# Communication System Design and Analysis for Asynchronous Molecular Timing Channels

## TL;DR

This paper introduces and analyzes three asynchronous molecular timing modulation techniques, deriving their noise characteristics, detection rules, and comparing their bit error rate performance, with one nearly matching synchronized modulation.

## Contribution

The paper proposes two novel asynchronous modulation schemes for molecular timing channels and provides a comprehensive analysis of their noise models, detection strategies, and performance comparison.

## Key findings

- All three modulation techniques can be modeled as additive noise channels.
- The noise has infinite variance, so geometric power and G-SNR are used for analysis.
- Asynchronous modulation with distinguishable particles nearly matches synchronized scheme performance.

## Abstract

Two new asynchronous modulation techniques for molecular timing (MT) channels are proposed. One based on modulating information on the time between two consecutive releases of indistinguishable information particles, and one based on using distinguishable particles. For comparison, we consider the synchronized modulation scheme where information is encoded in the time of release and decoded from the time of arrival of particles. We show that all three modulation techniques result in a system that can be modeled as an additive noise channel, and we derive the expression for the probability density function of the noise. Next, we focus on binary communication and derive the associated optimal detection rules for each modulation. Since the noise associated with these modulations has an infinite variance, geometric power is used as a measure for the noise power, and we derive an expression for the geometric SNR (G-SNR) for each modulation scheme. Numerical evaluations indicate that for these systems the bit error rate (BER) is constant at a given G-SNR, similar to the relation between BER and SNR in additive Gaussian noise channels. We also demonstrate that the asynchronous modulation based on two distinguishable particles can achieve a BER performance close to the synchronized modulation scheme.