We study a memoryless molecular communication channel with an additive inverse Gaussian noise (AIGN). We assume that information are encoded in the release time of molecules and the arrival time of the transmitted molecules at the receiver is the release time plus a propagation delay. Motivated by the Brownian motion, the propagation delay is modelled as an inverse Gaussian random variable. Lower- and upper bounds on the capacity are presented. In particular, we develop simple capacity expressions for cases either when the molecules have a high drift velocity or when the medium has a low diffusion coefficient.
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