Molecular communication in fluid media: The additive inverse Gaussian noise channel

We consider molecular communication, with information conveyed in the time of release of molecules. The main contribution of this paper is the development of a theoretical foundation for such a communication system. Specifically, we develop the additive inverse Gaussian (IG) noise channel model: a channel in which the information is corrupted by noise with an inverse Gaussian distribution. We show that such a channel model is appropriate for molecular communication in fluid media - when propagation between transmitter and receiver is governed by Brownian motion and when there is positive drift from transmitter to receiver. Taking advantage of the available literature on the IG distribution, upper and lower bounds on channel capacity are developed, and a maximum likelihood receiver is derived. Theory and simulation results are presented which show that such a channel does not have a single quality measure analogous to signal-to-noise ratio in the AWGN channel. It is also shown that the use of multiple molecules leads to reduced error rate in a manner akin to diversity order in wireless communications. Finally, we discuss some open problems in molecular communications that arise from the IG system model.Comment: 28 pages, 8 figures. Submitted to IEEE Transactions on Information Theory. Corrects minor typos in the first versio

Molecular Communication Using Brownian Motion with Drift

Inspired by biological communication systems, molecular communication has been proposed as a viable scheme to communicate between nano-sized devices separated by a very short distance. Here, molecules are released by the transmitter into the medium, which are then sensed by the receiver. This paper develops a preliminary version of such a communication system focusing on the release of either one or two molecules into a fluid medium with drift. We analyze the mutual information between transmitter and the receiver when information is encoded in the time of release of the molecule. Simplifying assumptions are required in order to calculate the mutual information, and theoretical results are provided to show that these calculations are upper bounds on the true mutual information. Furthermore, optimized degree distributions are provided, which suggest transmission strategies for a variety of drift velocities.Comment: 20 pages, 7 figures, Accepted for publication in IEEE Trans. on NanoBioscienc

Scaling laws for molecular communication

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., $\Theta(\log t)$ and $\Theta(\log m)$, 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., $\Theta(t)=\Theta(m)$.Comment: Accepted for publication in the 2014 IEEE International Symposium on Information Theor

Information Rates of ASK-Based Molecular Communication in Fluid Media

This paper studies the capacity of molecular communications in fluid media, where the information is encoded in the number of transmitted molecules in a time-slot (amplitude shift keying). The propagation of molecules is governed by random Brownian motion and the communication is in general subject to inter-symbol interference (ISI). We first consider the case where ISI is negligible and analyze the capacity and the capacity per unit cost of the resulting discrete memoryless molecular channel and the effect of possible practical constraints, such as limitations on peak and/or average number of transmitted molecules per transmission. In the case with a constrained peak molecular emission, we show that as the time-slot duration increases, the input distribution achieving the capacity per channel use transitions from binary inputs to a discrete uniform distribution. In this paper, we also analyze the impact of ISI. Crucially, we account for the correlation that ISI induces between channel output symbols. We derive an upper bound and two lower bounds on the capacity in this setting. Using the input distribution obtained by an extended Blahut-Arimoto algorithm, we maximize the lower bounds. Our results show that, over a wide range of parameter values, the bounds are close.Comment: 31 pages, 8 figures, Accepted for publication on IEEE Transactions on Molecular, Biological, and Multi-Scale Communication

Bounds on the Capacity of ASK Molecular Communication Channels with ISI

There are now several works on the use of the additive inverse Gaussian noise (AIGN) model for the random transit time in molecular communication~(MC) channels. The randomness invariably causes inter-symbol interference (ISI) in MC, an issue largely ignored or simplified. In this paper we derive an upper bound and two lower bounds for MC based on amplitude shift keying (ASK) in presence of ISI. The Blahut-Arimoto algorithm~(BAA) is modified to find the input distribution of transmitted symbols to maximize the lower bounds. Our results show that over wide parameter values the bounds are close.Comment: 7 pages, 4 figures, Accepted in IEEE GLOBECOM 201