The peak constrained additive inverse Gaussian noise channel

In molecular communication, messages are conveyed in patterns of particles (e.g., arranged in time), which propagate from transmitter to receiver by means of Brownian motion. If there is drift from transmitter to receiver, the first arrival time of the particles has the Inverse Gaussian distribution, leading to the additive inverse Gaussian noise channel. In this paper, we give a closed-form upper bound on capacity for this channel when the maximum waiting time is constrained, building on previous work in which only the mean waiting time was constrained.