we prove the global existence of strong solutions by the standard energy method
under the condition that the initial data are close to the constant equilibrium
state in $H^2$-framework. Second, optimal decay rates of strong solutions in
$L^2$-norm are obtained if the initial data belong to $L^1$ additionally.
Finally, we apply Fourier splitting method by Schonbek [Arch.Rational Mech.
Anal. 88 (1985)] to establish optimal decay rates for higher order spatial
derivatives of classical solutions in $H^3$-framework, which improves the work
of Fan et al.[Nonlinear Anal. Real World Appl. 22 (2015)].
