Normal Inverse Gaussian Approximation for Arrival Time Difference in Flow-Induced Molecular Communications

Abstract: In this paper, we consider molecular communications in one-dimensional flow-induced diffusion channels with a perfectly absorbing receiver. In such channels, the random propagation delay until the molecules are absorbed follows an inverse Gaussian (IG) distribution and is referred to as first hitting time. Knowing the distribution for the difference of the first hitting times of two molecules is very important if the information is encoded by a limited set of molecules and the receiver exploits their arrival time and/or order. Hence, we propose a moment matching approximation by a normal inverse Gaussian (NIG) distribution and we derive an expression for the asymptotic tail probability. Numerical evaluations showed that the NIG approximation matches very well with the exact solution obtained by numerical convolution of the IG density functions. Moreover, the asymptotic tail probability outperforms state-of-the-art tail approximations.