Truncated Lévy Statistics for Diffusion Based Molecular Communication

In this paper, we use the truncated Lévy distribution to model the first arrival time in a molecular communication channel where information on the release time of the molecules is modulated and the molecules have an exponentially distributed lifetime. The general statistics for a random variable described by a truncated Lévy distribution are developed. Considering systems where a large number of molecules is used so that the average arrival time can be represented by a truncated Lévy flight, we derive an expression for the number of molecules required for the cross-over from the Lévy regime to the Gaussian regime to occur. We also use these statistics to obtain bounds on the capacity of these channels in an information theoretic sense.

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