Fast and slow channels coordinate for better deadline communication
Fast-Slow Communication with Endogenous Transport
Information Theory
Summary
Some communication systems send urgent messages quickly and detailed messages slowly, but sometimes the fast channel also changes how the slow channel works. The authors studied how these two types of channels can share resources effectively, especially when there's a deadline to meet. They found precise conditions when the two channels help each other rather than compete, and described how this depends on physical properties like drift and diffusion. Their results are supported by mathematical proofs and examples that show practical relevance for channels experiencing noise and interference.
What this means in practice
- •For network schedulers: Design communication protocols that balance urgent fast signals and detailed slower signals efficiently under deadline constraints using joint resource allocation.
- •For biomedical device engineers: Develop timing-aware molecular communication systems where fast signaling triggers changes in slow molecular transport for improved information delivery.
Tested on simulated data.
Authors
Lav R. Varshney
Abstract
A communication system may convey urgent information through a fast physical stream and more specific information through a slower material stream. In several biological and engineered settings, however, the fast process also changes the transport law of the slow one. We study this architecture under a shared resource constraint, with a strictly increasing concave fast-channel capacity--cost function and a deadline-constrained slow molecular channel. We first characterize the capacity region under separated message routing and message-independent operating-point schedules, and identify the marginal criterion for complementarity rather than competition between the streams. For one-dimensional drift diffusion, we prove that arrival probability before a deadline is strictly log-concave in Péclet number. For a distinguishable-token deadline-erasure channel, any increasing concave transport-actuation law then yields an exact single-crossing theorem: complementarity exists if and only if an initial transport-assistance elasticity exceeds one, the transition is unique when it exists, and the decreasing allocation branch remains the Pareto boundary after convexification. For positive baseline drift and sufficiently strong coupling, a unique critical normalized deadline determines when complementarity disappears. Short- and long-deadline limits clarify the associated temporal regimes. Numerical examples for a finite-frame LTI-Poisson slow channel exhibit analogous allocation behavior with counting noise and intersymbol interference.