A survey on optimal stochastic signaling and detector randomization

In this paper, a survey on stochastic signaling and detector randomization is presented for average power-constrained binary communications systems. First, the case of a single fixed detector at the receiver is considered, and then the joint design of detector and optimal signaling is studied. In addition, the optimal receiver design is examined in the presence of detector randomization and stochastic signaling. It is observed that the average probability of error achieved via detector randomization cannot be larger than that achieved via stochastic signaling in the presence of optimal MAP detectors. Finally, a numerical study is presented to illustrate an example.