Capacity Limits of Diffusion-Based Molecular Timing Channels

This work introduces capacity limits for molecular timing (MT) channels, where information is modulated on the release timing of small information particles, and decoded from the time of arrival at the receiver. It is shown that the random time of arrival can be represented as an additive noise channel, and for the diffusion-based MT (DBMT) channel this noise is distributed according to the Lévy distribution. Lower and upper bounds on capacity of the DBMT channel are derived for the case where the delay associated with the propagation of information particles in the channel is finite. These bounds are also shown to be tight. Moreover, it is shown that by simultaneously releasing multiple particles, the capacity linearly increases with the number of particles. This is analogous to receive diversity as each particle takes a random independent path. This diversity of paths can be used to increase data rate significantly since, in molecular communication systems, it is possible to release many particles simultaneously and hence obtain the associated linear capacity increase.