  One of the main goals of modern cosmic microwave background (CMB) missions is
to measure the tensor-to-scalar ratio $r$ accurately to constrain inflation
models. Due to ignorance about the reionization history $X_{e}(z)$, this
analysis is usually done by assuming an instantaneous reionization $X_{e}(z)$
which, however, can bias the best-fit value of $r$. Moreover, due to the strong
mixing of B-mode and E-mode polarizations in cut-sky measurements, multiplying
the sky coverage fraction $f_{sky}$ by the full-sky likelihood would not give
satisfactory results. In this work, we forecast constraints on $r$ for the
Planck mission taking into account the general reionization scenario and
cut-sky effects. Our results show that by applying an N-point interpolation
analysis to the reionization history, the bias induced by the assumption of
instantaneous reionization is removed and the value of $r$ is constrained
within $5\%$ error level, if the true value of $r$ is greater than about 0.1 .
