A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Communication Systems and Information Theory. A Measure of Information. Coding for Discrete Sources. Discrete Memoryless Channels and Capacity. The Noisy-Channel Coding Theorem. Techniques for Coding and Decoding. Memoryless Channels with Discrete Time. Waveform Channels. Source Coding with a Fidelity Criterion. Index. <s> BIB001 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> By defining mutual information as a maximum over an appropriate space, channel capacities can be defined as double maxima and rate-distortion functions as double minima. This approach yields valuable new insights regarding the computation of channel capacities and rate-distortion functions. In particular, it suggests a simple algorithm for computing channel capacity that consists of a mapping from the set of channel input probability vectors into itself such that the sequence of probability vectors generated by successive applications of the mapping converges to the vector that achieves the capacity of the given channel. Analogous algorithms then are provided for computing rate-distortion functions and constrained channel capacities. The algorithms apply both to discrete and to continuous alphabet channels or sources. In addition, a formalization of the theory of channel capacity in the presence of constraints is included. Among the examples is the calculation of close upper and lower bounds to the rate-distortion function of a binary symmetric Markov source. <s> BIB002 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> A systematic and iterative method of computing the capacity of arbitrary discrete memoryless channels is presented. The algorithm is very simple and involves only logarithms and exponentials in addition to elementary arithmetical operations. It has also the property of monotonic convergence to the capacity. In general, the approximation error is at least inversely proportional to the number of iterations; in certain circumstances, it is exponentially decreasing. Finally, a few inequalities that give upper and lower bounds on the capacity are derived. <s> BIB003 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> A formula for the capacity of arbitrary single-user channels without feedback (not necessarily information stable, stationary, etc.) is proved. Capacity is shown to equal the supremum, over all input processes, of the input-output inf-information rate defined as the liminf in probability of the normalized information density. The key to this result is a new converse approach based on a simple new lower bound on the error probability of m-ary hypothesis tests among equiprobable hypotheses. A necessary and sufficient condition for the validity of the strong converse is given, as well as general expressions for /spl epsiv/-capacity. > <s> BIB004 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Biochemical signal-transduction networks are the biological information-processing systems by which individual cells, from neurons to amoebae, perceive and respond to their chemical environments. We introduce a simplified model of a single biochemical relay and analyse its capacity as a communications channel. A diffusible ligand is released by a sending cell and received by binding to a transmembrane receptor protein on a receiving cell. This receptor-ligand interaction creates a nonlinear communications channel with non-Gaussian noise. We model this channel numerically and study its response to input signals of different frequencies in order to estimate its channel capacity. Stochastic effects introduced in both the diffusion process and the receptor-ligand interaction give the channel low-pass characteristics. We estimate the channel capacity using a water-filling formula adapted from the additive white-noise Gaussian channel. <s> BIB005 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> In this paper, the problem of communicating using chemical messages propagating using Brownian motion, rather than electromagnetic messages propagating as waves in free space or along a wire, is considered. This problem is motivated by nanotechnological and biotechnological applications, where the energy cost of electromagnetic communication might be prohibitive. Models are given for communication using particles that propagate with Brownian motion, and achievable capacity results are given. Under conservative assumptions, it is shown that rates exceeding one bit per particle are achievable. <s> BIB006 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication is a novel communication paradigm which allows nanomachines to communicate using molecules as a carrier. Controlled molecule delivery between two nanomachines is one of the most important challenges which must be addressed to enable the molecular communication. Therefore, it is essential to develop an information theoretical approach to find out molecule delivery capacity of the molecular channel. In this paper, we develop an information theoretical approach for capacity of a molecular channel between two nanomachines. We first introduce a molecular communication model. Then, using the principles of mass action kinetics we give a molecule delivery model for the molecular communication between two nanomachines called as Transmitter Nanomachine (TN) and Receiver Nanomachine (RN). Then, we derive a closed form expression for capacity of the channel between TN and RN. Numerical results show that selecting appropriate molecular communication parameters such as temperature of environment, concentration of emitted molecules, distance between nanomachines and duration of molecule emission, it can be possible to achieve maximum capacity for the molecular communication channel between two nanomachines. <s> BIB007 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication is a novel paradigm that uses molecules as an information carrier to enable nanomachines to communicate with each other. Controlled molecule delivery between two nanomachines is one of the most important challenges which must be addressed to enable the molecular communication. Therefore, it is essential to develop an information theoretical approach to find out communication capacity of the molecular channel. In this paper, we develop an information theoretical approach for capacity of a molecular channel between two nanomachines. Using the principles of mass action kinetics, we first introduce a molecule delivery model for the molecular communication between two nanomachines called as Transmitter Nanomachine (TN) and Receiver Nanomachine (RN). Then, we derive a closed form expression for capacity of the channel between TN and RN. Furthermore, we propose an adaptive Molecular Error Compensation (MEC) scheme for the molecular communication between TN and RN. MEC allows TN to select an appropriate molecular bit transmission probability to maximize molecular communication capacity with respect to environmental factors such as temperature and distance between nanomachines. Numerical analysis show that selecting appropriate molecular communication parameters such as concentration of emitted molecules, duration of molecule emission, and molecular bit transmission probability it can be possible to achieve high molecular communication capacity for the molecular communication channel between two nanomachines. Moreover, the numerical analysis reveals that MEC provides more than % 100 capacity improvement in the molecular communication selecting the most appropriate molecular transmission probability. <s> BIB008 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication is a novel paradigm that uses molecules as an information carrier to enable nanomachines to communicate with each other. Interconnections of the nanomachines with molecular communication is envisioned as a nanonetwork. Nanonetworks are expected to enable nanomechines to cooperatively share information such as odor, flavour, light, or any chemical state. In this paper, we develop and present models for the molecular multiple-access, broadcast, and relay channels in a nanonetwork and derive their capacity expressions. Numerical results reveal that the molecular multiple-access of nanomachines to a single nanomachine can be possible with the high molecular communication capacity by selecting the appropriate molecular communication parameters. Similarly, the molecular broadcast can also allow a single nanomachine to communicate with a number of nanomachines with high molecular communication capacity. As a combination of the molecular multiple-access and broadcast channel, we show that the molecular relay channel can improve the molecular communication capacity between two nanomachines using a relay nanomachine. <s> BIB009 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication is a new nano-scale communication paradigm that enables nanomachines to communicate with each other by emitting molecules to their surrounding environment. Nanonetworks are also envisioned to be composed of a number of nanomachines with molecular communication capability that are deployed in an environment to share specific molecular information such as odor, flavour, light, or any chemical state. In this paper, using the principles of natural ligand-receptor binding mechanisms in biology, we first derive a capacity expression for single molecular channel in which a single Transmitter Nanomachine (TN) communicates with a single Receiver Nanomachine (RN). Then, we investigate the capacity of the molecular multiple-access channel in which multiple TNs communicate with a single RN. Numerical results reveal that high molecular communication capacities can be attainable for the single and multiple-access molecular channels. <s> BIB010 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Communication between a transmitter and a re- ceiver using electromagnetic waves does not scale to nano-sizes. To enable communication between nano-sized devices separated by a short distance, molecular communication has recently been proposed as a feasible scheme. The transmitter disperses molecules into the medium, which propagate to, and are sensed by, the receiver. In this paper, we wish to mathematically model such a system and subsequently characterize the information theoretic capacity of this channel. We present basic results on characterizing the mutual information between the transmitter and the receiver when information is encoded in the time of release of the molecule. To do so, we model the propagation of the molecule in this medium as Brownian motion, and derive the probability density function of the arrival time of the molecule at the receiver. Communications research has largely focused on systems based on electromagnetic propagation. However, at scales con- sidered in nano-technology it is not clear that these concepts apply. In this paper we consider communication based on molecules (1). Specifically, we consider the propagation of individual molecules between closely spaced transmitters and receivers embedded in a fluid medium. The transmitter en- codes information in the pattern of release of the molecules it disperses into the fluid medium. These molecules then propa- gate to the receiver, where they are detected. The receiver then tries to decode the information from the pattern of received molecules. For a comprehensive overview of the molecular communication system, refer to (2) and the references therein. As in any communication system, the potential rate of communication is determined by the characteristics of the channel. Here, propagation is determined by a mean drift velocity and is uncertain due to the Brownian motion within the fluid. In this preliminary work, our goal is to analyze the mutual information between the transmitter and receiver and hence the capacity of the channel. We would like to emphasize that, in order to gain insight, and to make the problem mathematically tractable, we consider a fairly simple model of a molecular communication system. In (3), the authors compute information theoretic bounds to capacity for a general diffusion channel. Our work is along similar lines, although we lay a greater emphasis on the mathematical modeling of the system. In (4), the authors study a system where the receiver chemically "reacts" with the molecules and forms "complexes". This is very different from the system model we consider. We assume that the receiver absorbs the molecule. Furthermore, we model the diffusion of the particle in the medium, and incorporate its effect in our calculations. <s> BIB011 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication is a new paradigm for communication between biological nanomachines over a nano- and microscale range. As biological nanomachines (or nanomachines in short) are too small and simple to communicate through traditional communication mechanisms (e.g., through sending and receiving of radio or infrared signals), molecular communication provides a mechanism for a nanomachine (i.e., a sender) to communicate information by propagating molecules (i.e., information molecules) that represent the information to a nanomachine (i.e., a receiver). This paper describes the design of an in vitro molecular communication system and evaluates various approaches to maximize the probability of information molecules reaching a receiver(s) and the rate of information reaching the receiver(s). The approaches considered in this paper include propagating information molecules (diffusion or directional transport along protein filaments), removing excessive information molecules (natural decay or receiver removal of excessive information molecules), and encoding and decoding approaches (redundant information molecules to represent information and to decode information). Two types of molecular communication systems are considered: a unicast system in which a sender communicates with a single receiver and a broadcast system in which a sender communicates with multiple receivers. Through exploring tradeoffs among the various approaches on the two types of molecular communication systems, this paper identifies promising approaches and shows the feasibility of an in vitro molecular communication system. <s> BIB012 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Abstract Abstract Molecular communication is a new communication paradigm that uses molecules for information transmission between nanomachines. Similar to traditional communication systems, several factors constitute limits over the performance of this communication system. One of these factors is the energy budget of the transmitter. It limits the rate at which the transmitter can emit symbols, i.e., produce the messenger molecules. In this paper, an energy model for the communication via diffusion system is proposed. To evaluate the performance of this communication system, first a channel model is developed, and also the probability of correct decoding of the information is evaluated. Two optimization problems are set up for system analysis that focus on channel capacity and data rate. Evaluations are carried out using the human insulin hormone as the messenger molecule and a transmitter device whose capabilities are similar to a pancreatic β -cell. Results show that distance between the transmitter and receiver has a minor effect on the achievable data rate whereas the energy budget’s effect is significant. It is also shown that selecting appropriate threshold and symbol duration parameters are crucial to the performance of the system. <s> BIB013 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication is a promising paradigm for nanoscale networks. The end-to-end (including the channel) models developed for classical wireless communication networks need to undergo a profound revision so that they can be applied for nanonetworks. Consequently, there is a need to develop new end-to-end (including the channel) models which can give new insights into the design of these nanoscale networks. The objective of this paper is to introduce a new physical end-to-end (including the channel) model for molecular communication. The new model is investigated by means of three modules, i.e., the transmitter, the signal propagation and the receiver. Each module is related to a specific process involving particle exchanges, namely, particle emission, particle diffusion and particle reception. The particle emission process involves the increase or decrease of the particle concentration rate in the environment according to a modulating input signal. The particle diffusion provides the propagation of particles from the transmitter to the receiver by means of the physics laws underlying particle diffusion in the space. The particle reception process is identified by the sensing of the particle concentration value at the receiver location. Numerical results are provided for three modules, as well as for the overall end-to-end model, in terms of normalized gain and delay as functions of the input frequency and of the transmission range. <s> BIB014 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Abstract Molecular communication enables nanomachines to exchange information with each other by emitting molecules to their surrounding environment. Molecular nanonetworks are envisioned as a number of nanomachines that are deployed in an environment to share specific molecular information such as odor, flavor, or any chemical state. In this paper, using the stochastic model of molecular reactions in biochemical systems, a realistic channel model is first introduced for molecular communication. Then, based on the realistic channel model, we introduce a deterministic capacity expression for point-to-point, broadcast, and multiple-access molecular channels. We also investigate information flow capacity in a molecular nanonetwork for the realization of efficient communication and networking techniques for frontier nanonetwork applications. The results reveal that molecular point-to-point, broadcast, and multiple-access channels are feasible with a satisfactorily high molecular communication rate, which allows molecular information flow in nanonetworks. Furthermore, the derived molecular channel model with input-dependent noise term also reveals that unlike a traditional Gaussian communication channel, achievable capacity is affected by both lower and upper bounds of the channel input in molecular communication channels. <s> BIB015 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> 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. <s> BIB016 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> In this paper, we consider molecular communication, with information conveyed in the time of release of molecules. These molecules propagate to the transmitter through a fluid medium, propelled by a positive drift velocity and Brownian motion. The main contribution of this paper is the development of a theoretical foundation for such a communication system; specifically, the additive inverse Gaussian noise (AIGN) channel model. In such a channel, the information is corrupted by noise that follows an IG distribution. We show that such a channel model is appropriate for molecular communication in fluid media. 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. Results are presented which suggest that this channel does not have a single quality measure analogous to signal-to-noise ratio in the additive white Gaussian noise 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, some open problems are discussed that arise from the IG channel model. <s> BIB017 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> In this paper, we consider a molecular relay channel in which signal molecules are transmitted by a sender of communication, propagated, amplified, removed in the channel, and sensed by the receiver of communication that decodes the signal molecules. To understand and characterize the communication capacity of the molecular relay channel, we develop an information communication model that consists of the transmitter, channel, and receiver. Mutual information is used to quantify the amount of information that is transfered from the transmitter through the channel to the receiver. The method employed and results presented in this paper may help elucidate design principles of biological systems as well as help in the design and engineering of synthetic biological systems from the perspective of information theory. <s> BIB018 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication has been recently proposed for interconnected nano-scale devices as an alternative to classical communication paradigms such as electromagnetic waves, acoustic or optical communication. In this novel approach, the information is encoded as molecules that are transported between nano-scale devices within different distances. For short distances (nm-mm ranges) there exist molecular motors and calcium signaling techniques to realize the communication. For long distances (mm-m ranges), pheromones are used to transport information. In this work, the medium-range is explored to cover distances from ?m to mm and a molecular network architecture is proposed to realize the communication between nano-machines that can be deployed over different (short, medium and long) distances. In addition, two new communication techniques, flagellated bacteria and catalytic nanomotors, are proposed to cover the medium-range. Both techniques are based on the transport of DNA encoded information between emitters and receivers by means of a physical carrier. Finally, a qualitative comparison of both communication techniques is carried out and some future research topics are pointed out. <s> BIB019 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication (MC) is a promising bio-inspired paradigm, in which molecules are used to encode, transmit and receive information at the nanoscale. Very limited research has addressed the problem of modeling and analyzing the MC in nanonetworks. One of the main challenges in MC is the proper study and characterization of the noise sources. The objective of this paper is the analysis of the noise sources in diffusion-based MC using tools from signal processing, statistics and communication engineering. The reference diffusion-based MC system for this analysis is the physical end-to-end model introduced in a previous work by the same authors. The particle sampling noise and the particle counting noise are analyzed as the most relevant diffusion-based noise sources. The analysis of each noise source results in two types of models, namely, the physical model and the stochastic model. The physical model mathematically expresses the processes underlying the physics of the noise source. The stochastic model captures the noise source behavior through statistical parameters. The physical model results in block schemes, while the stochastic model results in the characterization of the noises using random processes. Simulations are conducted to evaluate the capability of the stochastic model to express the diffusion-based noise sources represented by the physical model. <s> BIB020 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication (MC) will enable the exchange of information among nanoscale devices. In this novel bio-inspired communication paradigm, molecules are employed to encode, transmit and receive information. In the most general case, these molecules are propagated in the medium by means of free diffusion. An information theoretical analysis of diffusion-based MC is required to better understand the potential of this novel communication mechanism. The study and the modeling of the noise sources is of utmost importance for this analysis. The objective of this paper is to provide a mathematical study of the noise at the reception of the molecular information in a diffusion-based MC system when the ligand-binding reception is employed. The reference diffusion-based MC system for this analysis is the physical end-to-end model introduced in a previous work by the same authors, where the reception process is realized through ligand-binding chemical receptors. The reception noise is modeled in this paper by following two different approaches, namely, through the ligand-receptor kinetics and through the stochastic chemical kinetics. The ligand-receptor kinetics allows to simulate the random perturbations in the chemical processes of the reception, while the stochastic chemical kinetics provides the tools to derive a closed-form solution to the modeling of the reception noise. The ligand-receptor kinetics model is expressed through a block scheme, while the stochastic chemical kinetics results in the characterization of the reception noise using stochastic differential equations. Numerical results are provided to demonstrate that the analytical formulation of the reception noise in terms of stochastic chemical kinetics is compliant with the reception noise behavior resulting from the ligand-receptor kinetics simulations. <s> BIB021 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> 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. <s> BIB022 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> A diffusion-based molecular communication system has two major components: the diffusion in the medium, and the ligand-reception. Information bits, encoded in the time variations of the concentration of molecules, are conveyed to the receiver front through the molecular diffusion in the medium. The receiver, in turn, measures the concentration of the molecules in its vicinity in order to retrieve the information. This is done via ligand-reception process. In this paper, we develop models to study the constraints imposed by the concentration sensing at the receiver side and derive the maximum rate by which a ligand-receiver can receive information. Therefore, the overall capacity of the diffusion channel with the ligand receptors can be obtained by combining the results presented in this paper with our previous work on the achievable information rate of molecular communication over the diffusion channel. <s> BIB023 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> 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. <s> BIB024 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> 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. <s> BIB025 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Nanonetworks are the interconnection of nanomachines and as such expand the limited capabilities of a single nanomachine. Several techniques have been proposed so far to interconnect nanomachines. For short distances (nm-mm ranges), researchers are proposing to use molecular motors and calcium signaling. For long distances (mm-m), pheromones are envisioned to transport information. In this work we propose a new mechanism for medium-range communications (nm-µm): flagellated bacteria. This technique is based on the transport of DNA-encoded information between emitters and receivers by means of a bacterium. We present a physical channel characterization and a simulator that, based on the previous characterization, simulates the transmission of a DNA packet between two nanomachines. <s> BIB026 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> In molecular communication, gaps in the underlying theoretical and mathematical framework create numerous challenges. Currently, most researchers rely on simulations to study these systems. However, simulations can be time consuming and impractical. Moreover, due to the complexity and dependencies present in these systems, deriving a mathematical framework that can capture the essence of molecular communication systems is also challenging. In this work, we derive a simple mathematical model, based on some independence assumptions, to estimate the information rate of a molecular communication system employing active transport propagation. We show that the presented model estimates the simulated information rate closely for small communication time intervals. We also use the derived mathematical model to design and verify an optimal loading area that would maximize the information rate. <s> BIB027 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Recent developments in nanotechnology have enabled the fabrication of nanomachines with very limited sensing, computation, communication, and action capabilities. The network of communicating nanomachines is envisaged as nanonetworks that are designed to accomplish complex tasks such as drug delivery and health monitoring. For the realization of future nanonetworks, it is essential to develop novel and efficient communication and networking paradigms. In this paper, the first step toward designing a mobile ad hoc molecular nanonetwork (MAMNET) with electrochemical communication is taken. MAMNET consists of mobile nanomachines and infostations that share nanoscale information using electrochemical communication whenever they have a physical contact with each other. In MAMNET, the intermittent connectivity introduced by the mobility of nanomachines and infostations is a critical issue to be addressed. An analytical framework that incorporates the effect of mobility into the performance of electrochemical communication among nanomachines is presented. Using the analytical model, numerical analysis for the performance evaluation of MAMNET is obtained. Results reveal that MAMNET achieves adequately high throughput to enable frontier nanonetwork applications with acceptable communication latency. <s> BIB028 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> 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. <s> BIB029 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> The prospect of new biological and industrial applications that require communication in micro-scale, encourages research on the design of bio-compatible communication networks using networking primitives already available in nature. One of the most promising candidates for constructing such networks is to adapt and engineer specific types of bacteria that are capable of sensing, actuation, and above all, communication with each other. In this paper, we describe a new architecture for networks of bacteria to form a data collecting network, as in traditional sensor networks. The key to this architecture is the fact that the node in the network itself is a bacterial colony; as an individual bacterium (biological agent) is a tiny unreliable element with limited capabilities. We describe such a network under two different scenarios. We study the data gathering (sensing and multihop communication) scenario as in sensor networks followed by the consensus problem in a multinode network. We will explain as to how the bacteria in the colony collectively orchestrate their actions as a node to perform sensing and relaying tasks that would not be possible (at least reliably) by an individual bacterium. Each single bacterium in the colony forms a belief by sensing external parameter (e.g., a molecular signal from another node) from the medium and shares its belief with other bacteria in the colony. Then, after some interactions, all the bacteria in the colony form a common belief and act as a single node. We will model the reception process of each individual bacteria and will study its impact on the overall functionality of a node. We will present results on the reliability of the multihop communication for data gathering scenario as well as the speed of convergence in the consensus scenario. <s> BIB030 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> The design of biological networks using bacteria as the basic elements of the network is initially motivated by a phenomenon called quorum sensing. Through quorum sensing, each bacterium performs sensing the medium and communicating it to others via molecular communication. As a result, bacteria can orchestrate and act collectively and perform tasks impossible otherwise. In this paper, we consider a population of bacteria as a single node in a network. In our version of biological communication networks, such a node would communicate with one another via molecular signals. As a first step toward such networks, this paper focuses on the study of the transfer of information to the population (i.e., the node) by stimulating it with a concentration of special type of a molecules signal. These molecules trigger a chain of processes inside each bacteria that results in a final output in the form of light or fluorescence. Each stage in the process adds noise to the signal carried to the next stage. Our objective is to measure (compute) the maximum amount of information that we can transfer to the node. This can be viewed as the collective sensing capacity of the node. The molecular concentration, which carries the information, is the input to the node, which should be estimated by observing the produced light as the output of the node (i.e., the entire population of bacteria forming the node. The molecules are trapped in the bacteria receptors forming complexes inside the bacteria which affect the genes responsible for producing the light. We focus on the noise caused by the random process of trapping molecules at the receptors as well as the variation of outputs of different bacteria in the node. The optimal input distribution to maximize the mutual information between the output of the node, e.g., light, and the applied molecule concentration is derived. Further, the capacity variation with the number of bacteria in the node and the number of receptors per bacteria is obtained. Finally, we investigated the collective sensing capability of the node when a specific form of molecular signaling concentration (which resembles M-ary modulation) is used. The achievable sensing capacity and the corresponding error probabilities were obtained for such practical signaling techniques. <s> BIB031 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication is an expanding body of research. Recent advances in biology have encouraged using genetically engineered bacteria as the main component in the molecular communication. This has stimulated a new line of research that attempts to study molecular communication among bacteria from an information-theoretic point of view. Due to high randomness in the individual behavior of the bacterium, reliable communication between two bacteria is almost impossible. Therefore, we recently proposed that a population of bacteria in a cluster is considered as a node capable of molecular transmission and reception. This proposition enables us to form a reliable node out of many unreliable bacteria. The bacteria inside a node sense the environment and respond accordingly. In this paper, we study the communication between two nodes, one acting as the transmitter and the other as the receiver. We consider the case in which the information is encoded in the concentration of molecules by the transmitter. The molecules produced by the bacteria in the transmitter node propagate in the environment via the diffusion process. Then, their concentration sensed by the bacteria in the receiver node would decode the information. The randomness in the communication is caused by both the error in the molecular production at the transmitter and the reception of molecules at the receiver. We study the theoretical limits of the information transfer rate in such a setup versus the number of bacteria per node. Finally, we consider M-ary modulation schemes and study the achievable rates and their error probabilities. <s> BIB032 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> In this paper, we analyze the capacity of a molecular communication channel in a one dimensional environment where information is represented with molecules that are released by a transmitter nanomachine, propagate via Brownian motion, degrade over time, and stochastically reach the receiver nanomachine. The channel is modeled as a time slotted binary channel, and two modulation schemes are proposed: a naive modulation scheme and an extended modulation scheme with a redundant number of molecules. Our analysis demonstrates that the channel capacity is largely affected by the life expectancy of molecules. Our analysis also indicates that the extended modulation scheme can achieve nearly one bit per slot at the expense of extra molecules under optimal conditions. <s> BIB033 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication is a promising nanoscale communication paradigm that enables nanomachines to exchange information by using molecules as communication carrier. Up to now, the molecular communication channel between a transmitter nanomachine (TN) and a receiver nanomachine (RN) has been modeled as either concentration channel or timing channel. However, these channel models necessitate exact time synchronization of the nanomachines and provide a relatively low communication bandwidth. In this paper, the Molecular ARray-based COmmunication (MARCO) scheme is proposed, in which the transmission order of different molecules is used to convey molecular information without any need for time synchronization. The MARCO channel model is first theoretically derived, and the intersymbol interference and error probabilities are obtained. Based on the error probability, achievable communication rates are analytically obtained. Numerical results and performance comparisons reveal that MARCO provides significantly higher communication rate, i.e., on the scale of 100 Kbps, than the previously proposed molecular communication models without any need for synchronization. More specifically, MARCO can provide more than 250 Kbps of molecular communication rate if intersymbol time and internode distance are set to 2 μs and 2 nm, respectively. <s> BIB034 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Diffusion-based communication refers to the transfer of information using molecules as message carriers whose propagation is based on the law of molecular diffusion. Path loss can have a major impact on the link quality in molecular communication as the signal strength is shown inversely proportional to the cube of the communication distance. In this paper, various diversity techniques for Multi-Input Multi-Output (MIMO) transmissions based on molecular diffusion are proposed to improve the communication performance in nanonetworks in the presence of Multi-User Interference (MUI). Analogous to radio communication, the concept of diversity and Spatial Multiplexing (SM) can be successfully applied in molecular communication. To the best of our knowledge, our paper is the first which investigates the aspects of MIMO transmissions for molecular communication. Numerical results show that the proposed diversity techniques can successfully lower the error rate. Further performance improvement can be obtained by properly allocating molecules among the transmission nodes if the Channel State Information (CSI) is available at the transmitter end. To optimize the system throughput, a dynamic switching mechanism between the diversity mode and the Spatial Multiplexing (SM) mode can be employed. <s> BIB035 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> In this paper, a mathematical optimization formula for estimating the optimal channel dimensions of active transport molecular communication is presented. More specifically, rectangular channels with constant microtubule (MT) concentration are considered. It is shown, both using our formula and using Monte Carlo simulations, that square-shaped channels are optimal. Furthermore, when the value of time per channel use is on the order of a few minutes, which is the range of interest for a lot of potential applications such as diagnostic chips for healthcare, it is shown that our optimization formula can quickly and accurately estimate the optimal channel dimensions. <s> BIB036 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> We consider a confined space molecular communication system, where molecules or information carrying particles are used to transfer information on a microfluidic chip. Considering that information-carrying particles can follow two main propagation schemes: passive transport, and active transport, it is not clear which achieves a better information transmission rate. Motivated by this problem, we compare and analyze both propagation schemes by deriving a set of analytical and mathematical tools to measure the achievable information rates of the on-chip molecular communication systems employing passive to active transport. We also use this toolbox to optimize design parameters such as the shape of the transmission area, to increase the information rate. Furthermore, the effect of separation distance between the transmitter and the receiver on information rate is examined under both propagation schemes, and a guidepost to design an optimal molecular communication setup and protocol is presented. <s> BIB037 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication emerges as a promising communication paradigm for nanotechnology. However, solid mathematical foundations for information-theoretic analysis of molecular communication have not yet been built. In particular, no one has ever proven that the channel coding theorem applies for molecular communication, and no relationship between information rate capacity (maximum mutual information) and code rate capacity (supremum achievable code rate) has been established. In this paper, we focus on a major subclass of molecular communication - the diffusion-based molecular communication. We provide solid mathematical foundations for information theory in diffusion-based molecular communication by creating a general diffusion-based molecular channel model in measure-theoretic form and prove its channel coding theorems. Various equivalence relationships between statistical and operational definitions of channel capacity are also established, including the most classic information rate capacity and code rate capacity. As byproducts, we have shown that the diffusion-based molecular channel is with "asymptotically decreasing input memory and anticipation" and "d-continuous". Other properties of diffusion-based molecular channel such as stationarity or ergodicity are also proven. <s> BIB038 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Communication via diffusion is an effective and energy efficient method for transmitting information in nanonetworks. However, the histogram of the molecules hitting at the receiver has a long tail. The molecules constituting this long tail significantly decrease the data rate since the selection of a high symbol duration becomes mandatory to have acceptable bit error rates. In this paper, a novel signal shaping technique for nanonetworking is proposed. This technique aims to decrease the variance of the hitting times via special so-called “destroyer molecules”. This system is inspired by the neuromuscular junction in biology, in which Acetylcholinesterase molecules are used to clean the channel for further transmissions. We consider a molecular communication channel where a tunnel composed of destroyer molecules exist between the communicating pair. Simulation results show that the inclusion of such destroyer molecules decrease both the mean and the variance of the hitting time distribution, allowing better time-responsiveness and higher data rate for the communication via diffusion system. <s> BIB039 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular Communication (MC) is a communication paradigm based on the exchange of molecules. The implicit biocompatibility and nanoscale feasibility of MC make it a promising communication technology for nanonetworks. This paper provides a closed-form expression for the information capacity of an MC system based on the free diffusion of molecules, which is of primary importance to understand the performance of the MC paradigm. Unlike previous contributions, the provided capacity expression is independent from any coding scheme and takes into account the two main effects of the diffusion channel: the memory and the molecular noise. For this, the diffusion is decomposed into two processes, namely, the Fick's diffusion and the particle location displacement, which are analyzed as a cascade of two separate systems. The Fick's diffusion captures solely the channel memory, while the particle location displacement isolates the molecular noise. The MC capacity expression is obtained by combining the two systems as function of the diffusion coefficient, the temperature, the transmitter-receiver distance, the bandwidth of the transmitted signal, and the average transmitted power. Numerical results show that a few kilobits per second can be reached within a distance range of tenth of micrometer and for an average transmitted power around 1 pW. <s> BIB040 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication between biological entities is a new paradigm in communications. Recently, we studied molecular communication between two nodes formed from synthetic bacteria. Due to high randomness in behavior of bacteria, we used a population of them in each node. The reliability of such communication systems depends on both the maximum concentration of molecules that a transmitter node is able to produce at the receiver node as well as the number of bacteria in each nodes. This maximum concentration of molecules falls with distance which makes the communication to the far nodes nearly impossible. In order to alleviate this problem, in this paper, we propose to use a molecular relaying node. The relay node can resend the message either by the different or the same type of molecules as the original signal from the transmitter. We study two scenarios of relaying. In the first scenario, the relay node simply senses the received concentration and forwards it to the receiver. We show that this sense and forward scenario, depending on the type of molecules used for relaying, results in either increasing the range of concentration of molecules at the receiver or increasing the effective number of bacteria in the receiver node. For both cases of sense and forward relaying, we obtain the resulting improvement in channel capacity. We conclude that multi-type molecular relaying outperforms the single-type relaying. In the second scenario, we study the decode and forward relaying for the M-ary signaling scheme. We show that this relaying strategy increases the reliability of M-ary communication significantly. <s> BIB041 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> In this letter, a new molecular modulation scheme for nanonetworks is proposed. To evaluate the scheme, a system model based on the Poisson distribution is introduced. The error probability of the proposed scheme as well as that of two previously known schemes, the concentration and molecular shift keying modulations, are derived for the Poisson model by taking into account the error propagation effect of previously decoded symbols. The proposed scheme is shown to outperform the previously introduced schemes. This is due to the fact that the decoding of the current symbol in the proposed scheme does not encounter propagation of error, as the decoding of the current symbol does not depend on the previously transmitted and decoded symbols. Finally, fundamental limits on the probability of error of a practical set of encoders and decoders are derived using information theoretical tools. <s> BIB042 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication (MC) is a promising nanoscale communication paradigm that enables nanomachines to share information by using messenger molecules. In this paper, an expression for the achievable rate in MC is first given. Then, using this expression, an optimal transmission probability is developed to maximize the MC rate. Numerical results show that the MC rate is time-dependent and the molecules freely wandering in the medium negatively affect the MC performance. However, the proposed optimal transmission probability is shown to maximize the MC rate. <s> BIB043 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Abstract In this paper, we study a molecular communication system operating over a moving propagation medium. Using the convection–diffusion equation, we present the first separate models for the channel response and the corrupting noise. The flow-based molecular channel is shown to be linear but time-varying and the noise corrupting the signal is additive white Gaussian with a signal dependent magnitude. By modelling the ligand–receptor binding process, it is shown that the molecular communication reception process in this channel has a low-pass characteristic that colours the additive noise. A whitening filter is proposed to compensate for this low-pass characteristic. Simulation results demonstrate the benefit of the whitening filter and the effect of medium motion on bit error rate. <s> BIB044 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> In this paper we investigate the channel capacity of the calcium signalling system based on an inter-cellular calcium wave model for astrocytes in the literature. Calcium signalling is a good candidate for molecular communication due to its long communication range, possible usage of existing cellular infrastructure, and its minimally invasive nature. Calcium waves are formed by the cytosolic oscillations of Ca2+ ion concentration, which propagates through neighbouring cells via secondary messenger molecules. Understanding the dynamics and physical properties of inter-cellular calcium waves is expected to produce an effective solution for the nano device communication problem. Thus, we extend the models developed in the literature to offer a calcium signalling scheme built on two cells and investigate the channel capacity depending on noise level and symbol duration. To the best of our knowledge, this is the first channel capacity analysis of calcium wave model that includes intercellular dynamics. <s> BIB045 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Molecular communication (MC) is a promising paradigm to communicate at nanoscale and it is inspired by nature. One of the MC methods in nature is the gap junction (GJ) communication between cardiomyocytes. The GJ communication is achieved by diffusion of ions through GJ channels between the cells. The transmission of the information is realized by means of the propagation of the action potential (AP) signal. The probabilities of both the AP propagation failure and the spontaneous AP initiation are obtained. For the first time in the literature, the GJ communication channel is modeled and analyzed from the information theoretical perspective to find the communication channel capacity. A closed-form expression is derived for the capacity of the GJ communication channel. The channel capacity, propagation delay, and information transmission rate are analyzed numerically for a three-cell network. The results of the numerical analyses point out a correlation between an increase in the incidence of several cardiac diseases and a decrease in the channel capacity, an increase in the propagation delay, and either an increase or a decrease in the transmission rate. The method that we use and results that are presented may help in the investigation, diagnosis, and treatment of cardiac diseases as well as help in the design of nanodevices communicating via GJ channels. <s> BIB046 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> The goal of a drug delivery system (DDS) is to convey a drug where the medication is needed, while, at the same time, preventing the drug from affecting other healthy parts of the body. Drugs composed of micro- or nano-sized particles (particulate DDS) that are able to cross barriers which prevent large particles from escaping the bloodstream are used in the most advanced solutions. Molecular communication (MC) is used as an abstraction of the propagation of drug particles in the body. MC is a new paradigm in communication research where the exchange of information is achieved through the propagation of molecules. Here, the transmitter is the drug injection, the receiver is the drug delivery, and the channel is realized by the transport of drug particles, thus enabling the analysis and design of a particulate DDS using communication tools. This is achieved by modeling the MC channel as two separate contributions, namely, the cardiovascular network model and the drug propagation network. The cardiovascular network model allows to analytically compute the blood velocity profile in every location of the cardiovascular system given the flow input by the heart. The drug propagation network model allows the analytical expression of the drug delivery rate at the targeted site given the drug injection rate. Numerical results are also presented to assess the flexibility and accuracy of the developed model. The study of novel optimization techniques for a more effective and less invasive drug delivery will be aided by this model, while paving the way for novel communication techniques for Intrabody communication networks. <s> BIB047 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Flow-induced Molecular Communication (FMC), where molecular transport is performed via flow, is utilized in microfluidic channels to enhance diffusion-based molecular communication. The incorporation of the microfluidic channel and the transport of molecules by flow, i.e., convection, require a rigorous analysis to develop an end-to-end concentration propagation model and a design for microfluidic channels. To the best of our knowledge, this is the first attempt to analyze concentration propagation in microfluidic channels from FMC perspective and devise them specifically to enhance the FMC. In this paper, a system-theoretic analysis of molecular transport is presented first. The system-theoretic model incorporates the solution of flow velocity in microfluidic channels and yields an end-to-end transfer function for concentration propagation based on building blocks of microfluidic channels. Then, the design of microfluidic channels is performed based on the least-squares Finite Impulse Response (FIR) filtering to achieve the desired end-to-end transfer function in FMC. According to the desired pass and stop bands, the required length and aspect-ratio parameters of the microfluidic channels are obtained for FIR filtering. The transfer functions for FMC is elaborated via numerical results. Furthermore, two example designs of microfluidic channels are presented for least-squares FIR band-pass and band-stop filtering in FMC. <s> BIB048 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> We model the ligand-receptor molecular communication channel with a discrete-time Markov model, and show how to obtain the capacity of this channel. We show that the capacity-achieving input distribution is iid; further, unusually for a channel with memory, we show that feedback does not increase the capacity of this channel. <s> BIB049 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> Within the domain of molecular communications, researchers mimic the techniques in nature to come up with alternative communication methods for collaborating nanomachines. This letter investigates the channel transfer function for molecular communications via diffusion. In nature, information-carrying molecules are generally absorbed by the target node via receptors. Using the concentration function, without considering the absorption process, as the channel transfer function implicitly assumes that the receiver node does not affect the system. In this letter, we propose a solid analytical formulation and analyze the signal metrics (attenuation and propagation delay) for molecular communication via diffusion channel with an absorbing receiver in a 3-D environment. The proposed model and the formulation match well with the simulations without any normalization. <s> BIB050 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> The design of biologically-inspired wireless communication systems using bacteria as the basic element of the system is initially motivated by a phenomenon called Quorum Sensing. Due to high randomness in the individual behavior of a bacterium, reliable communication between two bacteria is almost impossible. Therefore, we have recently proposed that a population of bacteria in a cluster is considered as a bio node in the network capable of molecular transmission and reception. This proposition enables us to form a reliable bio node out of many unreliable bacteria. In this paper, we study the communication between two nodes in such a network where information is encoded in the concentration of molecules by the transmitter. The molecules produced by the bacteria in the transmitter node propagate through the diffusion channel. Then, the concentration of molecules is sensed by the bacteria population in the receiver node which would decode the information and output light or fluorescent as a result. The uncertainty in the communication is caused by all three components of communication, i.e., transmission, propagation and reception. We study the theoretical limits of the information transfer rate in the presence of such uncertainties. Finally, we consider M-ary signaling schemes and study their achievable rates and corresponding error probabilities. <s> BIB051 </s> A Comprehensive Survey of Recent Advancements in Molecular Communication <s> A. Channel Models <s> In molecular communication, small particles such as molecules are used to convey information. These particles are released by a transmitter into a fluidic environment, where they propagate freely (e.g. through diffusion) or through externals means (e.g. different types of active transport) until they arrive at the receiver. Although there are a number of different mathematical models for the diffusion-based molecular communication, active transport molecular communication (ATMC) lacks the necessary theoretical framework. Previous works had to rely almost entirely on full Monte Carlo simulations of these systems. However, full simulations can be time consuming because of the computational complexities involved. In this paper, a Markov channel model has been presented, which could be used to reduce the amount of simulations necessary for studying ATMC without sacrificing accuracy. Moreover, a mathematical formula for calculating the transition probabilities in the Markov chain model is derived to complete our analytical framework. Comparing our proposed models with full simulations, it is shown that these models can be used to calculate parameters such channel capacity accurately in a timely manner. <s> BIB052
Information theory  is the mathematical foundation of any communication system. One of the most basic theoretical models for a communication system is the channel model. Physically, the channel is the environment over which the transmission signal propagates. Mathematically, the channel relates the transmission information, which would be the channel input, to the received information, which would be the channel output. There is an uncertainty associated with a communication channel. The received signal at the receiver can be different from the transmitted signal because of the noise introduced by the channel. In molecular communication one source of noise is the random propagation of information particles. Figure 10 shows a block diagram representation of the channel. The mathematical model of the channel can be described as follows. Let x ∈ X be the symbol (i.e., message) that a transmitter wants to send to the receiver, where X is the set of all possible symbols (i.e., messages) that the transmitter could send. In typical radio based communication, the signal sent by the transmitter gets attenuated and corrupted before it reaches the receiver. For example, the source of this corruption could be thermal noise from the electronic equipment, interference with other signals, and signal fading. Therefore, at the receiver the detected symbol (i.e., message) could be incorrect. Let y ∈ Y be the detected symbol at the receiver, where Y is the set of all possible detection symbols. Because the receiver has no prior knowledge of the original transmission symbol, the actual transmitted symbol can be considered a random variable X. Also, because the original transmitted symbol can be corrupted by noise, the detected symbol can be represented by a random variable Y . The communication channel can therefore be characterized by the conditional probability mass function (PMF) P (Y |X). In molecular communication channels, the main source of noise is the random motion of the information-carrying particles. All propagation schemes described in the previous sections are random in nature; although some are more random (pure molecular diffusion), and some are more directional (active transport). There are two important measures associated with any noisy channel in a communication system: the achievable information rate, and the channel capacity  . Achievable information rate is a theoretical measure of how many bits can be transmitted across the channel in a given period of time. For a discrete memoryless channel, where the current received symbol is independent of all the previous transmission symbols, achievable information rate can be computed from the PMFs P (Y |X) and P (X) as where I(X; Y ) is also called the mutual information between X and Y . Channel capacity is the maximum achievable information rate, which is the maximum number of transmission bits that can be transferred over the channel in a given period of time. Mathematically channel capacity is represented as where C is the channel capacity. For a discrete memoryless channel the mutual information is concave with respect to P (x)  . Therefore, if P (Y |X) is known, Blahut-Arimoto algorithm BIB002 , BIB003 could be used to find the maximizing P (x) and the channel capacity for the channel. Unfortunately, most practical molecular communication channels have memory. In this case, channel capacity is calculated differently BIB001 . Let x n be a sequence of n consecutive transmission symbols, and y n be the corresponding sequence of n consecutive received symbols. If the channel is information stable then the channel capacity is given by BIB004  The makes calculation of channel capacity much more difficult compared to the discrete memoryless channels. Because channel models play a central role in designing communication systems, one of the first problems that communication engineers tacked was modelling the molecular communication channel BIB006 , BIB007 . As mentioned in Section III-B different propagation schemes are possible for molecular communication channels. Moreover, information can be encoded or modulated differently as will be discussed later. Therefore, for each propagation scheme and modulation technique, a different channel model can be derived. 1) Diffusion Channel Models: In Sections III and IV we described the diffusion propagation scheme for both microscale and macroscale molecular communication. In BIB038 , the molecular diffusion channel with first hitting was considered and some information theoretical properties are proven. After defining the ADIMA channel, they first proved that the channel is stationary and ergodic, then provided the proof of the channel beingd-continuous. In BIB005 the molecular diffusion channel was considered. Using simulations, it was shown that the molecular diffusion channel can be a low pass filter that cuts out high frequency components of the signal. Also a very simple estimation of the channel capacity is derived using the frequency response of the channel and simplifying assumptions. In BIB007 the authors considered a molecular communication channel where the information was conveyed through number of molecules transmitted. In this scheme, if the transmission bit is 0, no molecules were transmitted and if the transmission bit is 1, A molecules were transmitted. Note that any symbol (message) can be converted into a binary sequence of 0s and 1s before transmission. At the receiver, it was assumed that ligand-receptors are used for detecting the information molecules. The authors used a simple model and showed that the channel model can be reduced to a binary symmetric channel  . In a binary symmetric channel, if bit-1 is transmitted, bit-1 is received with probability p 1 and bit-0 is received with probability (1−p 1 ). Similarly, if 0 is transmitted, bit-0 is received with probability p 0 and bit-1 is received with probability (1 − p 0 ). In BIB008 , the same authors extended the results and proposed a very rough algorithm for finding the optimal probability of transmitting bit-1 (i.e., A molecules) such that the error due to random propagation was compensated. The authors then extended their model from BIB007 to multiple access, broadcast, and relay channels BIB009 . The authors presented another simple model for single and multiple-access channels in BIB010 . At the receiver side, molecules react with the receptors over the receiver node surface and are removed from the environment. In nature, most of the receptor types remove the information-carrying molecules from the environment once they arrive at the receiver  . If the receptors do not remove molecules from the environment, they have other mechanisms to guarantee that each molecule contributes to the signal only once (e.g., acetylcholinesterase breaks down the molecules in neuromuscular junctions) BIB039 . Depending on the application and the medium, if the molecules contribute to the signal once then considering first hitting model becomes essential. In BIB006 the first generalized model for diffusion based molecular communication was derived. This model was developed based on a 1 dimensional diffusion model with first hitting time assumption. The channel capacity was derived and it was shown that for this simplified channel, more than one bit of information can be transmitted per information particle. Similarly, fraction of hitting molecules in 3 dimensional environment to a perfectly absorbing spherical receiver is derived in BIB050 . Having the closed form formula for 3 dimensional diffusion model with first hitting enabled the derivation of channel characteristics for diffusion based molecular communications. In BIB013 , a channel model for diffusion based molecular communication channels was presented, where different number of molecules was used to represent the binary transmission bits 1 and 0. The authors then derived energy models for the end-to-end communication channel, which could be used to calculate the maximum number of information particles that can be generated and transported based given the system parameters. Using this model an optimal transmission strategy that maximized the channel capacity was presented. In BIB014 an end-to-end gain (attenuation factor) and delay function were derived for continuous molecular diffusion channels with ligand receptors for detection. To derive these terms the authors used techniques from circuit theory to calculate the transfer function for the transmission, diffusion, and reception process. Using these transfer functions they calculated the end-to-end gains and delays. This derivation is based on the solutions to continuous diffusion equations (diffusion equations presented in Section IV). In practice, solutions for continuous diffusion channels are just the average behavior across many trials. Moreover, the number of particles that are released by the transmitter are continuous rather than discrete. Therefore, in BIB020 the authors attempted to make a more realistic model of diffusion based molecular communication channel by considering the discrete nature of the number of information particles and randomness of the diffusion propagation. They assumed that discreteness can be modeled as quantization noise and the random propagation as an additive noise which are added to the solution of continuous diffusion equations. Similarly, in BIB021 the authors captured the inherent randomness in ligand-binding reception as noise. Simplifying assumptions and Markov chains were used in the derivation of a closed-form expression of random ligand binding process. In BIB040 the authors derived a closed-form expression for the lower bound on channel capacity of diffusion molecular communication in gaseous environments. They showed that this lower bond capacity increases linearly with the bandwidth of the transmission signal. In this derivation it was assumed that the receiver and the transmitter are perfect, and the derivation was purely based on the diffusion transport process. In BIB015 , based on some simplifying assumptions, the authors derived different expressions for the transmission rate of diffusion based molecular communication with receptor based detection for point-to-point, broadcast, and multipleaccess channels. In BIB028 the authors considered a diffusion based molecular communication channel where the transmitter and the receiver were assumed to be genetically modified cells that are moving themselves. The information was transported through a three phase process: collision, adhesion, and neurospike transmission. In this scheme, two cells (the transmitter and the receiver) moved according to the laws of diffusion, until they collided and stuck to one another. The information was then transported from one cell to another using molecular neurospike communication. Through some simplifying assumption, the authors derived the channel models for this communication scheme. In BIB029 a model based on reaction-diffusion master equation, which is a well known model in physics and chemistry for jointly modeling diffusion and chemical reactions, was proposed. The model which is called reaction-diffusion master equation with exogenous input (RDMEX), discretizes time and space and uses a Markov model, where the states of the model are the number of information particles in discrete locations of space. During each discrete time step, the state of the Markov model changes according to the laws of diffusion and chemical reactions. The model can be used effectively to simulate and study diffusion based molecular communication with chemical reactions at the receiver. In BIB022 the diffusion based molecular communication was considered. Because in diffusion molecules move randomly, there could be inter-symbol-interference (ISI) between consecutive transmission symbols. In order to reduce the ISI effect the authors considered a symbol dependent symbol duration, where the transmission time for the current symbol was selected based on the current and the previous symbols. This channel was then modeled as a Markov chain and achievable rates were derived. The authors then completed their analysis in BIB023 , where they modeled the ligand receptor channel as a Markov Chain and derived the capacity and achievable rates for this channel. In BIB030 the authors proposed the use of microbial colonies collectively as the transmitter and the receiver entities in diffusion based molecular communication. In this scheme, the transmitter and the receiver were essentially made from colonies of genetically modified bacteria that would collectively transmit and receive information particles. This would increase the number of information particles that can be released by the transmitter, or detected by the receiver. The authors mathematically modeled the receiver as well as the intra-node communication (i.e., communication between the bacteria in the same colony) and inter-node communication (i.e., communication between the bacteria in different colonies). In BIB031 the sensing capacity of bacterial nodes was developed. To derive the capacity, it was assumed that the bacteria react to the concentration of information particles by emitting light. The higher was the concentration of the information particles at the receiver node, the higher was the luminance of the bacterial colony. The optimal input distribution and the corresponding sensing capacity were obtained based on the received power. The communication channel between two nodes made of bacterial colonies was considered in BIB032 . In this paper it was assumed that the transmitter is made of colony of bacteria as well, and the transmission of information particles is a two stage process. Signaling molecules of type I were used to control the amount of information particles (which the authors called type II molecules) released by the transmitter colony. In this scheme, the transmitter colony collectively detects the concentration of type I molecules, and based on this concentration the colony releases a certain amount of information particles (type II molecules). The released information particles diffuse until they arrive at the receiver colony, where they are detected by ligand receptors, which then initiates a fluorescent light generation response that is dependent on the concentration of the received molecules. Model for this transmission process was presented in BIB032 , while an end-to-end channel model was presented in BIB051 . In BIB041 the authors extended their previous work on bacterial colonies to a relaying scheme similar to relaying in traditional radio-based communication. In this scenario, three nodes, each of which is made up from a bacteria colony act as the transmitter, the relay and the receiver. The relay senses the concentration of information particles at its vicinity and releases some concentration of the same information particles or a different type of information particles. These relayed information particles diffuse and are sensed by the receiver. The authors considered different relaying schemes and presented the channel model for each. They showed that using relays the information rates could be improved. In BIB033 the authors considered a diffusion based molecular communication channel where the information particles degenerate over time according to exponential probability distribution. The authors presented a slotted binary channel model for this system (i.e., a channel model with a predefined constant transmission bit interval). They then assumed two different modulation scheme, which are essentially different variations of on-off-keying, where a certain number of molecules are released in case of transmission bit one and a different number of molecules are released in case of transmission bit zero. The authors showed that the life time of information particles had a significant effect on channel capacity, and that almost one bit per channel use was possible if a large number of molecules were used for modulation. In BIB034 the authors considered a diffusion based molecular communication channel, where the information was encoded in the order that two different types of information particles were released. The authors named this scheme Molecular ARray-based COmmunication (MARCO). To encode bit-0, information particle a is transmitted followed by information particle b, and to encode bit-1, b is transmitted followed by a. This channel was then modeled using simplifying assumptions and achievable information rates were derived. In BIB042 , similar technique is used with alternating the molecule type in a synchronized time slots. In the proposed system, two types of molecules are used in an alternating fashion. Transmitter uses A 1 molecules in odd time slots and A 2 type molecules in even time slots. As the molecule types are different in two subsequent time slots, the previous symbol interference is significantly reduced. In BIB024 the authors considered diffusion based molecular communication channel that used on-off-keying for encoding informations. In this scheme, during a predefined constant bit interval, the transmitter releases a single information particle if the information bit is 1, and no information particle if the information bit is 0. The authors showed that in the case where there was no interference with the other molecules from previous transmissions, the channel could be represented as a z-channel. Moreover, the authors considered a very simplified inter-symbol interference model, where the interference could effect only the next transmission. The achievable information rates were then calculated using computer simulations and the results were presented. In  , diffusion based molecular communication channel was considered with on-off-keying modulation. The authors used the solution of the diffusion equation with a point source to model the channel. They then presented expressions for the optimal decision threshold and the channel mutual information. In BIB035 a very basic multiple-input multiple-output (MIMO) scheme was proposed for molecular communication. In particular, it was assumed that there were multiple transmitter and multiple receivers that were collectively transferring and receiving information. Based on simplifying assumptions and the solution of continuous diffusion equations the authors derived the channel models for this MIMO system. In BIB043 a slotted diffusion channel was considered with onoff keying where one and zero are represented by transmission of a single and zero information particles, respectively. It was shown that this communication scheme can be represented as an additive noise channel, where the noise has a Poisson-Binomial PMF. Using this channel model the optimal transmission probabilities were derived. As mentioned in Section III-B, flow could be used to assist the speed of propagation of diffusion. In BIB011 a general framework for molecular communication based on diffusion with flow (also called drift here) was presented. In BIB016 the authors presented a model for diffusion molecular communication with drift, where the information was encoded in the time of release of information particles. The work was then extended in BIB017 , where it was shown that such a channel could be modeled with an additive inverse Gaussian noise (AIGN). The authors then derived lower and upper bounds for the channel capacity of AIGN channel. They showed that their bonds were tight for low flow rates, but the bounds became separated as the flow rate increased or as it approached zero. They used the derived channel models to design a receiver based on a maximum likelihood estimator. In BIB025 the authors presented a stochastic model for three different effects of the channel environment on information particles: particle absorption (where the particles are absorbed in the environment), particle generation (where a single information particle becomes two information particles through reactions in the medium), and spontaneous emission (where information particles are spontaneously generated through chemical reactions). Through simplifying assumptions, a model was derived using birth-and-death processes. The model was then applied to diffusion based molecular communication with and without flow. In BIB044 channel models for diffusion based molecular communication with flow was presented. To derive their model, the authors used the diffusion equations with a moving coordinate frame, which moves according to the flow velocity vector. It was shown that diffusion channels with flow are linear but time-varying. Therefore, a time varying channel impulse response could be used to model these systems. The authors then demonstrated that the random motion of information particles could be represented using the solution to the convection-diffusion equation plus additive white Gaussian noise term. When ligand receptor model was employed for detection, it is demonstrated that the noise becomes a colored noise process. 2) Other Channel Models: As was presented in the previous section, many different channel models are proposed for diffusion based molecular communication. However, for other propagation schemes presented in Section III-B, there are not many channel models. In this sections we survey some of the work on these propagation schemes. In BIB012 simulations were used to compare the arrival probabilities of diffusion channels, and active transport channels based on a microtubule track that connects the transmitter to the receiver and kinesin motor proteins as carries of information particles. A hybrid approach based on combination of these propagation schemes was also considered. It was shown that diffusion had low rate of delivery and lower channel capacity for separation distances in the order of micrometers compared to the active transport and the hybrid schemes. In BIB018 gap junction channels with calcium ion signaling molecules were considered. In this scheme, it was assumed that the transmitter and the receiver are cells or artificial lattice structures that are connected together through a series of cells or artificial lattice structures all of which are connected through gap junction channels. Calcium ions are generated by the transmitter and propagate through the gap junction channels, traveling from lattice to lattice until they arrive at the receiver. It was assumed that on-off-keying is used for encoding information. The channel was then simulated and achievable information rates were presented. In BIB045 the channel capacity of the calcium signaling system based on an inter-cellular calcium wave model for astrocytes is investigated. Calcium waves are formed by the cytosolic oscillations of Ca +2 ion concentration, which propagates through neighboring cells via secondary messenger molecules. Authors extended the models in the literature for calcium signaling between two nanonetworking nodes. Channel capacity of the investigated system is analyzed under different noise levels and the symbol durations. In BIB046 the gap junction communication between cardiac muscle cells, called cardiomyocytes, was modeled. In particular the propagation of action potential, which helps to regulates the hear beat was modeled as a communication channel using previously published work in biology. The authors then simulated this system to calculate the channel capacity. It was shown that some cardiac diseases decrease the channel capacity of this system. In BIB019 , BIB026 a molecular communication channel was modeled in which information particles such as DNA strands are embedded in flagellated bacteria that propagate from a transmitter to a receiver. It was assumed that the receiver uses attractant molecules to attract these bacteria. The motion of the bacteria from the transmitter to the receiver was modeled and simulated. In BIB047 a channel model for blood flow through arteries was developed using harmonic transfer matrix and some simplifying assumptions. Two different models were used for small and large arteries, and the models were then combined to form a complete model of blood flow through the arteries in the body. A model for drug injection propagation in the arteries was then presented based on this model. In BIB048 channel models for flow based molecular communication in microfluidic channels was presented. The authors derived the transfer function of the straight channel, the turning channel, bifurcation channel, and combining channel. They showed that the transfer function of any channel configuration can be made using the transfer function of these channels. Using this model the authors demonstrated that finite impulse response (FIR) filters could be implemented on a microfluidic device. In BIB027 a mathematical model for active transport molecular communication using stationary kinesin and microtubule filament was presented. In particular, these models were developed to decrease the simulation time of these channels. Previous works had relied of simulations for studying these channels because of the complex motion of the microtubules. In BIB052 the results of BIB036 was improved, and a Markov chain channel model for kinesin/microtubule motility was presented. It was shown that the new channel model can reduce the simulation time of these channels, and can be used to calculate different channel parameters such as channel capacity fairly accurately. In BIB037 on-chip molecular communication channels were considered in confined environments. In particular, the channel capacity of diffusion based, flow based, and stationary kinesin with mobile microtubule filaments based molecular communication channels were compared using Monte Carlo simulations. It was shown that at short distances, diffusion and flow based propagations achieve higher channel capacities, while at longer distances active transport and flow based propagations achieve higher channel capacities. In BIB049 simple intercellular signal transduction channels were considered, where information particles were detected using ligand receptors. The paper abstracted the concept of propagation and assumed the input to the channel is the concentration level at the vicinity of the receiver, which was equipped with ligand receptors. The detection process was then represented as a discrete-time Markov model. It was shown how the capacity can be obtained for this channel. It was also shown that the capacity achieving input distribution is iid, which is unusual for channels with memory. Furthermore, it was demonstrated that feedback does not increase the capacity of this channel.