# Capacity of Molecular Channels with Imperfect Particle-Intensity Modulation and Detection

## TL;DR

This paper models a molecular communication channel considering imperfect particle release and detection, characterizes the optimal input distribution, and derives capacity limits, especially under binary input constraints.

## Contribution

It introduces the particle-intensity channel model, analyzes the optimal input distribution, and derives capacity expressions for diffusive molecular communication with practical constraints.

## Key findings

- Optimal input distribution has mass points at zero and maximum particles.
- Binary input can be capacity-achieving under certain conditions.
- Capacity expression derived for diffusive particle transport.

## Abstract

This work introduces the particle-intensity channel (PIC) as a model for molecular communication systems and characterizes the properties of the optimal input distribution and the capacity limits for this system. In the PIC, the transmitter encodes information, in symbols of a given duration, based on the number of particles released, 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 number of particles released, and the receiver may not detect all the particles that arrive. We demonstrate that the optimal input distribution for this channel always has mass points at zero and the maximum number of particles that can be released. We then consider diffusive particle transport, derive the capacity expression when the input distribution is binary, and show conditions under which the binary input is capacity-achieving. In particular, we demonstrate that when the transmitter cannot generate particles at a high rate, the optimal input distribution is binary.