Scaling laws for molecular communication

Andrew W. Eckford; Chan-Byoung Chae

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arXiv · 1404.0346

Scaling laws for molecular communication

Andrew W. Eckford·Chan-Byoung Chae

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Abstract

In this paper, we investigate information-theoretic scaling laws, independent from communication strategies, for point-to-point molecular communication, where it sends/receives information-encoded molecules between nanomachines. Since the Shannon capacity for this is still an open problem, we first derive an asymptotic order in a single coordinate, i.e., i) scaling time with constant number of molecules $m$ and ii) scaling molecules with constant time $t$. For a single coordinate case, we show that the asymptotic scaling is logarithmic in either coordinate, i.e., $Θ(\log t)$ and $Θ(\log m)$, respectively. We also study asymptotic behavior of scaling in both time and molecules and show that, if molecules and time are proportional to each other, then the asymptotic scaling is linear, i.e., $Θ(t)=Θ(m)$.

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Andrew W. Eckford, Chan-Byoung Chae. 2014-04-01. Scaling laws for molecular communication. https://arxiv.org/abs/1404.0346

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