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Analysis of Diffusion Based Molecular Communication with Multiple Transmitters having Individual Random Information Bits

In this paper, we present an analytical framework to derive the performance of a molecular communication system where a transmitter bio-nano-machine (TBN) is communicating with a fully-absorbing spherical receiver bio-nano-machine (RBN) in a diffusive propagation medium in the presence of other TBNs. We assume that transmit bits at each TBN is random and different than transmit bits at other TBNs. We model the TBNs using a marked Poisson point process (PPP) with their locations as points of PPP and transmit symbols as marks. We consider both inter-symbol interference (ISI) and co-channel interference (CCI). ISI is caused by molecules transmitted in the previous slots while CCI is due to the molecules emitted from other TBNs. We derive the bit error probability of this system by averaging over the distribution of the transmit bits as opposed to the past approaches consisting of conditioning on previous transmit bits and/or assuming the transmit bits of every TBN are the same. Using numerical results, we validate our analysis and provide various design insights about the system, for example, the impact of detection threshold on the system performance. We also show the importance of accurately incorporating the randomness of transmit bits in the analysis.