  This paper considers a diffusion-based molecular communication system where
the transmitter uses Reaction Shift Keying (RSK) as the modulation scheme. We
focus on the demodulation of RSK signal at the receiver. The receiver consists
of a front-end molecular circuit and a back-end demodulator. The front-end
molecular circuit is a set of chemical reactions consisting of multiple
chemical species. The optimal demodulator computes the posteriori probability
of the transmitted symbols given the history of the observation. The derivation
of the optimal demodulator requires the solution to a specific Bayesian
filtering problem. The solution to this Bayesian filtering problem had been
derived for a few specific molecular circuits and specific choice(s) of
observed chemical species. The derivation of such solution is also lengthy. The
key contribution of this paper is to present a general solution to this
Bayesian filtering problem which can be applied to any molecular circuit and
any choice of observed species.
