Diffusion-based communications refers to the transfer of information using particles as message carriers whose propagation is based on the law of particle diffusion. Though still at an early stage, there have been growing interests and research efforts dedicated to this communication technology. It has been identified that diffusion-based communications is one of the most promising approaches for end-to-end communication between nanoscale devices in the near future. In this paper, the design of a binary digital communication system is proposed based on particle diffusion. Stochastic signaling through On-Off Keying (OOK) for random particle emission and a diffusion channel with memory is considered. The diffusion is considered in the cases of one, two, and three dimensions. The receiver detection problem is formulated by using an information-theoretic approach. The optimal decision threshold for the receiver detection is derived through mutual information maximization for two cases, namely, when the a priori probability of bit transmission is fixed and known to the receiver and when this probability is unknown to the receiver. Numerical results indicate that in the case of diffusion in one or two dimensions, the information of a priori probability plays a key role in optimizing the system performance, while it does not when considering the diffusion in three dimensions.