A General Upper Bound On Point-To-Point Particle Timing Channel Capacity Under Constant Particle Emission Intensity

The past decade has produced a large body of work on communication channels which use chemicals to communicate. Some work uses a finest grain model wherein the arrival times of individual emitted particles convey information. Others consider a related particle intensity system where the time is binned at the transmitter/receiver and the number of particles released and counted conveys information. Still others consider a macroscopic model that uses an Avogradrian number of particles and thus concentration as the information carrier. However, given the myriad emission, carrier transport and uptake/sensing methods studied, it has been difficult to precisely relate timing, intensity and concentration results. Here we attempt a partial unification through a simple upper bound applicable to any finite-mean first-passage time transport mechanism under an assumption of constant particle emission intensity (lambda) over bar. Our result is expressed in terms of three quantities: the particle emission rate mu, the average particle uptake rate (lambda) over bar, and the entropy of the first-passage time distribution, h(D).