Cellular signaling is key for organisms to survive immediate stresses from fluctuating environments as well as relaying important information about external stimuli. Effective mechanisms have evolved to ensure appropriate responses for an optimal adaptation process. For them to be functional despite the noise that occurs in biochemical transmission, the cell needs to be able to infer reliably what was sensed in the first place. For example Saccharomyces cerevisiae are able to adjust their response to osmotic shock depending on the severity of the shock and initiate responses that lead to near perfect adaptation of the cell. We investigate the Sln1-Ypd1-Ssk1-phosphorelay as a module in the high-osmolarity glycerol pathway by incorporating a stochastic model. Within this framework, we can imitate the noisy perception of the cell and interpret the phosphorelay as an information transmitting channel in the sense of C.E. Shannon's "Information Theory". We refer to the channel capacity as a measure to quantify and investigate the transmission properties of this system, enabling us to draw conclusions on viable parameter sets for modeling the system.