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 $1sigma$ raw contrast of $sim3cdot10^{-11}- 8 cdot 10^{-11}$ between 1 and 18 $lambda / D$.
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