In some rate-distortion-type problems, the required fidelity of information is affected by past actions. As a result, the distortion function depends not only on the instantaneous distortion between a source symbol and its representation symbol, but also on past representations. In this paper, we give a formal definition of this problem and introduce both inner (achievable) and outer bounds on the rate-distortion tradeoff. We also discuss convexification of the problem, which makes it easier to find bounds. Problems of this type arise in biological information processing, as well as in recommendation engines; we provide an example applied to a simplified biological information processing problem.

In an information-processing investment game, such as the growth of a population of organisms in a changing environment, Kelly betting maximizes the expected log rate of growth. In this paper, we show that Kelly bets are closely related to optimal single-letter codes (i.e., they can achieve the rate-distortion bound with equality). Thus, natural information processing systems with limited computational resources can achieve information-theoretically optimal performance. We show that the rate-distortion tradeoff for an investment game has a simple linear bound, and that the bound is achievable at the point where the corresponding single-letter code is optimal. Moreover, since evolution is expected to optimize an organism’s information processing capabilities, this bound allows prediction of biological behaviour. Examples illustrating the results in simplified biological scenarios are presented.

We consider a multistate extension of the Poissontype channel, originally introduced by Kabanov, in which the channel is a continuous-time Markov chain with transition rates modulated by the input signal. There exist many physical examples of such channels, from optical communication to biological signal transduction: for example, biological systems often transmit information by inducing conformational changes in proteins through varying intensities of light, voltage, or concentration of signaling molecules. Going beyond Kabanov, the multistate extension is crucial for understanding these systems. We focus on the case where the channel is fully observable, i.e., the output is the channel state, and only one state transition is sensitive to the input. Under stationarity, we derive a one-dimensional variational formula for the Shannon capacity. The structural information of the channel is encoded through the invariant measure of an associated Markov chain, and we numerically demonstrate the effect of the underlying graphical structure on the channel's communication capability.

Cooperative molecular communication (MC) is a key enabler for communication between nanomachines in the Internet of Bio-Nano Things (IoBNT). However, its performance is significantly constrained by the limited availability of free energy, which is essential for molecular transport. This paper introduces a novel transmitter model that encodes information by utilizing free energy to transport molecules from a reservoir to the external environment, creating specific concentration ratios in the reservoir for reliable information transmission. The transmitter’s performance is primarily influenced by energy consumption, which directly impacts the system’s bit error rate (BER) in IoBNT. To address these challenges, this study focuses on optimizing energy allocation among multiple transmitters in cooperative MC systems to enhance BER performance. For scenarios with two transmitters, a theoretical analysis of optimal energy allocation is performed, while reinforcement learning (RL) is utilized to determine optimal energy allocation strategies for systems with more than two transmitters. Numerical results demonstrate the effectiveness of the proposed strategies in minimizing BER and improving the overall performance of cooperative MC systems under energy constraints.

Cooperative molecular communication (MC) is a promising technology for facilitating communication between nanomachines in the Internet of Bio-Nano Things (IoBNT) field. However, the performance of IoBNT is limited by the availability of energy for cooperative MC. This paper presents a novel transmitter design scheme that utilizes molecule movement between reservoirs, creating concentration differences through the consumption of free energy, and encoding information on molecule types. The performance of the transmitter is primarily influenced by energy costs, which directly impact the overall IoBNT system performance. To address this, the paper focuses on optimizing energy allocation in cooperative MC for enhanced transmitter performance. Theoretical analysis is conducted for two transmitters. For scenarios with more than two users, a genetic algorithm is employed in the energy allocation to minimize the total bit error rate (BER). Finally, numerical results show the effectiveness of the proposed energy allocation strategies in the considered cooperative MC system.

In some molecular communication (MC) designs, signaling molecules are held in reservoirs of different concentrations. This paper explores two thermodynamic implications of creating such a transmitter. First, it requires energy to generate reservoirs at different concentrations, since their chemical potential is different from the environment. Second, it requires an enormous energy cost to create a pure (or nearly pure) reservoir, so the transmitter is necessarily imperfect. Drawing from the Maxwell's Demon thought experiment, we consider the separation of an environmental mixture into reservoirs of differing concentrations, which requires free energy, but which allows information to be encoded in the difference of concentration. Both theoretical and simulation results indicate that the performance of the transmitter is positively correlated with the amount of consumed free energy. Furthermore, our simulation results indicate that there may be a fundamental thermodynamic tradeoff between energy per bit and bit error rate in MC.

In this work, we study the impact of THz signaling on controlling protein conformational changes. Specifically, due to the imposed variability of the intra-body medium on signal propagation, we study the effect of the channel randomness on THz-induced protein interactions. To do so, we demonstrate how the impinging nanoantenna force affects the energy absorbed by the protein structure. We specifically focus on analyzing the impact of the slowly varying force on the capability to control the dynamics of the desired protein population. We later introduce the probability of selectivity outage as a metric that is calculated based on a pre-defined selectivity threshold. Our results indicate that a trade-off must exist in the system since the higher the selectivity threshold, the higher the probability of selectivity outage, which increases the constraints imposed on the intra-body system design. The presented work provides a better understanding and characterization of the electromagnetically triggered protein molecules, their micro-environment, and their interaction with surrounding particles.

Bacteria generally live in complicated structures called biofilms, consisting of communicating bacterial colonies and extracellular polymeric substance (EPS). Since biofilms are related to detrimental effects such as infection or antibiotic resistance in different settings, it is essential to model their formation. In this paper, a stochastic model is proposed for biofilm formation, using bacterial quorum sensing (QS). In this model, the biological processes in the biofilm formation are modeled as a chemical reaction network which includes bacterial reproduction, productions of autoinducer and EPS, and their diffusion. The modified explicit tau-leap simulation algorithm is adapted based on the two-state QS mechanism. Our approach is validated by using the experimental results of Pseudomonas putida IsoF bacteria for autoinducer and bacteria concentration. It is also shown that the percentage of EPS in the biofilm increases significantly after the state change in QS, while it decreases before QS is activated. The presented work shows how the biofilm growth can be modeled realistically by using the QS mechanism in stochastic simulations of chemical reactions.

Airborne pathogen transmission mechanisms play a key role in the spread of infectious diseases such as COVID-19. In this work, we propose a computational fluid dynamics (CFD) approach to model and statistically characterize airborne pathogen transmission via pathogen-laden particles in turbulent channels from a molecular communication viewpoint. To this end, turbulent flows induced by coughing and the turbulent dispersion of droplets and aerosols are modeled by using Reynolds-averaged Navier-Stokes equations coupled with realizable$k-\epsilon$model and the discrete random walk model, respectively. Via the simulations realized by a CFD simulator, statistical data for the number of received particles are obtained. These data are post-processed to obtain the statistical characterization of the turbulent effect in the reception and to derive the probability of infection. Our results reveal that the turbulence has an irregular effect on the probability of infection which shows itself by the multimodal distributions as a weighted sum of normal and Weibull distributions.

Overcoming inter-symbol interference (ISI) is one of the key challenges in the design of molecular communication systems. In this paper, we propose a scheme for optimizing the detection interval to minimize the impact of ISI while ensuring the acquisition of effective information. Our detection interval optimization applies to both the absorbing and passive receivers. For analysis, we consider as the performance metrics signal-to-interference difference (SID) and signal-to-interference and noise amplitude ratio (SINAR) proposed in the literature rather than the intractable bit error rate (BER). Accordingly, we derive the optimal detection interval in closedform. Finally, simulation results in terms of BER verify the theoretical analysis and also show the promising advantages of the proposed scheme in signal detection.

In this paper, we propose a theoretical intra-body propagation model for signal transmission in the THz frequency band. The channel of interest is a blood vessel composed of red blood cells (RBCs), where propagation occurs between a nanoantenna transmitter and a protein receiver. The presented model accounts for signal losses due to molecular absorption and scattering through both line-of-sight (LOS) and non-line-of-sight (NLOS) links. The RBCs between the antenna and the protein act as obstacles that attenuate the signal power giving rise to shadowing. By conducting Monte Carlo simulations, we develop the random characteristics of the transmission medium. Inspired by radar systems, an expression for the received power is derived using the bistatic radar model and the total path loss is computed through the different links. The results are validated by means of electromagnetic wave propagation simulations. The presented work indicates that a reliable communication link exists between the nanoantenna and the protein through both the LOS and NLOS transmission. Our work facilitates the accurate design of in-vivo wireless nanosensor networks and paves the path towards selective intra-body interactions.

Existing molecular communication systems, both theoretical and experimental, are characterized by low information rates. In this paper, inspired by time-of-flight mass spectrometry, we consider the design of a molecular communication system in which the channel is a vacuum, and demonstrate that this method has the potential to increase achievable information rates by many orders of magnitude. We use modelling results from TOFMS to obtain arrival time distributions for accelerated ions, and use it to analyze several species of ions, including hydrogen, nitrogen, argon, and benzene. Using a simplified communication model, we show that data rates in excess of 100 Mbit/s/molecule are achievable.

In this paper, we propose a two-layer heterogeneous network to realize the remote monitoring and advanced warning for infectious diseases spread by airborne pathogens, whose detection can be considered as a binary detection problem. To intuitively study the detection process, we abstract it as a molecular communication via diffusion (MCvD) model and uncover that one of the key factors to impact the detection performance is inter-symbol interference (ISI), i.e., the viral aerosol from other biological entities. Therefore, overcoming ISI is imperative to ensure reliable detection. In the abstracted MCvD model, the detection performance can be described by the bit error rate (BER) performance. Following this assumption, we propose to optimize the detection interval to minimize the impact of ISI while ensuring the accurate detection of the transmitted information symbol, which is suitable for both the absorbing and passive receivers. For tractability, based on the signal-to-interference difference (SID) and signal-to-interference-and-noise amplitude ratio (SINAR), we design a modified-SINAR (mSINAR) to measure BER performance for the MCvD system with a variable detection interval. Besides, we derive the optimal detection interval in closed-form. Using simulation results, we show that in terms of BER, our proposed mSINAR scheme is superior to the competitive schemes, and performs similarly to the scheme with optimal intervals determined by the exhaustive search.

The evolutionary consequences of quorum sensing in regulating bacterial cooperation are not fully understood. In this study, we reveal unexpected effects of regulating public good production through quorum sensing on bacterial population dynamics, showing that quorum sensing can be a collectively harmful alternative to unregulated production. We analyze a birth-death model of bacterial population dynamics accounting for public good production and the presence of non-producing cheaters. Our model demonstrates that when demographic noise is a factor, the consequences of controlling public good production according to quorum sensing depend on the cost of public good production and the growth rate of populations in the absence of public goods. When public good production is inexpensive, quorum sensing is a destructive alternative to unconditional production, in terms of the mean population extinction time. When costs are higher, quorum sensing becomes a constructive strategy for the producing strain, both stabilizing cooperation and decreasing the risk of population extinction.

In this paper, we consider a mobile molecular communication (MC) system consisting of two mobile nanomachines, a transmitter and a receiver, propelled by a positive drift velocity and Brownian motion in a realistic blood-vessel-type flow regime. Considering the nonlinear movement of the nanomachines, an extended Kalman filter is employed to estimate the distance from the transmitter. Furthermore, based on the predicted distance, to keep the number of received molecules for bit 1 at a stable level, we employ power control on the number of transmitted molecules based on the distance between the transmitter and the receiver and the residual molecules in the channel from the previous transmission. Finally, the optimal detection threshold is obtained by minimizing the error probability. It is verified that a fixed optimal detection threshold can be effective for the power control scheme in the mobile MC. The bit error rate (BER) performance of our scheme is verified via simulation results.

Distance and velocity estimation is challenging in mobile molecular communication, since estimates may be stale by the time the terminals gather the required information. To address both the difficulty and the delay of estimation, we propose an extended Kalman filter to predict both the distance between transmitter and receiver, and the drift velocity of the receiver, in a realistic blood-vessel-type flow regime. The extended Kalman filter is appropriate for the problem, as it can be used to predict quadratic quantities such as distance, and has manageable computational complexity. We derive the extended Kalman filter and show that it delivers excellent performance in predicting both distance and velocity in the presence of nonuniform flow.

It has been established that interfacing Terahertz (THz) band signals with protein molecules excites their resonant modes. In this work, we develop a model that bridges the mechanical system of proteins, modeled as harmonic oscillators, and the probability of protein conformal changes. We deploy the Langevin stochastic equation under the influence of an external force to capture the protein dynamics. The average energy driving the protein to alter its conformation is derived and used to determine the probability of protein folding. Our numerical analysis results show that the energy transferred from the nanoantenna and stored in the protein is capable of inducing a conformal change in the protein. This illustrates the power of THz waves in enabling protein interactions with high selectivity. It also sheds light on various opportunities that impact applications concerning targeted therapy, biosensing as well as disease control and prevention.

In quorum sensing (QS), bacteria exchange molecular signals to work together. An analytically-tractable model is presented for characterizing QS signal propagation within a population of bacteria and the number of responsive cooperative bacteria (i.e., cooperators) in a two-dimensional (2D) environment. Unlike prior works with a deterministic topology and a simplified molecular propagation channel, this work considers continuous emission, diffusion, degradation, and reception among randomly-distributed bacteria. Using stochastic geometry, the 2D channel response and the corresponding probability of cooperation at a bacterium are derived. Based on this probability, new expressions are derived for the moment generating function and different orders of moments of the number of cooperators. The analytical results agree with the simulation results obtained by a particle-based method. In addition, the Poisson and Gaussian distributions are compared to approximate the distribution of the number of cooperators and the Poisson distribution provides the best overall approximation. The derived channel response can be generally applied to any molecular communication model where single or multiple transmitters continuously release molecules into a 2D environment. The derived statistics of the number of cooperators can be used to predict and control the QS process, e.g., predicting and decreasing the likelihood of biofilm formation.

In this paper, we consider non-coherent detection schemes for molecular communication systems in the presence of inter-symbol-interference. In particular, we study non-coherent detectors based on memory-bits-based thresholds in order to achieve low bit-error-ratio (BER) transmission. The main challenge of realizing detectors based on memory-bits-based thresholds is to obtain the channel state information based only on the received signals. We tackle this issue by reformulating the thresholds through intermediate variables, which can be obtained by clustering multi-dimensional data from the received signals, and by using the K-means clustering algorithm. In addition to estimating the thresholds, we show that the transmitted bits can be retrieved from the clustered data. To reduce clustering errors, we propose iterative clustering methods from one-dimensional to multi-dimensional data, which are shown to reduce the BER. Simulation results are presented to verify the effectiveness of the proposed methods.

Nanosized devices operating inside the human body open up new prospects in the healthcare domain. On the one hand, molecular communication enables biological nanomachines to communicate by exchanging molecules and performing application-dependent tasks. On the other hand, electromagnetic (EM) nano-communication points to the Terahertz Band (0.1-10 THz) as the frequency range for communication among nano-biosensors. In this paper, we propose a stimuli-responsive paradigm which integrates EM and molecular communication by stimulating proteins in the human body. Our model capitalizes on the fact that proteins act as an interface between both mediums, in which triggering proteins by THz waves changes their conformational structure. This allows biochemical and biomechanical activities to be carried out in a controlled manner. The stochasticity involved in the folding and unfolding of proteins is modeled using a Markov chain. A closed form expression for the mutual information rate by which proteins receive information is derived and maximized to find the capacity. By illustrating the information rates theoretically achievable, we hope to spark research into the EM-based control of protein networks.

This paper considers information-theoretic aspects of mechanosensitive based communication signals in living organisms such as plants and bacteria. Mechanosensitive ion channels function as mechanosensitive transducers, which generate an activation signal in response to a mechanical stimulus. This activation signal is necessary for performing different functions, such as the coordination of growth or determining a response to a stress. The activation signal works by releasing a number of protein molecules carrying information in the transmitter cell which is the input signal of the system. These protein molecules propagate to the receiver cells through a diffusion based medium and react with receptors to produce output protein molecules, forming a molecular communication system. In this paper we develop a communication system model for mechanosensitive systems, and study the mutual information and the information propagation speed associated with their signals.

The exchange of small molecular signals within microbial populations is generally referred to as quorum sensing (QS). QS is ubiquitous in nature and enables microorganisms to respond to fluctuations in living environments by working together. In this study, a QS- based molecular communication system within a microbial population in a two-dimensional (2D) environment is analytically modeled. Microorganisms are randomly distributed on a 2D circle where each one releases molecules at random times. The number of molecules observed at each randomly-distributed bacterium is first derived by characterizing the diffusion and degradation of molecules within the population. Using the derived result and some approximation, the expected density of cooperative bacteria is derived. Our model captures the basic features of QS. The analytical results for noisy signal propagation agree with simulation results where the Brownian motion of molecules is simulated by a particle- based method. Therefore, we anticipate that our model can be used to predict the density of cooperators in a variety of QS-coordinated activities, e.g., biofilm formation and antibiotic resistance.

Biochemical signal transduction, a form of molecular communication, can be modeled using graphical Markov channels with input-modulated transition rates. Such channel models are strongly non-Gaussian. In this paper we use a linear noise approximation to construct a novel class of Gaussian additive white noise channels that capture essential features of fully- and partially-observed intensity- driven signal transduction. When channel state transitions that are sensitive to the input signal are directly observable, high-frequency information is transduced more efficiently than low-frequency information, and the mutual information rate per bandwidth (spectral efficiency) is significantly greater than when sensitive transitions and observable transitions are disjoint. When both observable and hidden transitions are input-sensitive, we observe a superadditive increase in spectral efficiency.

This paper focuses on different properties of an electrochemical signal based model for inter-cellular communication in plants. The input signal in this communication system can be either composed of (a) a number of fast moving charged molecules or (b) randomly diffusing molecules, which are driven by an action potential (AP) signal. APs are usually generated by an external stimulus such as change in temperature or light. We use a model of AP generation in this paper from previous works. The three main contributions of this paper are: firstly we consider the impact of multiple AP signals on the mutual information of the system for multiple (varying) numbers of receiver cells in different configurations, second, we compare the impact of different propagation mechanisms (i.e. fast active movement and random diffusion of molecules) on the output molecules and mutual information of the system, and finally we study the impact of multiple APs on the information propagation speed of the system and compare it for the different receiver cell configurations.

This paper considers an electro-chemical signal based model for inter-cellular communication in plants. The input signal, composed of fast moving charged molecules is driven by an action potential (AP). APs, generated by an external stimulus, are part of the communication mechanism in plants. We extend the simple model for AP generation presented in previous work to incorporate the AP signal arriving from neighboring cells. Furthermore in this model we study the transfer of information between cells via fast moving ions. Unlike previous work, this paper does not consider diffusion but only reactions between molecules at each step. We then use an information-theoretic analysis to compute the mutual information between the input and output of this system. The key aim is to study the impact of an increase in population of cells on the mutual information. We calculate the mutual information for a large group of cells (up to 100) in three different topologies i.e., parallel, series and mixed. Finally we study the impact of a single AP on multiple cells in the system.

In this paper, symbol-by-symbol maximum likelihood (ML) detection is proposed for a cooperative diffusion-based molecular communication (MC) system. In this system, the transmitter (TX) sends a common information symbol to multiple receivers (RXs) and a fusion center (FC) chooses the TX symbol that is more likely, given the likelihood of its observations from all RXs. The transmission of a sequence of binary symbols and the resultant intersymbol interference are considered in the cooperative MC system. Three ML detection variants are proposed according to different RX behaviors and different knowledge at the FC. The system error probabilities for two ML detector variants are derived, one of which is in closed form. The optimal molecule allocation among RXs to minimize the system error probability of one variant is determined by solving a joint optimization problem. Also for this variant, the equal distribution of molecules among two symmetric RXs is analytically shown to achieve the local minimal error probability. Numerical and simulation results show that the ML detection variants provide lower bounds on the error performance of simpler, non-ML cooperative variants and demonstrate that these simpler cooperative variants have error performance comparable to ML detectors.

We consider scheduling and resource allocation in long-term evolution (LTE) networks across voice over the LTE (VoLTE) and best-effort data users. The difference between these two is that VoLTE users get scheduling priority to receive their required quality of service. As we show, strict priority causes data services to suffer. We propose new scheduling and resource allocation algorithms to maximize the sum or proportional fair (PF) throughout amongst data users while meeting VoLTE demands. Essentially, we use VoLTE as an example application with both a guaranteed bit-rate and strict application-specific requirement. We first formulate and solve the frame-level optimization problem for throughput maximization; however, this leads to an integer problem coupled across the LTE transmission time intervals (TTIs). We then propose a TTI-level problem to decouple scheduling across TTIs. Finally, we propose a heuristic scheme, with extremely low complexity. The formulations illustrate the details required to realize resource allocation in an implemented standard. The numerical results show that the performance of the TTI-level scheme is very close to that of the frame-level upper bound. Similarly, the heuristic scheme works well compared to TTI-level optimization and a baseline scheduling algorithm. Finally, we show that our PF optimization retains the high fairness index characterizing PF-scheduling.

This paper considers an electro-chemical based communication model for intercellular communication in plants. Many plants, such as Mimosa pudica (the "sensitive plant"), employ electrochemical signals known as action potentials (APs) for communication purposes. In this paper we present a simple model for action potential generation. We make use of the concepts from molecular communication to explain the underlying process of information transfer in a plant. Using the information-theoretic analysis, we compute the mutual information between the input and output in this work. The key aim is to study the variations in the information propagation speed for varying number of plant cells for one simple case. Furthermore we study the impact of the AP signal on the mutual information and information propagation speed. We further aim to explore the impact of increasing number of cells on the information propagation speed.

In this paper, symbol-by-symbol maximum likelihood (ML) detection is proposed for a cooperative diffusion-based molecular communication (MC) system. In this system, a fusion center (FC) chooses the transmitter's symbol that is more likely, given the likelihood of the observations from multiple receivers (RXs). We propose three different ML detection variants according to different constraints on the information available to the FC, which enables us to demonstrate trade- offs in their performance versus the information available. The system error probability for one variant is derived in closed form. Numerical and simulation results show that the ML detection variants provide lower bounds on the error performance of the simpler cooperative variants and demonstrate that majority rule detection has performance comparable to ML detection when the reporting is noisy.

This paper predicts the ability to externally control the firing times of a cortical neuron whose behavior follows the Izhikevich neuron model. The Izhikevich neuron model provides an efficient and biologically plausible method to track a cortical neuron's membrane potential and its firing times. The external control is a simple optogenetic model represented by a constant current source that can be turned on or off. This paper considers a firing frequency that is sufficiently low for the membrane potential to return to its resting potential after it fires. The time required for the neuron to charge and for the neuron to recover to the resting potential are fitted to functions of the Izhikevich neuron model parameters. Results show that linear functions of the model parameters can be used to predict the charging times with some accuracy and are sufficient to estimate the highest firing frequency achievable without interspike interference.

In this paper, we consider the energy cost of communicating using molecular communication. In a simplified scenario, we show that the energy bound in Landauer's principle can be achieved, implying that molecular communication can approach fundamental thermodynamic limits.

In this paper, we consider a two-hop molecular communication relay system, called the relay BIND channel. Based on the cyclic adenosine monophosphate (cAMP) model system for signal transduction, our ligand-receptor binding mechanism is modelled as a discrete-time finite state Markov channel. We show how to calculate the mutual information (MI) of the relay BIND channel, for binary finite input alphabets, binary channel state, and binary output. Further, our simulation and analytical results show that the relay BIND channel can improve the molecular communication capacity between two nanomachines using the relay.

Optogenetics is an emerging field of neuroscience where neurons are genetically modified to express light-sensitive receptors that enable external control over when the neurons fire. Given the prominence of neuronal signaling within the brain and throughout the body, optogenetics has significant potential to improve the understanding of the nervous system and to develop treatments for neurological diseases. This paper uses a simple optogenetic model to compare the timing distortion between a randomly-generated target spike sequence and an externally-stimulated neuron spike sequence. The distortion is measured by filtering each sequence and finding the root mean square error between the two filter outputs. The expected distortion is derived in closed form when the target sequence generation rate is sufficiently low. Derivations are verified via simulations.

Molecular communication requires low-complexity symbol detection algorithms to deal with the many sources of uncertainty that are inherent in these channels.This paper proposes two variants of a high-performance asynchronous peak detection algorithm for a receiver that makes independent observations.The first variant has low complexity and measures the largest observation within a sampling interval.The second variant adds decision feedback to mitigate inter-symbol interference.Although the algorithm does not require synchronization between the transmitter and receiver, results demonstrate that the bit error performance of symbol-by-symbol detection using the first variant is better than using a single sample whose sampling time is chosen a priori.The second variant is shown to have performance comparable to that of an energy detector.Both variants of the algorithm demonstrate better resilience to timing offsets than that of existing detectors.

Bacteria populations rely on mechanisms such as quorum sensing to coordinate complex tasks that cannot be achieved by a single bacterium. Quorum sensing is used to measure the local bacteria population density, and it controls cooperation by ensuring that a bacterium only commits the resources for cooperation when it expects its neighbors to reciprocate. This paper proposes a simple model for sharing a resource in a bacterial environment, where knowledge of the population influences each bacterium's behavior. Game theory is used to model the behavioral dynamics, where the net payoff (i.e., utility) for each bacterium is a function of its current behavior and that of the other bacteria. The game is first evaluated with perfect knowledge of the population. Then, the unreliability of diffusion introduces uncertainty in the local population estimate and changes the perceived payoffs. The results demonstrate the sensitivity to the system parameters and how population uncertainty can overcome a lack of explicit coordination.

In this paper, a cooperative diffusion-based molecular communication system is considered where distributed receivers collaboratively determine a transmitter's signal. In this system, the receivers first make local hard decisions about the current transmitted bit and then report these decisions to a fusion center (FC). The FC combines the local hard decisions to make a global decision using an N-out-of-K fusion rule. Asymmetric and symmetric topologies are considered and for each topology, two reporting scenarios, namely, perfect reporting and noisy reporting, are addressed. Closed-form analytical expressions for the expected global error probability are derived for all considered topologies and scenarios. Numerical and simulation results show that system reliability can be greatly improved by combining the detection information of distributed receivers.

This work studies the impact of time-synchronization in molecular timing (MT) channels by analyzing three different modulation techniques. The first requires transmitter-receiver synchronization and is based on modulating information on the release timing of information particles. The other two are asynchronous and are based on modulating information on the relative time between two consecutive releases of information particles using indistinguishable or distinguishable particles. All modulation schemes result in a system that relate the transmitted and the received signals through an additive noise, which follows a stable distribution. As the common notion of the variance of a signal is not suitable for defining the power of stable distributed signals (due to infinite variance), we derive an expression for the geometric power of a large class of stable distributions, and then use this result to characterize the geometric signal-to-noise ratio (G-SNR) for each of the modulation techniques. In addition, for binary communication, we derive the optimal detection rules for each modulation technique. Numerical evaluations indicate that the bit error rate (BER) is constant for a given G-SNR, and the performance gain obtained by using synchronized communication is significant. Yet, it is also shown that by using two distinguishable particles per bit instead of one, the BER of the asynchronous technique can approach that of the synchronous one.

Information theory provides powerful tools for understanding communication systems. This analysis can be applied to intercellular signal transduction, which is a means of chemical communication among cells and microbes. We discuss how to apply information-theoretic analysis to ligand-receptor systems, which form the signal carrier and receiver in intercellular signal transduction channels. We also discuss the applications of these results to neuroscience.

This work introduces capacity limits for molecular timing (MT) channels, where information is modulated on the release timing of small information particles, and decoded from the time of arrival at the receiver. It is shown that the random time of arrival can be represented as an additive noise channel, and for the diffusion-based MT (DBMT) channel, this noise is distributed according to the Lévy distribution. Lower and upper bounds on the capacity of the DBMT channel are derived for the case where the delay associated with the propagation of information particles in the channel is finite. These bounds are also shown to be tight.

Cyclic adenosine monophosphate (cAMP) is considered a model system for signal transduction, the mechanism by which cells exchange chemical messages. Our previous work calculated the Shannon capacity of a single cAMP receptor; however, a typical cell may have thousands of receptors operating in parallel. In this paper, we calculate the capacity of a cAMP signal transduction system with an arbitrary number of independent, indistinguishable receptors. By leveraging prior results on feedback capacity for a single receptor, we show (somewhat unexpectedly) that the capacity is achieved by an IID input distribution, and that the capacity for n receptors is n times the capacity for a single receptor.

In this special issue, we cover some recent results in the following four emerging areas: 5G cellular systems, big data systems, bio/nano/molecular networks, and smart grids. In the past several years, there are various technologies emerging, which are either directly or indirectly related to communication. Some of them are over the evolution of traditional communication systems, while others are over new systems such as smart grids, molecular networks, and big data systems.

In diffusion-based molecular communication, information transport is governed by diffusion through a fluid medium. The achievable data rates for these channels are very low compared to the radio-based communication system, since diffusion can be a slow process. To improve the data rate, a novel multiple-input multiple-output (MIMO) design for molecular communication is proposed that utilizes multiple molecular emitters at the transmitter and multiple molecular detectors at the receiver (in RF communication these all correspond to antennas). Using particle-based simulators, the channel's impulse response is obtained and mathematically modeled. These models are then used to determine interlink interference (ILI) and intersymbol interference (ISI). It is assumed that when the receiver has incomplete information regarding the system and the channel state, low complexity symbol detection methods are preferred since the receiver is small and simple. Thus, four detection algorithms are proposed-adaptive thresholding, practical zero forcing with channel models excluding/including the ILI and ISI, and Genie-aided zero forcing. The proposed algorithms are evaluated extensively using numerical and analytical evaluations.

We model biochemical signal transduction, based on a ligand-receptor binding mechanism, as a discrete-time finite-state Markov channel, which we call the binding in discrete time channel. We show how to obtain the capacity of this channel, for the case of binary output, binary channel state, and arbitrary finite input alphabets. We show that the capacity-achieving input distribution is identically and independently distributed. Furthermore, we show that feedback does not increase the capacity of this channel. We show how the capacity of the discrete-time channel approaches the capacity of Kabanov's Poisson channel, in the limit of short time steps and rapid ligand release.

In this work, we consider diffusion-based molecular communication timing channels. Three different timing channels are presented based on three different modulation techniques, i.e., i) modulation of the release timing of the information particles, ii) modulation on the time between two consecutive information particles of the same type, and iii) modulation on the time between two consecutive information particles of different types. We show that each channel can be represented as an additive noise channel, where the noise follows one of the subclasses of stable distributions. We provide expressions for the probability density function of the noise terms, and numerical evaluations for the probability density function and cumulative density function. We also show that the tails are longer than Gaussian distribution, as expected.

This paper proposes a novel design of reliable end-to-end molecular communication. In molecular communication proposed in this paper, source and destination bio-nanomachines exchange molecular packets through intermediate bio-nanomachines. A source bio-nanomachine forms a molecular packet and transmits the molecular packet into the environment. An intermediate bio-nanomachine detects a molecular packet and produces its copies. A destination bio-nanomachine, upon reception of a molecular packet, produces an acknowledgment molecular packet and transmits back to the source bio-nanomachine. Further, a source bio-nanomachine retransmits a molecular packet if no acknowledgment molecular packet is returned within a time-out period. In this paper, we develop an analytical framework to study propagation delay in the reliable end-to-end molecular communication proposed in this paper. We also show how the proposed molecular communication is biochemically implemented using ribonucleic acid (RNA) molecules.

In this paper, we propose an end-to-end channel model for molecular communication systems with metal-oxide sensors. In particular, we focus on the recently developed table top molecular communication platform. The system is separated into two parts: the propagation and the sensor detection. There is derived, based on this, a more realistic end-to-end channel model. However, since some of the coefficients in the derived models are unknown, we collect a great deal of experimental data to estimate these coefficients and evaluate how they change with respect to the different system parameters. Finally, a noise model is derived for the system to complete an end-to-end system model for the tabletop platform.

In this paper, we propose a novel design for molecular communication in which both the transmitter and the receiver have, in a 3-dimensional environment, multiple bulges (in RF communication this corresponds to antenna). The proposed system consists of a fluid medium, information molecules, a transmitter, and a receiver. We simulate the system with a one-shot signal to obtain the channel's finite impulse response. We then incorporate this result within our mathematical analysis to determine interference. Molecular communication has a great need for low complexity, hence, the receiver may have incomplete information regarding the system and the channel state. Thus, for the cases of limited information set at the receiver, we propose three detection algorithms, namely adaptive thresholding, practical zero forcing, and Genie-aided zero forcing.

Wave-based signals have been successful in reliably and efficiently transferring data between two or more well defined points (e.g., known location area). However, it is challenged when the transmitter is hidden and the receivers are absent. Essentially, the transmitter and the receivers have no location knowledge of each other. We demonstrate that unlike wave-based transmissions, the total molecular energy doesn't monotonically degrade as a function of time. This paper uses a bio-inspired method of communicating data from a hidden transmitter to a group of absent receivers. A specialized molecular communication system is designed, including how to embed vital location information in the structure of a heterogeneous biochemical molecule. Like message in a bottle, there is a growing probability of receiving the location message over a period of several years. The only caveat is that there is an initial delay of a few hours to days, depending on the proximity of the rescue team to the crash site. This will provide an attractive alternative to current wave-based communications for delay-tolerant crash recovery.

In molecular communication information is conveyed through chemical signals. In this work, we have considered a novel communication scheme where information is encoded in chemical barcodes, through use of persistent chemical tags. We have assumed that this information is already encoded in the environment, and we have devised a robotic platform for reading the chemical tag. We have performed many experiments to find the optimal encoding scheme and an algorithm for reading and decoding the chemically tagged information. We have demonstrated that chemical tags can be decoded using simple algorithms and inexpensive, off-the-shelf sensors. Finally, we have evaluated and presented the bit error rate performance of our devised algorithm.

In molecular communication information is transferred with the use of molecules. Molecular multiple-input multiple- output (MIMO) system with drift (positive velocity) at macro- scale will be presented and the improvement against single- input single-output (SISO) molecular communication systems will be verified via our testbed. Until now it was unclear whether MIMO techniques, which are extensively used in modern radio frequency (RF) communications, could be applied to molecular communication. In the demonstration, using our MIMO testbed we will show that we can achieve nearly 1.7 times higher data rate than SISO molecular communication systems. Moreover, signal-to-inter-link-interfeence metric for one-shot signal will be depicted for a given symbol duration.

Assuming a network of infinite extent, several researchers have analyzed small-cell networks using a Poisson point process (PPP) location model, leading to simple analytic expressions. The general assumption has been that these results apply to finite-area networks as well. However, do the results of infinite-area networks apply to finite-area networks? In this paper, we answer this question by obtaining an accurate approximation for the achievable signal-to-interference-plus-noise ratio (SINR) and user capacity in the downlink of a finite-area network with a fixed number of access points (APs). The APs are uniformly distributed within the area of interest. Our analysis shows that, crucially, the results of infinite-area networks are very different from those for finite-area networks of low-to-medium AP density. Comprehensive simulations are used to illustrate the accuracy of our analysis. For practical values of signal transmit powers and AP densities, the analytic expressions capture the behavior of the system well. As an added benefit, the formulations developed here can be used in parametric studies for network design. Here, the analysis is used to obtain the required number of APs to guarantee a desired target capacity in a finite-area network.

In this paper, we propose a realistic channel model for a table-top molecular communication platform that is capable for transmitting short text messages across a room. The observed system response for this experimental platform does not match the theoretical results in the literature. This is because many simplifying assumptions regarding the flow, the sensor, and environmental conditions, which were used in derivations of previous theoretical models do not hold in practice. Therefore, in this paper, based on experimental observations, theoretical models are modified to create more realistic channel models.

In this paper, we investigate information-theoretic scaling laws, independent from communication strategies, for point-to-point molecular communication, where it sends/receives information-encoded molecules between nanomachines. Since the Shannon capacity for this is still an open problem, we first derive an asymptotic order in a single coordinate, i.e., i) scaling time with constant number of molecules m and ii) scaling molecules with constant time t. For a single coordinate case, we show that the asymptotic scaling is logarithmic in either coordinate, i.e., Θ(log t) and Θ(log m), respectively. We also study asymptotic behavior of scaling in both time and molecules and show that, if molecules and time are proportional to each other, then the asymptotic scaling is linear, i.e., Θ(t) = Θ(m).

The articles in this special issue focus on the technologies and applications that support molecular, biological, and multiscale communication.

Recently, a tabletop molecular communication platform has been developed for transmitting short text messages across a room. The end-to-end system impulse response for this platform does not follow previously published theoretical works because of imperfect receiver, transmitter, and turbulent flows. Moreover, it is observed that this platform resembles a nonlinear system, which makes the rich body of theoretical work that has been developed by communication engineers not applicable to this platform. In this work, we first introduce corrections to the previous theoretical models of the end-to-end system impulse response based on the observed data from experimentation. Using the corrected impulse response models, we then formulate the nonlinearity of the system as noise and show that through simplifying assumptions it can be represented as Gaussian noise. Through formulating the system's nonlinearity as the output a linear system corrupted by noise, the rich toolbox of mathematical models of communication systems, most of which are based on linearity assumption, can be applied to this platform.

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.

In femtocell networks, large numbers of femtocell access points (FAPs) are deployed and integrated into a cellular network. In this paper, a novel architecture for femtocell networks is proposed, known as fractional cooperation. Using this method, connections from mobile users to multiple FAPs are permitted. This architecture is analogous to fractional cooperation in wireless relay networks. Analytical and simulation results are presented, which indicate that large gains are possible over conventional cellular-style architectures.

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.

In molecular communication, messages are conveyed in patterns of particles (e.g., arranged in time), which propagate from transmitter to receiver by means of Brownian motion. If there is drift from transmitter to receiver, the first arrival time of the particles has the Inverse Gaussian distribution, leading to the additive inverse Gaussian noise channel. In this paper, we give a closed-form upper bound on capacity for this channel when the maximum waiting time is constrained, building on previous work in which only the mean waiting time was constrained.

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.

In this letter, resource allocation is considered for large multi-source, multi-relay networks employing fractional cooperation, in which each potential relay only allocates a fraction of its resources to relaying. Using a Gaussian approximation, it is shown that the optimization can be posed as a linear program, where the relays use a demodulate-and-forward (DemF) strategy, and where the transmissions are protected by low-density parity-check (LDPC) codes. This is useful since existing optimization schemes for this problem are nonconvex.

Fractional cooperation is a decentralized, low-complexity wireless networking protocol in which nodes have the ability to dynamically select a fraction of its resources to commit to forwarding, and where sources may use more than one relay to convey information to the destination. In this paper, an implementation and a series of experiments are presented to demonstrate the practical performance and effectiveness of fractional cooperation. A low-complexity MAC layer protocol is used, which employs fractional cooperation using LT codes in the absence of central coordination. Experimental results from real-world trials are given, which show that this protocol can maintain a reasonable throughput when nodes are abruptly entering and leaving, making it ideal for a dynamically changing system, such as an ad-hoc network. The redundancy of information seen in the network makes this scheme robust to unfavourable channel conditions.

In a cooperative wireless network, there may be many potential relays within radio range of a source; similarly, there may be many potential sources seeking to use relays. Allocating these resources is a non-trivial optimization problem. In this paper, fractional cooperation is considered, where each potential relay only allocates a fraction of its resources to relaying. It is shown that linear programming can be used to optimally allocate resources in multi-source, multi-relay net- works, where the relays use a demodulate-and-forward (DemF) strategy, and where the transmissions are protected by low-density parity-check (LDPC) codes. Compared with existing optimization schemes, this method is particularly suitable for very large networks with numerous sources and relays. Simulation results are presented to demonstrate the performance of this scheme.

In fractional cooperation, many relays simultaneously assist the source, and each relay is responsible to relay only a fraction of the source transmission. In this paper, the problem of fractional cooperation is considered in the presence of multiple sources and multiple relays. In particular, optimization problems are formulated that can be used to allocate the relay resources between multiple sources to either minimize the energy consumed to achieve a given probability of error threshold, or minimize the maximum probability of error experienced by each source node.

In fractional cooperation, each available relay node selects a small fraction of the source's transmission to be relayed. In previous work, it was assumed that every node relayed the same number of source symbols, and large diversity order gains were observed. In this paper, a theoretical basis is developed for irregular fractional cooperation, in which each node relays a different number of symbols. A general expression of the system diversity order is derived. A bound is introduced on the system performance of fractional cooperation, known as the erasure channel bound. Distributions of diversity order using this bound are given when the fraction relayed by each user is random.

In this paper, an ordering result is given for Markov channels with respect to mutual information, under the assumption of an independent and identically distributed (i.i.d.) input distribution. For those Markov channels in which the capacity-achieving input distribution is i.i.d., this allows ordering of the channels by capacity. The complexity of analyzing general Markov channels is mitigated by this ordering, since it is possible to immediately determine that a wide class of channels, with different numbers of states, has a smaller mutual information than a given channel.

A simplified method of analysis and design based on the Bhattacharyya parameter (BP) in conjunction with the union bound and weight enumeration is presented for relay channels using coded cooperation. This method is particularly suitable for low-complexity relay systems employing demodulate-and-forward, focusing on the problems of relay selection and outage analysis. These applications are chosen to illustrate the use of the BP in scenarios where analytical solutions are otherwise unattainable. In terms of relay selection, it is shown that BP-based relay selection has essentially the same performance as density evolution, though with much lower complexity. It is further shown that BP-based relay selection can be applied to fractional cooperation, where each relay only forwards a fraction of the source codeword. In terms of analysis, it is shown that weight enumeration with BP can be used to provide a close approximate to the upper bound on the outage probability of fractional cooperation, again with much lower computational complexity than density evolution.

Relay systems have large and complex parameter spaces, which makes it difficult to determine the parameter region where the system achieves a given performance criterion, such as probability of frame error. In this paper, we show that the union bound (UB) and the Bhattacharyya parameter (BP) can be used for fast analysis of the parameter space when error-control coding is used. This is applicable when amplify-and-forward (AF) or demodulate-and-forward (DemF) are used. For a given code ensemble, the associated UB threshold is found and can be used to define the signal-to-noise region where a given frame error rate can be achieved. Using asymptotic results, the UB threshold can be used to specify the signal-to-noise ratio region where successful decoding can be achieved for large blocklength. In addition, the UB with BP can be used when fractional cooperation is used, where each relay only relays a fraction of the source codeword. This makes the UB with BP a valuable tool in the system design of relay networks.

Demodulate-and-forward (DmF) is an attractive approach when using cooperative diversity schemes in networks where only nodes with strict complexity constraints are allowed, such as sensor networks. In using DmF, the relay only demodulates, but does not decode, the received signal from the source node. Coding can be used at the relay to improve the performance over the relay-destination link. In unrelated work, relay selection has been shown to achieve full diversity order with low overhead by choosing the best relay node out of a pool of available relays to assist the source. A simple heuristic scheme for relay selection while using DmF is available, but this involves the exchange of channel parameters between the nodes, hence increasing the overhead. In this paper, we propose the use of the Bhattacharyya parameter (BP) to facilitate relay selection. The use of BP has the distinct advantage of incorporating the specific coding scheme used while retaining low computation load. As illustrated in our simulation results, the use of BP provides frame error rates quite similar to that obtained from exhaustive search. We should note that this BP-based relay selection scheme can also be applied to cooperation schemes where decoding is performed at the relay.

Owing to recent interest in sensor networks for military and security applications, studies of the security vulnerabilities of these networks are becoming increasingly important. In the present paper, the problem of estimating the topology of an adversarial sensor network is considered. The adversarial network is assumed to employ strong encryption, so that its transmitted packets are assumed to be unreadable by the observer. Thus, the algorithms are required to make use of the time correlations in channel uses by the adversarial network. Assuming the use of the MACA protocol, our algorithms are capable of estimating both the routes used by nodes in the adversarial sensor network, and as the identities of the nodes that are within each other's neighborhood (i.e., within radio range of each other), so that an attack could be designed for maximum effect. Results are presented which show that route estimation can be accomplished quickly using our algorithm, and that neighborhood estimation can be accomplished in a reasonable amount of time.

In this paper, two fixed per-information symbol complexity lossless source coding algorithms are modified for estimation and incremental LT decoding over piecewise stationary memoryless channels (PSMC's) with a bounded number of abrupt changes in channel statistics. In particular, as a class of PSMC's, binary symmetric channels are considered with a crossover probability that changes a bounded number of times with no repetitions in the statistics. Simulation results are given which illustrate the benefits of using our algorithms, both in terms of probability of error and in terms of redundancy.

LDPC codes are analyzed and optimized for a noncoherent block fading channel in which there is correlation between the blocks. This extends related work in the literature which considered independent blocks. Low-complexity estimation and estimation-decoding algorithms based on Kalman smoothing are developed, and density evolution is used to analyze and optimize the resulting code. Results indicate that significant gains can be realized by taking inter-block correlation into account, compared to architectures in which the blocks are assumed to be independent.

Wireless networks, and especially wireless sensor networks, have complexity and energy constraints, within which they must confront the challenging wireless fading environment. In this paper, fractional cooperation is introduced, which is shown to provide energy-efficient and low-complexity diversity gains for constant energy costs per bit throughout the network. To minimize complexity, cooperation is based on demodulate- and-forward, wherein the relay nodes encode demodulated, not decoded symbols. A scheme is presented for cooperative error- control coding in complexity-constrained networks, using low- density generator-matrix codes and repeat-accumulate codes, both chosen for being simple to encode, as well as for their easily adaptable rates. It is shown that these codes, coupled with fractional cooperation, are robust to system parameters and conditions, and introduce little added complexity at the receiver, while providing excellent performance.

This paper explores relay selection and selection diversity for coded cooperation in wireless sensor networks, with complexity constraints for the sensor nodes. In previous work, a relaying scheme based on repeat-accumulate (RA) codes was introduced, where it was assumed that the relay does not perform decoding and simply uses demodulated bits to form codewords. However, in a network setting with multiple potential relays where relays do not decode the source transmission, it is not obvious how to select the best relay. The optimal choice involves finding the best relay possibly using density evolution, but is quite complex and time-consuming. It is shown here that the mutual information of the equivalent relay channel, which is much simpler than using DE, is a good selection heuristic. With surprisingly poor performance when a naive selection scheme is used, the importance of a good relay selection scheme is emphasized.

Since the introduction of cooperative diversity, many different implementations have been proposed to increase the reliability and/or power efficiency of distributed networks via relaying. One simple and flexible scheme introduced is coded demodulate-and-forward, where the relay only demodulates, instead of decodes, the received data, to create and forward a new codeword to the destination. This reduces the complexity of hardware as well as the energy consumption by the relay. In this paper, we consider another flexible feature of the coded demodulate-and-forward scheme, where the relay uses only a fraction of its codeword to assist the source, and saves the rest of the codeword for transmitting its own information. Previous schemes have generally focused on all-or-nothing cooperation where a relay either contributes all its resources or none at all to the source. Depending on the channel conditions, improved diversity order of the source codeword can be achieved with some small loss in the relay's own transmission performance. Here we identify the necessary criterion for the source to achieve a diversity order of 2.

In previous work, an ordering result was given for the symbolwise probability of error using general Markov channels, under iterative decoding of LDPC codes. In this paper, the ordering result is extended to mutual information, under the assumption of an iid input distribution. For certain channels, in which the capacity-achieving input distribution is iid, this allows ordering of the channels by capacity. The complexity of analyzing general Markov channels is mitigated by this ordering, since it is possible to immediately determine that a wide class of channels, with different numbers of states, has a smaller mutual information than a given channel.

This paper presents a reduced-complexity approximate density evolution (DE) scheme for low-density parity-check (LDPC) codes in channels with memory in the form of a hidden Markov chain. This approximation is used to design degree sequences representing some of the best known LDPC code ensembles for the Gilbert-Elliott channel, and example optimizations are also given for other Markov channels. The problem of approximating the channel estimation is addressed by obtaining a specially constructed message-passing schedule in which the channel messages all approach their stable densities. It is shown that this new schedule is much easier to approximate than the standard schedule, but has the same ultimate performance in the limits of long block length and many decoding iterations. This result is extended to show that all message-passing schedules that satisfy mild conditions will have the same threshold under density evolution

A partial ordering on general finite-state Markov channels is given, which orders the channels in terms of probability of symbol error under iterative estimation decoding of a low-density parity-check (LDPC) code. This result is intended to mitigate the complexity of characterizing the performance of general finite-state Markov channels, which is difficult due to the large parameter space of this class of channel. An analysis tool, originally developed for the Gilbert-Elliott channel, is extended and generalized to general finite-state Markov channels. In doing so, an operator is introduced for combining finite-state Markov channels to create channels with larger state alphabets, which are then subject to the partial ordering. As a result, the probability of symbol error performance of finite-state Markov channels with different numbers of states and wide ranges of parameters can be directly compared. Several examples illustrating the use of the techniques are provided, focusing on binary finite-state Markov channels and Gaussian finite-state Markov channels. Furthermore, this result is used to order Gilbert-Elliott channels with different marginal state probabilities, which was left as an open problem by previous work.

Given limitations with current technology, nodes in a sensor network have stringent energy and complexity constraints. This paper presents a scheme for cooperative error-control coding, using rateless and low-density generator-matrix codes, for sensor networks. Assuming knowledge of the source-relay channel quality, we show that the proposed scheme achieves good performance and a good energy tradeoff despite low computational complexity. The scheme exploits the flexibility of rateless and LDGM codes to permit, depending on the channel conditions, independent, relay and cooperative modes of operation. As a motivating example, we analyze networks of two cooperating nodes communicating with a more sophisticated receiver. We also discuss the generalization of our framework to a multi-node system.

An iterative estimation and decoding technique for memoryless additive white Gaussian noise (AWGN) channels with several abrupt changes in noise variance during transmission of a codeword is introduced. A technique developed for source coding of piecewise-stationary memoryless sources is adapted to estimate the unknown channel transition points. Then, maximum-likelihood (ML) estimation is used to estimate the unknown noise variance in each segment This process is carried out on an estimated noise sequence of the currently hypothesized codeword. Simulations using turbo codes show performance almost as good as that of a receiver with perfect knowledge of the channel

This paper deals with the design and analysis of low-density parity-check (LDPC) codes for the Slepian-Wolf problem. The main contribution is a code design method based on a density evolution (DE) analysis for the cases where multiple LDPC codes are simultaneously decoded at the decoder. Good source codes are designed both for memoryless sources and sources with Markov memory. Further, simultaneous decoding is generalized to the case of source splitting, which allows non-corner points of the Slepian-Wolf region to be achieved even for sources with equiprobable marginal distributions

This paper derives an iterative receiver for noncoherent fading channels that exhibit block fading with correlation between blocks. Pilot symbols and Kalman smoothing are used in conjunction with sum-product decoding of LDPC codes to implement an iterative channel estimation and decoding structure. Density evolution is employed to analyze the performance of such a structure and to optimize the degree profile of LDPC codes. The resulting receiver performs significantly better than receivers in which channel estimation and decoding are carried out in a tandem (non-iterative) fashion

This paper proposes iterative estimation and decoding techniques for memoryless channels with a bounded number of abrupt changes in channel statistics. Specifically, the channel under consideration is a binary symmetric channel with a crossover probability that changes a bounded number of times during the transmission of a codeword; the channel state information to be estimated consists of the crossover probabilities of the different segments and the location(s) of the transition point(s). To estimate the transition points, a technique developed for source coding of piecewise-stationary memoryless sources is adapted; then the expectation-maximization algorithm is used to estimate the crossover probabilities. This segmentation/estimation is carried out on the error sequence of the currently hypothesized frame. Simulation results using turbo codes indicate that the proposed receiver performs almost as well as a receiver that has perfect knowledge of the channel.

Density evolution analysis of low-density parity-check (LDPC) codes in memoryless channels is extended to the Gilbert-Elliott (GE) channel, which is a special case of a large class of channels with hidden Markov memory. In a procedure referred to as estimation decoding, the sum-product algorithm (SPA) is used to perform LDPC decoding jointly with channel-state detection. Density evolution results show (and simulation results confirm) that such decoders provide a significantly enlarged region of successful decoding within the GE parameter space, compared with decoders that do not exploit the channel memory. By considering a variety of ways in which a GE channel may be degraded, it is shown how knowledge of the decoding behavior at a single point of the GE parameter space may be extended to a larger region within the space, thereby mitigating the large complexity needed in using density evolution to explore the parameter space point-by-point. Using the GE channel as a straightforward example, we conclude that analysis of estimation decoding for LDPC codes is feasible in channels with memory, and that such analysis shows large potential gains.

We present a reduced-complexity approximate density evolution scheme that is particularly suitable for Markov-modulated channels, based on the semiGaussian approximation. We propose a design algorithm whose complexity is comparable to the memoryless case, assuming unlimited precomputation is allowed. We also present degree sequences representing some of the best known codes in the GE channel which were designed using this technique. This design tool can be easily extended to more complicated Markov-modulated channels

This paper presents a density evolution analysis of the sum-product algorithm used for channel estimation and decoding of low density parity check (LDPC) codes on correlated and uncorrelated two-state block fading channels. The channels under consideration use binary symmetric channels and binary-input Gaussian channels as components, and the thresholds for regular LDPC codes on these channels are calculated. The analysis shows that for both correlated and uncorrelated block fading channels, the threshold increases with the memory length. If the memory length is fixed, introducing correlation between successive blocks increases the threshold; as the memory length increases, this effect diminishes