  The exploration of circumstellar environments by means of direct imaging to
search for Earth-like exoplanets is one of the challenges of modern astronomy.
One of the current limitations are evolving non-common path aberrations (NCPA)
that originate from optics downstream of the main wavefront sensor. The
self-coherent camera (SCC) is an integrated coronagraph and focal-plane
wavefront sensor that generates wavefront information-encoding Fizeau fringes
in the focal plane by adding a reference hole (RH) in the Lyot stop. Here, we
aim to show that by featuring a polarizer in the RH and adding a polarizing
beamsplitter downstream of the Lyot stop, the RH can be placed right next to
the pupil. We refer to this new variant of the SCC as the polarization-encoded
self-coherent camera (PESCC). We study the performance of the PESCC
analytically and numerically, and compare it, where relevant, to the SCC. We
show analytically that the PESCC relaxes the requirements on the focal-plane
sampling and spectral resolution with respect to the SCC by a factor of 2 and
3.5, respectively. Furthermore, we find via our numerical simulations that the
PESCC has effectively access to $\sim$16 times more photons, which improves the
sensitivity of the wavefront sensing by a factor of $\sim4$. We also show that
without additional measurements, the RH point-spread function (PSF) can be
calibrated using PESCC images, enabling coherent differential imaging (CDI) as
a contrast-enhancing post-processing technique for every observation. In
idealized simulations (clear aperture, charge two vortex coronagraph, perfect
DM, no noise sources other than phase and amplitude aberrations) and in
circumstances similar to those of space-based systems, we show that WFSC
combined with CDI can achieve a $1\sigma$ raw contrast of $\sim3\cdot10^{-11}-
8 \cdot 10^{-11}$ between 1 and 18 $\lambda / D$.
