We propose a new design for a passive photonic reservoir computer on a silicon photonics chip which can be used in the context of optical communication applications, and study it through detailed numerical simulations. The design consists of a photonic crystal cavity with a quarter-stadium shape, which is known to foster interesting mixing dynamics. These mixing properties turn out to be very useful for memory-dependent optical signal processing tasks, such as header recognition. The proposed, ultra-compact photonic crystal cavity exhibits a memory of up to 6 bits, while simultaneously accepting bitrates in a wide region of operation. Moreover, because of the inherent low losses in a high-Q photonic crystal cavity, the proposed design is very power efficient.