Elsevier

Nano Communication Networks

Volume 2, Issue 4, December 2011, Pages 205-212
Nano Communication Networks

A stochastic model for molecular communications

https://doi.org/10.1016/j.nancom.2011.04.005Get rights and content

Abstract

In this paper we present a stochastic model for molecular communication, which accounts for particle dynamics and noise. Differently from existing approaches, we consider that molecules carrying information may interact with the transmission medium. These interactions are modelled by means of absorption, duplication and spontaneous emission phenomena. Using tools from stochastic processes we provide a complete statistical characterization of the evolution over time of the number of molecules present in the transmission medium. The model is applied to the study of flow-based and diffusion-based molecular communication.

Introduction

Molecular communication represents a novel paradigm for transmitting information among nanomachines [17], [1]. In molecular communications, nanomachines communicate via the exchange of molecules, or particles, carrying information content. The information can be encoded in the type of molecules, in their number (or concentration) or in the time at which they are emitted. Molecules carrying information may be conveyed by means of active propagation (either through molecular motors or leveraging the presence of a flow in a fluidic transmission medium) or passive propagation (whereby molecules diffuse as a consequence of thermal motion and diffusion) [11].

Various models have been proposed for characterizing the behaviour and performance of molecular communication systems. A model based on ligand–receptor binding and release reaction kinetic is described in [2]. In this model, the information is encoded in the concentration of molecules at the transmitter. The model accounts for the dynamics of the ligand–receptor chemical reaction, and the concentration value related to the encoding of a ‘1’ information bit decreases exponentially over time. The model is used to derive an expression for the mutual information and a first mathematical characterization of the capacity of molecular channels. In [10], a computational model for studying the effect of noise in molecular communications is proposed. A number of design choices in molecular communication systems are presented and modelled; the performance improvements attainable are evaluated by means of numerical simulations. In [16], [6], a molecular communication system where information is encoded in the emission time of molecules is studied. Assuming that molecules diffuse due to thermal noise according to a Brownian motion, it is shown that the system can be modelled as a timing channel, characterized by an additive inverse Gaussian noise. The capacity of the resulting communication system is then derived. Results for active transport have been obtained by means of simulations in [7] and in [8]. In [3], a fluid-flow diffusion model for the evolution of molecules’ concentration in a diffusive medium is derived. This model is further used to characterize the information theoretical capacity of point-to-point, broadcast and multiple access molecular channels. An extensive deterministic fluid-flow model of a complete molecular communication system (including emission, diffusion and reception) is presented in [11]. A complete study of the impact of noise in diffusion-based molecular communications is [12]. In such a work, two types of noise (particle sampling noise and particle counting noise) are analysed starting from the characterization of the underpinning physical processes, and consistent stochastic models are then derived.

In this work, we consider a molecular communication system in which molecules carrying information content may interact with other molecules present in the transmission medium, resulting in absorption or generation of new molecules. Further, we allow for spontaneous emission of molecules to take place in the transmission medium. Using tools from the theory of stochastic processes, and in particular birth-and-death processes and Poisson processes, we obtain the complete statistical characterization—under some simplifying assumptions—of the dynamics of molecules propagation and noise. The obtained results are used to characterize the performance of flow-based and diffusion-based molecular communications.

The main contributions of this work can be summarized as follows:

  • We propose a stochastic model for describing the evolution over time of the number of molecules present in a molecular communication channel, able to account for interactions (in the form of absorption, generation and spontaneous emission) between molecules and the transmission medium.

  • We apply the aforementioned model to two types of molecular communications (flow-based and diffusion-based) and show how, under some simplifying assumptions, it can be used to characterize the reception process of molecules at the receiver.

The remainder of the paper is organized as follows. In Section 2 we present a stochastic model for the propagation of molecules in a noisy medium. In Section 3 we show how the model can be applied to molecular communication systems. Section 4 reports some numerical results obtained by means of the proposed model. Section 5 concludes the paper pointing out issues and challenges in the extension and application of the model.

Section snippets

A stochastic model for particle propagation

In this section we aim at modelling the time evolution of the number of particles in a molecular communication channel. Differently from what done in the literature, we assume that the molecules used to convey information (be the information encoded in the number of molecules emitted, in their concentration, in the time instant of release etc.) can interact with the transmission medium. In particular we account for three phenomena. First, information-carrying molecules may react with other

Application to molecular communications

In the previous section, we developed a model able to characterize the time evolution of the number of molecules present in a molecular communication channel. In this section we show how the model can be applied to the analysis of two types of molecular communications: flow-based, where the propagation of molecules is guided by the presence of a flow in a fluidic transmission medium, and diffusion-based, where molecules move according to a diffusion process driven by thermal noise. For both

Numerical results

In this section we report some numerical results obtained by means of the model introduced in the previous sections. The aim is to illustrate in an intuitive form the behaviour of the model. Throughout the section, we will use the parameters listed in Table 1. For flow-based molecular communications, we took the propagation speed to be equal to 0.1 m/s, considered an approximate value for the flow rate of blood in a normal segment of an artery.

We first consider the model for particle

Conclusions

In this paper we have presented a stochastic model for molecule dynamics and noise in molecular communication systems. Differently from existing literature, the model explicitly accounts for possible interactions between molecules carrying information and the transmission medium, in the form of absorption, duplication and spontaneous emission. The model builds upon some memoryless and independence assumptions, and yields the complete statistical characterization of the arrival process of

Daniele Miorandi is the head of the iNSPIRE Area at CREATE-NET, Italy. He received a Ph.D. in Communications Engineering from Univ. of Padova, Italy, in 2005, and a Laurea degree (summa cum lauda) in Communications Engineering from Univ. of Padova, Italy, in 2001. He joined CREATE-NET in Jan. 2005, where he is leading the iNSPIRE (Networking and Security Solutions for Pervasive Computing Systems: Research & Experimentation). His research interests include bio-inspired approaches to networking

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Daniele Miorandi is the head of the iNSPIRE Area at CREATE-NET, Italy. He received a Ph.D. in Communications Engineering from Univ. of Padova, Italy, in 2005, and a Laurea degree (summa cum lauda) in Communications Engineering from Univ. of Padova, Italy, in 2001. He joined CREATE-NET in Jan. 2005, where he is leading the iNSPIRE (Networking and Security Solutions for Pervasive Computing Systems: Research & Experimentation). His research interests include bio-inspired approaches to networking and service provisioning in large-scale computing systems, modelling and performance evaluation of wireless networks, prototyping of wireless mesh solutions. Dr. Miorandi has co-authored more than 90 papers in internationally refereed journals and conferences. He serves on the Steering Committee of various international events (WiOpt, Autonomics, ValueTools), for some of which he was a co-founder (Autonomics and ValueTools). He also serves on the TPC of leading conferences in the networking field, including, e.g., IEEE INFOCOM, IEEE ICC, IEEE Globecom. He is a member of IEEE, ACM and ICST.

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