This paper considers a diffusion-based molecular communication system, where the transmitter uses reaction shift keying (RSK) as the modulation scheme. We focus on the demodulation of RSK signal at the receiver. The receiver consists of a front-end molecular circuit and a back-end demodulator. The front-end molecular circuit is a set of chemical reactions consisting of multiple chemical species. The optimal demodulator computes the posteriori probability of the transmitted symbols given the history of the observation. The derivation of the optimal demodulator requires the solution to a specific Bayesian filtering problem. The solution to this Bayesian filtering problem had been derived for a few specific molecular circuits and specific choice(s) of observed chemical species. The derivation of such solution is also lengthy. The key contribution of this paper is to present a general solution to this Bayesian filtering problem, which can be applied to any molecular circuit and any choice of observed species.
Different models have been used in molecular communication literature to model the transmission medium. The papers @cite_8 @cite_16 assume that medium is continuous while in this paper, as well as in our previous work @cite_20 @cite_23 , we assume that the medium is divided into cubic voxels. The use of voxels allows us to model the end-to-end communication system using reaction diffusion master equation (RDME) @cite_6 @cite_5 @cite_20 , which is a continuous-time Markov Process (CTMP). An alternative end-to-end model appears in @cite_32 @cite_4 which is based on particle tracking. An advantage of the RDME approach is that we can use the Markovian properties to analyse molecular communication @cite_36 @cite_20 .
@cite_4 @cite_8 @cite_36 @cite_32 @cite_6 @cite_23 @cite_5 @cite_16 @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 diffusion-based molecular communications, messages can be conveyed via the variation in the concentration of molecules in the medium. In this paper, we intend to analyze the achievable capacity in transmission of information from one node to another in a diffusion channel. We observe that because of the molecular diffusion in the medium, the channel possesses memory. We then model the memory of the channel by a two-step Markov chain and obtain the equations describing the capacity of the diffusion channel. By performing a numerical analysis, we obtain the maximum achievable rate for different levels of the transmitter power, i.e., the molecule production rate. 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. We consider a channel model based on the diffusion of particles in the medium which is motivated by the natural communication mechanisms between biological cells based on exchange of molecules. In this model, the transmitter secretes particles into the medium via a particle dissemination rate. The concentration of particles at any point in the medium is a function of its distance from the transmitter and the particle dissemination rate. The reception process is a doubly stochastic Poisson process whose rate is a function of the concentration of the particles in the vicinity of the receiver. We derive a closed-form for the mutual information between the input and output processes in this communication scenario and establish useful properties about the mutual information. We also provide a signaling strategy using which we derive a lower bound on the capacity of the diffusion channel with Poisson reception process under average and peak power constraints. Furthermore, it is shown that the capacity of discretized diffusion channel can be a negligible factor of the capacity of continuous time diffusion channel. Finally, the application of the considered model to the molecular communication systems is discussed.