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Molecular circuit for approximate maximum a posteriori demodulation of concentration modulated signals

This paper builds on our earlier work on designing demodulators for diffusion-based molecular communication using a Markovian approach. The demodulation filters take the form of an ordinary differential equation which computes log-posteriori probability of observing a transmission symbol given the continuous history of receptor activities. This work considers the realisation of these demodulation filters using molecular circuits, i.e. a set of chemical reactions. There are two key issues to overcome. First, these filters require the computation of a derivative. Second, these filters require a model of the expected signal and one needs to derive a method to encode this expected signal. In this paper, we use time-scale separation to handle the derivative computation. For the case where the transmitter uses rectangular pulses as its transmitting symbols, we show how the expected signal can be encoded. We show that the output of the derived molecular circuit is approximately equal to the log-posteriori probability calculated by the demodulation filter if the log-posteriori probability is positive.