On Binary Detection with Hysteresis

A binary detector with hysteresis-type nonlinearity is investigated. The detector is proposed as a suboptimal solution for a bit rate transparent midspan repeater in all optical networks. It is shown that key computations for the bit error rate are reduced to the well-known "exit problem" of stochastic differential equation theory. This formalism is employed to derive closed form expressions in the transform domain for the probability density function of the detector output in the presence of additive noise. Applying inverse transformations, these expressions can be utilized to determine various performance measures of binary detectors with hysteresis.