We consider molecular communication networks consisting of transmitters and receivers distributed in a fluidic medium. In such networks, a transmitter sends one or more signaling molecules, which are diffused over the medium, to the receiver to realize the communication. In order to be able to engineer synthetic molecular communication networks, mathematical models for these networks are required. This paper proposes a new stochastic model for molecular communication networks called reaction-diffusion master equation with exogenous input (RDMEX). The key idea behind RDMEX is to model the transmitters as time series of signaling molecule counts, while diffusion in the medium and chemical reactions at the receivers are modeled as Markov processes using master equation. An advantage of RDMEX is that it can readily be used to model molecular communication networks with multiple transmitters and receivers. For the case where the reaction kinetics at the receivers is linear, we show how RDMEX can be used to determine the mean and covariance of the receiver output signals, and derive closed-form expressions for the mean receiver output signal of the RDMEX model. These closed-form expressions reveal that the output signal of a receiver can be affected by the presence of other receivers. Numerical examples are provided to demonstrate the properties of the model.
There are ample examples in using PDE --- in particular diffusion PDE, telegraph equation and RDPDE --- to model molecular communication. For natural networks, @cite_1 @cite_8 use RDPDE to study the noise in receptor binding in chemotaxis, and @cite_24 uses RDPDE to study signalling cascades. However, these papers do not consider the transmitters. For synthetic networks, telegraph or diffusion PDEs (or their kernels) have been used to characterise the diffusion of signalling molecules in @cite_20 @cite_0 @cite_9 @cite_27 @cite_31 and others. However, these papers do not consider the coupling effect between diffusion and receiver reaction kinetics. In our earlier work in @cite_19 , we use a RDPDE in the form of , as a deterministic model for molecular communication network. The RDPDE in @cite_19 is solved numerically and no analytic solution is provided. In this paper, we derived a RDPDE model for molecular communication and provide an interpretation of the model as the mean receiver output of molecular communication networks. In addition, we present an analytical solution to this RDPDE and show that it can be used to accurately predict mean receiver output in molecular communication networks.
@cite_8 @cite_9 @cite_1 @cite_24 @cite_0 @cite_27 @cite_19 @cite_31 @cite_20
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We consider molecular communication networks consisting of transmitters and receivers distributed in a fluidic medium. In such networks, a transmitter sends one or more signaling molecules, which are diffused over the medium, to the receiver to realize the communication. In order to be able to engineer synthetic molecular communication networks, mathematical models for these networks are required. This paper proposes a new stochastic model for molecular communication networks called reaction-diffusion master equation with exogenous input (RDMEX). The key idea behind RDMEX is to model the transmitters as time series of signaling molecule counts, while diffusion in the medium and chemical reactions at the receivers are modeled as Markov processes using master equation. An advantage of RDMEX is that it can readily be used to model molecular communication networks with multiple transmitters and receivers. For the case where the reaction kinetics at the receivers is linear, we show how RDMEX can be used to determine the mean and covariance of the receiver output signals, and derive closed-form expressions for the mean receiver output signal of the RDMEX model. These closed-form expressions reveal that the output signal of a receiver can be affected by the presence of other receivers. Numerical examples are provided to demonstrate the properties of the model. In a diffusion-based molecular communication network, transmitters and receivers communicate by using signalling molecules (or ligands) in a fluid medium. This paper assumes that the transmitter uses different chemical reactions to generate different emission patterns of signalling molecules to represent different transmission symbols, and the receiver consists of receptors. When the signalling molecules arrive at the receiver, they may react with the receptors to form ligand-receptor complexes. Our goal is to study the demodulation in this setup assuming that the transmitter and receiver are synchronised. We derive an optimal demodulator using the continuous history of the number of complexes at the receiver as the input to the demodulator. We do that by first deriving a communication model which includes the chemical reactions in the transmitter, diffusion in the transmission medium and the ligand-receptor process in the receiver. This model, which takes the form of a continuous-time Markov process, captures the noise in the receiver signal due to the stochastic nature of chemical reactions and diffusion. We then adopt a maximum a posteriori framework and use Bayesian filtering to derive the optimal demodulator. We use numerical examples to illustrate the properties of this optimal demodulator. Molecular communication networks can be used to realise communication between nanoscale devices. In a molecular communication network, transmitters and receivers communicate by using signalling molecules. At the receivers, the signalling molecules react, via a chain of chemical reactions, to produce output molecules. The counts of output molecules over time is the output signal of the receiver. The output signal is noisy due to the stochastic nature of diffusion and chemical reactions. This paper aims to characterise the properties of the output signal. We do this by modelling the transmission medium, transmitter and receiver. In order to simplify the analysis, we model the transmitter as a sequence which specifies the number of molecules emitted by the transmitter over time. This paper considers two receiver reaction mechanisms, reversible conversion and linear catalytic, which can be used to approximate, respectively, ligand-receptor binding and enzymatic reactions. These two mechanisms are chosen because, if we consider them on their own (i.e. without the transmitter and diffusion), the ordinary differential equations describing the mean behaviour of these two reaction mechanisms have the same form; however, if we consider the end-to-end behaviour from the transmitter signal to the mean variance of the number of output molecules, then these two receiver reaction mechanisms have very different behaviours. We show this by deriving analytical expressions for the mean, variance and frequency properties of the number of output molecules of these two receiver reaction mechanisms. In addition, for reversible conversion, we are able to derive the exact probability distribution of the number of output molecules. Our model allows us to study the impact of design parameters on the communication performance. For example, we assume that our receiver is enclosed by a membrane and we study the impact of the diffusibility of molecules across this membrane on the communication performance. Abstract Simulation-based and information theoretic models for a diffusion-based short-range molecular communication channel between a nano-transmitter and a nano-receiver are constructed to analyze information rates between channel inputs and outputs when the inputs are independent and identically distributed (i.i.d.). The total number of molecules available for information transfer is assumed to be limited. It is also assumed that there is a maximum tolerable delay bound for the overall information transfer. Information rates are computed via simulation-based methods for different time slot lengths and transmitter–receiver distances. The rates obtained from simulations are then compared to those computed using information theoretic channel models which provide upper bounds for information rates. The results indicate that a 4-input–2-output discrete channel model provides a very good approximation to the nano-communication channel, particularly when the time slot lengths are large and the distance between the transmitter and the receiver is small. It is shown through an extensive set of simulations that the information theoretic channel capacity with i.i.d. inputs can be achieved when an encoder adjusts the relative frequency of binary zeros to be higher (between 50 and 70 for the scenarios considered) than binary ones, where a ‘zero’ corresponds to not releasing and a ‘one’ corresponds to releasing a molecule from the transmitter.