  The shape of the faint-end of the high-z galaxy luminosity function (LF)
informs early star formation and reionization physics during the Cosmic Dawn
and Epoch of Reionization. Until recently, based on the strong gravitational
lensing cluster deep surveys, the Hubble Frontier Fields (HFF) has found a
potential turnover in the ultraviolet (UV) LF at z$\sim$6. In this paper, we
analyze the contribution of extremely faint galaxies with the magnitude larger
than the turnover magnitude in LF to cosmic reionization. We apply the
measurement from HFF to our suppressed star formation efficiency model,
including three free parameters: halo mass threshold $M_t$, curvature parameter
$\beta$ and a UV conversion factor $l_{\rm UV}$. According to our fit of 68\%
confidence level, the high-redshift star formation in haloes smaller than $
M_t=1.82^{+2.86}_{-1.08}\times10^{10} \rm M_{\odot}$ is found to be dampened.
The turnover magnitude $\rm \gtrsim -13.99-2.45$, correspondingly the halo mass
$\lesssim(4.57+20.03)\times10^{9} \rm M_{\odot}$. We find that the absorption
trough in the global 21-cm signal is sensitive to our SFE model parameters.
Together with ($\beta$, $l_{\rm UV}$) = ($2.17^{+2.42}_{-1.72}$,
$9.33^{+0.43}_{-0.42} \rm ~erg~yr ~s^{-1}M_{\odot}^{-1})$, the trough locates
at $\sim$ $134^{+10}_{-17}$ $\rm MHz$ with an amplitude of $\sim$
$-237^{-6}_{+7}$ $\rm mK$, compared to (106\rm MHz, -212\rm mK) in the absence
of turnover. Besides, we find that the star formation of faint galaxies has
also an impact on the 21-cm power spectra. The best fitting peak power
decreases by $\sim4\%$ and shifts towards smaller scales from $0.88 h \rm
Mpc^{-1}$ to $0.91 h \rm Mpc^{-1}$. According to our calculation, such impact
is distinguishable with the forthcoming Square Kilometre Array.
