A perpendicular medium microstructure consisting of fully exchange coupled grains with densely distributed nonmagnetic pinning sites, referred to as the percolated perpendicular medium, is proposed. In this medium, the ferromagnetic exchange coupling between the grains ensures sufficient thermal stability, while the densely distributed domain wall pinning sites ensure relatively smooth transition boundaries. The detailed magnetic hysteresis properties and recording characteristics of the percolated perpendicular media are investigated via micromagnetic modeling. The study found that the percolated medium could offer much improved recording properties in terms of enhanced transition sharpness and reduced transition noise while maintaining thermal stability in comparison to present granular perpendicular medium.