On the capacity-achieving input for additive inverse Gaussian channels

In a molecular communication system, molecules convey the information by traversing from the transmitter to the receiver through the medium, which is often liquid. The time for a molecule to travel a fixed distance according to Brownian motion with a constant drift has the inverse Gaussian distribution. Hence the molecular communication channel is modeled by an additive inverse Gaussian noise channel, the input of which is the release times of the molecules. This paper studies the capacity-achieving input distribution for such a channel, where the release time is subject to both peak and average constraints. Several properties of the capacity-achieving input are established. A numerical method for computing the optimal input distribution is developed. The result complements some existing bounds on the capacity of molecular channel.