Variance-Constrained Capacity of the Molecular Timing Channel with Synchronization Error

TL;DR

This paper investigates the capacity limits of molecular timing channels with synchronization errors, deriving bounds that reveal practical conditions under which synchronization drift does not significantly impact capacity.

Contribution

It introduces a model incorporating synchronization error into molecular timing channels and derives bounds on capacity constrained by variance, providing practical insights.

Findings

Synchronization drift velocity need not be much higher than information link drift velocity.

Derived bounds on capacity highlight the impact of synchronization errors.

Numerical evaluations demonstrate the practical relevance of the bounds.

Abstract

Molecular communication is set to play an important role in the design of complex biological and chemical systems. An important class of molecular communication systems is based on the timing channel, where information is encoded in the delay of the transmitted molecule---a synchronous approach. At present, a widely used modeling assumption is the perfect synchronization between the transmitter and the receiver. Unfortunately, this assumption is unlikely to hold in most practical molecular systems. To remedy this, we introduce a clock into the model---leading to the molecular timing channel with synchronization error. To quantify the behavior of this new system, we derive upper and lower bounds on the variance-constrained capacity, which we view as the step between the mean-delay and the peak-delay constrained capacity. By numerically evaluating our bounds, we obtain a key practical insight: the drift velocity of the clock links does not need to be significantly larger than the drift velocity of the information link, in order to achieve the variance-constrained capacity with perfect synchronization.