Capacities and Optimal Input Distributions for Particle-Intensity Channels

TL;DR

This paper models molecular communication as a particle-intensity channel, characterizes its capacity limits, and develops an efficient algorithm to find optimal input distributions, revealing they often have mass points at zero and one.

Contribution

It introduces the particle-intensity channel model, characterizes capacity-achieving inputs, and proposes the dynamic assignment Blahut-Arimoto algorithm for this purpose.

Findings

Capacity-achieving input distributions have mass points at zero and one.

The DAB algorithm efficiently finds optimal input distributions.

Conditions for two-mass-point capacity-achieving inputs are derived.

Abstract

This work introduces the particle-intensity channel (PIC) as a model for molecular communication systems and characterizes the capacity limits as well as properties of the optimal (capacity-achieving) input distributions for such channels. In the PIC, the transmitter encodes information, in symbols of a given duration, based on the probability of particle release, and the receiver detects and decodes the message based on the number of particles detected during the symbol interval. In this channel, the transmitter may be unable to control precisely the probability of particle release, and the receiver may not detect all the particles that arrive. We model this channel using a generalization of the binomial channel and show that the capacity-achieving input distribution for this channel always has mass points at probabilities of particle release of zero and one. To find the capacity-achieving input distributions, we develop an efficient algorithm we call dynamic assignment Blahut-Arimoto (DAB). For diffusive particle transport, we also derive the conditions under which the input with two mass points is capacity-achieving.