Markov Chain Modeling of the End-to-End Molecular Communication System Using Ligand Receiver

Molecular communication (MC) makes use of molecules as information carriers for nanoscale and macroscale applications. In this paper, an end-to-end biochemical communication modeling of an MC system is presented. The transmitter is assumed to be a point source, and the receiver is embedded with finite ligand receptors. The inherent memory in the fluid channel is represented by a Markov chain and additionally a novel Markov chain is proposed which takes into effect the aggregated decision of the receiver corresponding to the number of molecules received on the finite individual receptors. The proposed discrete-time Markov chain can potentially replace the block of the finite number of Markov chains for different ligand receptors followed by a threshold comparator. Moreover, the capacity of the ligand channel is analyzed for independent and identically distributed (IID) binary source and upper and lower bounds on the mutual information (MI) rate are derived for the Markov inputs to the ligand channel. The performance analysis for the end-to-end MC system is done by deriving the analytical expressions of the bit error rate for both IID and Markov inputs. Finally, we find the simulated probability of error and observe that the analytical results are corroborated by the simulated ones.