  We present a statistical detection of 1.5 GHz radio continuum emission from a
sample of faint z~4 Lyman-break galaxies (LBGs). LBGs are key tracers of the
high-redshift star formation history and important sources of UV photons that
ionized the intergalactic medium in the early universe. In order to better
constrain the extinction and intrinsic star formation rate (SFR) of
high-redshift LBGs, we combine the latest ultradeep Karl G. Jansky Very Large
Array 1.5 GHz radio image and the Hubble Space Telescope Advance Camera for
Surveys (ACS) optical images in the Great Observatories Origins Deep
Survey-North. We select a large sample of 1771 z~4 LBGs from the ACS catalogue
using $\bband$-dropout color criteria. Our LBG samples have $\iband$~25-28
(AB), ~0-3 magnitudes fainter than M*_UV at z~4. In our stacked radio images,
we find the LBGs to be point-like under our 2" angular resolution. We measure
their mean 1.5 GHz flux by stacking the measurements on the individual objects.
We achieve a statistical detection of $S_{1.5GHz}$=0.210+-0.075 uJy at ~3
sigma, first time on such a faint LBG population at z~4. The measurement takes
into account the effects of source size and blending of multiple objects. The
detection is visually confirmed by stacking the radio images of the LBGs, and
the uncertainty is quantified with Monte Carlo simulations on the radio image.
The stacked radio flux corresponds to an intrinsic SFR of 16.0+-5.7 M/yr, which
is 2.8X the SFR derived from the rest-frame UV continuum luminosity. This
factor of 2.8 is in excellent agreement with the extinction correction derived
from the observed UV continuum spectral slope, using the local calibration of
meurer99. This result supports the use of the local calibration on
high-redshift LBGs for deriving the extinction correction and SFR, and also
disfavors a steep reddening curve such as that of the Small Magellanic Cloud.
