  We present a progress report on our calculation of the decay constants $f_B$
and $f_{B_s}$ from lattice-QCD simulations with highly-improved staggered
quarks. Simulations are carried out with several heavy valence-quark masses on
$(2+1+1)$-flavor ensembles that include charm sea quarks. We include data at
six lattice spacings and several light sea-quark masses, including an
approximately physical-mass ensemble at all but the smallest lattice spacing,
0.03 fm. This range of parameters provides excellent control of the continuum
extrapolation to zero lattice spacing and of heavy-quark discretization errors.
Finally, using the heavy-quark effective theory expansion we present a method
of extracting from the same correlation functions the charm- and bottom-quark
masses as well as some low-energy constants appearing in the heavy-quark
expansion.
