ESO and a large European consortium completed the phase-A study of EPICS, an instrument dedicated to exoplanets direct imaging for the EELT. The very ambitious science goals of EPICS, the imaging of reflected light of mature gas giant exoplanets around bright stars, sets extremely strong requirements in terms of instrumental contrast achievable. The segmented nature of an ELT appears as a very large source of quasi-static high order speckles that can impair the detection of faint sources with small brightness contrast with respect to their parent star. The paper shows how the overall system has been designed in order to maximize the efficiency of quasi-static speckles rejection by calibration and post-processing using the spectral and polarization dependency of light waves. The trade-offs that led to the choice of the concepts for common path and diffraction suppression system is presented. The performance of the instrument is predicted using simulations of the extreme Adaptive Optics system and polychromatic wave-front propagation through the various optical elements.