  On large angular scales, the polarization of the CMB contains information
about the evolution of the average ionization during the epoch of reionization.
Interpretation of the polarization spectrum usually requires the assumption of
a fixed functional form for the evolution, e.g. instantaneous reionization. We
develop a model-independent method where a small set of principal components
completely encapsulate the effects of reionization on the large-angle E-mode
polarization for any reionization history within an adjustable range in
redshift. Using Markov Chain Monte Carlo methods, we apply this approach to
both the 3-year WMAP data and simulated future data. WMAP data constrain two
principal components of the reionization history, approximately corresponding
to the total optical depth and the difference between the contributions to the
optical depth at high and low redshifts. The optical depth is consistent with
the constraint found in previous analyses of WMAP data that assume
instantaneous reionization, with only slightly larger uncertainty due to the
expanded set of models. Using the principal component approach, WMAP data also
place a 95% CL upper limit of 0.08 on the contribution to the optical depth
from redshifts z>20. With improvements in polarization sensitivity and
foreground modeling, approximately five of the principal components can
ultimately be measured. Constraints on the principal components, which probe
the entire reionization history, can test models of reionization, provide
model-independent constraints on the optical depth, and detect signatures of
high-redshift reionization.
