  We give a progress report on a project aimed at a high-precision calculation
of the decay constants $f_B$ and $f_{B_s}$ from simulations with HISQ heavy and
light valence and sea quarks. Calculations are carried out with several heavy
valence-quark masses on ensembles with 2+1+1 flavors of HISQ sea quarks at five
lattice spacings and several light sea-quark mass ratios $m_{ud}/m_s$,
including approximately physical sea-quark masses. This range of parameters
provides excellent control of the continuum limit and of heavy-quark
discretization errors. We present a preliminary error budget with projected
uncertainties of 2.2~MeV and 1.5~MeV for $f_B$ and $f_{B_s}$, respectively.
