  Cosmic Reionization imprints its signature on the temperature and
polarization anisotropies of the cosmic microwave background (CMB). Advances in
CMB telescopes have already placed a significant constraint on the history of
reionization. As near-future CMB telescopes target the maximum sensitivity, or
observations limited only by the cosmic variance (CV), we hereby forecast the
potential of future CMB observations in constraining the history of
reionization. In this study, we perform Markov Chain Monte Carlo analysis for
CV-limited E-mode polarization observations such as the LiteBIRD (Light
satellite for the studies of B-mode polarization and Inflation from cosmic
background Radiation Detection), based on a few different methods that vary in
the way of sampling reionization histories. We focus especially on estimating
the very early history of reionization that occurs at redshifts $z>15$, which
is quantified by the partial CMB optical depth due to free electrons at $z>15$,
$\tau_{z>15}$. We find that reionization with $\tau_{z>15} \sim 0.008$, which
are well below the current upper limit $\tau_{z>15} \sim 0.02$, are achievable
by reionization models with minihalo domination in the early phase and can be
distinguished from those with $\tau_{z>15} \lesssim 5\times 10^{-4}$ through
CV-limited CMB polarization observations. An accurate estimation of
$\tau_{z>15}$, however, remains somewhat elusive. We investigate whether
resampling the E-mode polarization data with limited spherical-harmonic modes
may resolve this shortcoming.
