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In this paper, we propose a new model for indoor THz communication assisted by RIS. We conduct a realistic modeling of indoor obstacles and analyze their impact on performance. Order statistics are applied to calculate the cumulative distribution functions (CDFs) of distances from the transmitter to the selected RIS, i.e., the nearest RIS in the bounded indoor environment to the transmitter, and from the selected RIS to the receiver. We calculate the coverage probability (CP) as a function of RIS number, obstacle density, room size, and the transmitter's location. By comparing the numerical results obtained from the analytical expressions with Monte Carlo simulations, we verify the accuracy of our analysis. Through numerical results, it is observed that room size and obstacle density affect the CP in a significant way. However, by optimizing the transmitter's location and increasing the RIS number deployed in the room, the CP can be significantly improved (e.g., an increase of around 15% by optimizing the transmitter's location, and an increase of around 30% by increasing the RIS number deployed in the room)., Comment: 11 pages, 11 figures, submitted to IEEE Transactions on Wireless Communications

In this paper, we propose an online algorithm mspace for forecasting node features in temporal graphs, which captures spatial cross-correlation among different nodes as well as the temporal auto-correlation within a node. The algorithm can be used for both probabilistic and deterministic multi-step forecasting, making it applicable for estimation and generation tasks. Comparative evaluations against various baselines, including temporal graph neural network (TGNN) models and classical Kalman filters, demonstrate that mspace performs at par with the state-of-the-art and even surpasses them on some datasets. Importantly, mspace demonstrates consistent performance across datasets with varying training sizes, a notable advantage over TGNN models that require abundant training samples to effectively learn the spatiotemporal trends in the data. Therefore, employing mspace is advantageous in scenarios where the training sample availability is limited. Additionally, we establish theoretical bounds on multi-step forecasting error of mspace and show that it scales linearly with the number of forecast steps $q$ as $\mathcal{O}(q)$. For an asymptotically large number of nodes $n$, and timesteps $T$, the computational complexity of mspace grows linearly with both $n$, and $T$, i.e., $\mathcal{O}(nT)$, while its space complexity remains constant $\mathcal{O}(1)$. We compare the performance of various mspace variants against ten recent TGNN baselines and two classical baselines, ARIMA and the Kalman filter across ten real-world datasets. Additionally, we propose a technique to generate synthetic datasets to aid in evaluating node feature forecasting methods, with the potential to serve as a benchmark for future research. Lastly, we have investigate the interpretability of different mspace variants by analyzing model parameters alongside dataset characteristics to derive model and data-centric insights., Comment: 23 pages

This document aims to familiarize readers with temporal graph learning (TGL) through a concept-first approach. We have systematically presented vital concepts essential for understanding the workings of a TGL framework. In addition to qualitative explanations, we have incorporated mathematical formulations where applicable, enhancing the clarity of the text. Since TGL involves temporal and spatial learning, we introduce relevant learning architectures ranging from recurrent and convolutional neural networks to transformers and graph neural networks. We also discuss classical time series forecasting methods to inspire interpretable learning solutions for TGL., Comment: 19 pages, 47 equations

In this paper, we study the problem of graph compression with side information at the decoder. The focus is on the situation when an unlabelled graph (which is also referred to as a structure) is to be compressed or is available as side information. For correlated Erd\H{o}s-R\'enyi weighted random graphs, we give a precise characterization of the smallest rate at which a labelled graph or its structure can be compressed with aid of a correlated labelled graph or its structure at the decoder. We approach this problem by using the entropy-spectrum framework and establish some convergence results for conditional distributions involving structures, which play a key role in the construction of an optimal encoding and decoding scheme. Our proof essentially uses the fact that, in the considered correlated Erd\H{o}s-R\'enyi model, the structure retains most of the information about the labelled graph. Furthermore, we consider the case of unweighted graphs and present how the optimal decoding can be done using the notion of graph alignment., Comment: 21 pages, 2 figures, submitted to the IEEE Journal on Selected Areas in Information Theory

The stochastic block model (SBM) is extensively used to model networks in which users belong to certain communities. In recent years, the study of information-theoretic compression of such networks has gained attention, with works primarily focusing on lossless compression. In this work, we address the lossy compression of SBM graphs by characterizing the rate-distortion function under a Hamming distortion constraint. Specifically, we derive the conditional rate-distortion function of the SBM with community membership as side information. We approach this problem as the classical Wyner-Ziv lossy problem by minimising mutual information of the graph and its reconstruction conditioned on community labels. Lastly, we also derive the rate-distortion function of the Erd\H{o}s-R\'enyi (ER) random graph model., Comment: 9 pages, 1 figure, Accepted for presentation at Asilomar Conference on Signals, Systems, and Computers, 2023

Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their information-theoretic limit. Additionally, the lack of models for random generation of trees is very much felt in mathematical modeling of trees and graphs. In this paper, a number of existing tree generation models such as simply generated trees are discussed, and their information content is analysed by means of information theory and Shannon's entropy. Subsequently, a new model for generating trees based on practical appearances of trees is introduced, and an upper bound for its entropy is calculated. This model is based on selecting a random tree from possible spanning trees of graphs, which is what happens often in practice. Moving on to tree compression, we find approaches to universal tree compression of the discussed models. These approaches first transform a tree into a sequence of symbols, and then apply a dictionary-based compression method. Conditions for the universality of these method are then studied and analysed.

The Internet of Things (IoT) is an emerging next-generation technology in the fourth industrial revolution. In industrial IoT networks, sensing devices are largely deployed to monitor various types of physical processes. They are required to transmit the collected data in a timely manner to support real-time monitoring, control and automation. The timeliness of information is very important in such systems. Recently, an information-theoretic metric named the "value of information" (VoI) has been proposed to measure the usefulness of information. In this work, we consider an industrial IoT network with a set of heterogeneous sensing devices and an intelligent mobile entity. The concept of the value of information is applied to study a joint path planning and user scheduling optimisation problem. We aim to maximise the network-level VoI under mobility and communication constraints. We formulate this problem as a Markov decision process (MDP), and an efficient algorithm based on reinforcement learning is proposed to solve this problem. Through numerical results, we show that the proposed method is able to capture the usefulness of data from both time and space dimensions. By exploiting the correlation property of the data source, the proposed method is suitable for applications in resource-limited networks.

Routing is one of the critical and ongoing challenges in Wireless Sensor Networks. The main challenge has always been to have a routing protocol that reduces the communication overhead, hence saving the energy of the sensors in the network. Hierarchical routing protocols are known to be the most energy-efficient routing protocols for Wireless Sensor Networks. In this paper, a more generalized hierarchical routing protocol is introduced for Wireless Sensor Network, which is based on tree data structures. The clustering in the proposed protocol has the format of a general tree, which is constructed in an adaptive manner based on the distance of the sensors. Results show that the proposed tree-based protocol introduces a significant benefit in energy consumption and lifetime of the network over the existing hierarchical approaches.

We consider a multi-user two-ray ground reflection scenario with unknown distances between transmitter and receivers. By using two frequencies per user in parallel, we can mitigate possible destructive interference and ensure ultra-reliability with only very limited knowledge at the transmitter. In this work, we consider the problem of assigning two frequencies to each receiver in a multi-user communication system such that the average minimum receive power is maximized. In order to solve this problem, we introduce a generalization of the quadratic multiple knapsack problem to include heterogeneous profits and develop an algorithm to solve it. Compared to random frequency assignment, we report a gain of around 6 dB in numerical simulations., Comment: 8 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2206.13459

In this paper, we investigate the performance of a reconfigurable intelligent surface (RIS) assisted large-scale network by characterizing the coverage probability and the average achievable rate using stochastic geometry. Considering the spatial correlation between transmitters (TXs) and RISs, their locations are jointly modelled by a Gauss-Poisson process (GPP). Two association strategies, i.e., nearest association and fixed association, are both discussed. For the RIS-aided transmission, the signal power distribution with a direct link is approximated by a gamma random variable using a moment matching method, and the Laplace transform of the aggregate interference power is derived in closed form. Based on these expressions, we analyze the channel hardening effect in the RIS-assisted transmission, the coverage probability, and the average achievable rate of the typical user. We derive the coverage probability expressions for the fixed association strategy and the nearest association strategy in an interference-limited scenario in closed form. Numerical results are provided to validate the analysis and illustrate the effectiveness of RIS-assisted transmission with passive beamforming in improving the system performance. Furthermore, it is also unveiled that the system performance is independent of the density of TXs with the nearest association strategy in the interference-limited scenario.

Routing tables in ad hoc and wireless routing protocols can be represented using rooted trees. The constant need for communication and storage of these trees in routing protocols demands an efficient rooted tree coding algorithm. This efficiency is defined in terms of the average code length, and the optimality of the algorithm is measured by comparing the average code length with the entropy of the source. In this work, TreeExplorer is introduced as an easy-to-implement and nearly optimal algorithm for coding rooted tree structures. This method utilizes the number of leaves of the tree as an indicator for choosing the best method of coding. We show how TreeExplorer can improve existing routing protocols for ad hoc and wireless systems, which normally entails a significant communication overhead.

We consider a two-ray ground reflection scenario with unknown distance between transmitter and receiver. By utilizing two frequencies in parallel, we can mitigate possible destructive interference and ensure ultra-reliability with only very limited knowledge at the transmitter. In order to achieve this ultra-reliability, we optimize the frequency spacing such that the worst-case receive power is maximized. Additionally, we provide an algorithm to calculate the optimal frequency spacing. Besides the receive power, we also analyze the achievable rate and outage probability. It is shown that the frequency diversity scheme achieves a significant improvement in terms of reliability over using a single frequency. In particular, we demonstrate the effectiveness of the proposed approach by a numerical simulation of an unmanned aerial vehicle (UAV) flying above flat terrain., Comment: 15 pages, 13 figures

A novel Markovian network evolution model is introduced and analysed by means of information theory. It will be proved that the model, called Network Evolution Chain, is a stationary and ergodic stochastic process. Therefore, the Asymptotic Equipartition Property can be applied to it. The model's entropy rate and typical sequences are also explored. Extracting particular information from the network and methods to simulate network evolution in the continuous time domain are discussed. Additionally, the Erdos-Renyi Network Evolution Chain is introduced as a subset of our model with the additional property of its stationary distribution matching the Erdos-Renyi random graph model. The stationary distributions of nodes and graphs are calculated for this subset alongside its entropy rate. The simulation results at the end of the paper back up the proved theorems and calculated values.

Due to dependence between codeword elements, index modulation (IM) and related modulation techniques struggle to provide simple solutions for practical problems such as Gray coding between information bits and constellation points; and low-complexity log-likelihood ratio (LLR) calculations for channel-encoded information bits. In this paper, we show that a modulation technique based on a simple maximum distance separable (MDS) code, in other words, MDS modulation, can provide simple yet effective solutions to these problems, rendering the MDS techniques more beneficial in the presence of coding. We also compare the coded error performance of the MDS methods with that of the IM methods and demonstrate that MDS modulation outperforms IM., Comment: 5 Pages, 3 Figures

In this paper, we investigate the performance of an intelligent omni-surface (IOS) assisted downlink non-orthogonal multiple access (NOMA) network with phase quantization errors and channel estimation errors, where the channels related to the IOS are spatially correlated. First, upper bounds on the average achievable rates of the two users are derived. Then, channel hardening is shown to occur in the proposed system, based on which we derive approximations of the average achievable rates of the two users. The analytical results illustrate that the proposed upper bound and approximation on the average achievable rates are asymptotically equivalent in the number of elements. Furthermore, it is proved that the asymptotic equivalence also holds for the average achievable rates with correlated and uncorrelated channels. Additionally, we extend the analysis by evaluating the average achievable rates for IOS assisted orthogonal multiple access (OMA) and IOS assisted multi-user NOMA scenarios. Simulation results corroborate the theoretical analysis and demonstrate that: i) low-precision elements with only two-bit phase adjustment can achieve the performance close to the ideal continuous phase shifting scheme; ii) The average achievable rates with correlated channels and uncorrelated channels are asymptotically equivalent in the number of elements; iii) IOS-assisted NOMA does not always perform better than OMA due to the reconfigurability of IOS in different time slots.

In this paper, we propose two novel modulation concepts based on a simple maximum distance separable (MDS) code { and show that these concepts can achieve better error performance than index modulation (IM) and related schemes.} In the first concept, we use amplitude and phase levels to form a simple MDS code, whereas, in the second one, in-phase and quadrature components of codeword elements are used to construct the MDS code. We depict practical schemes for using the proposed concepts with orthogonal frequency division multiplexing (OFDM). We analyze the performance in terms of the minimum Euclidean distance and bit error rate. We also show that the proposed techniques exhibit desirable properties such as efficient low-complexity detection, very simple bits-to-symbols, and symbols-to-bits mappings, and a better error performance when compared to the OFDM-IM and related schemes. More importantly, contrary to the vast majority of IM studies that focus on showing the superiority of the IM techniques against conventional modulation techniques, we show that modulation concepts based on a well-known MDS code can achieve better error performance than the IM and related schemes while exhibiting a structure as simple as these schemes., Comment: Submitted for publication in IEEE

We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in $[0,1]$ that connect if they are within the connection range $r\in[0,1]$. We provide bounds on the number of possible structures which give universal upper bounds on the structural entropy that hold for any $n$, $r$ and distribution of the node locations. For fixed $r$, the number of structures is $\Theta(a^{2n})$ with $a=a(r)=2 \cos{\left(\frac{\pi}{\lceil 1/r \rceil+2}\right)}$, and therefore the structural entropy is upper bounded by $2n\log_2 a(r) + O(1)$. For large $n$, we derive bounds on the structural entropy normalized by $n$, and evaluate them for independent and uniformly distributed node locations. When the connection range $r_n$ is $O(1/n)$, the obtained upper bound is given in terms of a function that increases with $n r_n$ and asymptotically attains $2$ bits per node. If the connection range is bounded away from zero and one, the upper and lower bounds decrease linearly with $r$, as $2(1-r)$ and $(1-r)\log_2 e$, respectively. When $r_n$ is vanishing but dominates $1/n$ (e.g., $r_n \propto \ln n / n$), the normalized entropy is between $\log_2 e \approx 1.44$ and $2$ bits per node. We also give a simple encoding scheme for random structures that requires $2$ bits per node. The upper bounds in this paper easily extend to the entropy of the labeled random graph model, since this is given by the structural entropy plus a term that accounts for all the permutations of node labels that are possible for a given structure, which is no larger than $\log_2(n!) = n \log_2 n - n + O(\log_2 n)$., Comment: 44 pages, 9 figures; revised some of results; significant additional results included

A novel compression scheme for compressing the outcome of $n$ independent Bernoulli trials is introduced and analysed. The resulting algorithm, BernoulliZip, is a fast and near-optimal method to produce prefix codes for a Bernoulli process. BernoulliZip's main principle is to first represent the number of 1s in the sequence and then specify the sequence. The application of BernoulliZip on compressing Erdos-Renyi graphs is explored., Comment: Submitted to ITW 2021

This article investigates a novel electrophoretic molecular communication mechanism that utilizes a time-varying electric field, which induces time-varying molecule velocities and in turn improves communication performance. For a sinusoidal field, we specify favorable signal parameters (e.g., phase and frequency) that yield excellent communication link performance. We also analytically derive an optimized field function by formulating an appropriate cost function and solving the Euler-Lagrange equation. In our setup, the field strength is proportional to the molecular velocity; we verify this assumption by solving the Basset-Boussinesq-Oseen equation for a given time-varying electric field (forcing function) and examining its implications for practical physical parameterizations of the system. Our analysis and Monte-Carlo simulation results demonstrate that the proposed time-varying approach can significantly increase the number of information-carrying molecules expected to be observed at the receiver and reduce the bit-error probability compared to the constant field benchmark., Comment: 19 pages, 6 figures

In this paper, a general framework is formalised to characterise the value of information (VoI) in hidden Markov models. Specifically, the VoI is defined as the mutual information between the current, unobserved status at the source and a sequence of observed measurements at the receiver, which can be interpreted as the reduction in the uncertainty of the current status given that we have noisy past observations of a hidden Markov process. We explore the VoI in the context of the noisy Ornstein-Uhlenbeck process and derive its closed-form expressions. Moreover, we investigate the effect of different sampling policies on VoI, deriving simplified expressions in different noise regimes and analysing statistical properties of the VoI in the worst case. We also study the optimal sampling policy to maximise the average information value under the sampling rate constraint. In simulations, the validity of theoretical results is verified, and the performance of VoI in Markov and hidden Markov models is also analysed. Numerical results further illustrate that the proposed VoI framework can support timely transmission in status update systems, and it can also capture the correlation properties of the underlying random process and the noise in the transmission environment., Comment: 14 pages, 11 figures

In this paper, we propose a novel modulation concept which we call \emph{index and composition modulation (ICM)}. In the proposed concept, we use indices of active/deactive codeword elements and compositions of an integer to encode information. In this regard, we first determine the activated codeword elements, then we exploit energy levels of these elements to identify the compositions. We depict a practical scheme for using ICM with orthogonal frequency division multiplexing (OFDM) and show that OFDM with ICM (OFDM-ICM) can enhance the spectral efficiency (SE) and error performance of OFDM-IM. We design an efficient low-complexity detector for the proposed technique. Moreover, we analyze the error and SE performance of the OFDM-ICM technique and show that it is capable of outperforming existing OFDM benchmarks in terms of error and SE performance., Comment: 5 pages, 4 figures. arXiv admin note: text overlap with arXiv:2006.14400

We analyse the performance of a communication link assisted by an intelligent reflective surface (IRS) positioned in the far field of both the source and the destination. A direct link between the transmitting and receiving devices is assumed to exist. Perfect and imperfect phase adjustments at the IRS are considered. For the perfect phase configuration, we derive an approximate expression for the outage probability in closed form. For the imperfect phase configuration, we assume that each element of the IRS has a one-bit phase shifter (0{\deg}, 180{\deg}) and an expression for the outage probability is obtained in the form of an integral. Our formulation admits an exact asymptotic (high SNR) analysis, from which we obtain the diversity orders for systems with and without phase errors. We show these are N + 1 and (N + 3)/2, respectively. Numerical results confirm the theoretical analysis and verify that the reported results are more accurate than methods based on the central limit theorem (CLT)., Comment: 6 pages, 3 figures. Accepted in 2020 IEEE GLOBECOM

In this paper, a general value of information (VoI) framework is formalised for latent variable models. In particular, the mutual information between the current status at the source node and the observed noisy measurements at the destination node is used to evaluate the information value, which gives the theoretical interpretation of the reduction in uncertainty in the current status given that we have measurements of the latent process. Moreover, the VoI expression for a hidden Markov model is obtained in this setting. Numerical results are provided to show the relationship between the VoI and the traditional age of information (AoI) metric, and the VoI of Markov and hidden Markov models are analysed for the particular case when the latent process is an Ornstein-Uhlenbeck process. While the contributions of this work are theoretical, the proposed VoI framework is general and useful in designing wireless systems that support timely, but noisy, status updates in the physical world., Comment: 6 pages, 7 figures

We analyze the outage probability of an intelligent reflecting surface (IRS)-assisted communication network. A tight upper bound on the outage probability is formulated based on the Chernoff inequality. Furthermore, through an exact asymptotic (a large number of reflecting elements) analysis based on a saddlepoint approximation, we derive closed-form expressions of the outage probability for systems with and without a direct link and obtain the corresponding diversity orders. Simulation results corroborate our theoretical analysis and show the inaccuracies inherent in using the central limit theorem (CLT) to analyze system performance. Our analysis is accurate even for a small number of IRS elements in the high signal-to-noise ratio (SNR) regime., Comment: 5 pages, 2 figures

We present a flexible family of 3D mobility models suitable for unmanned aerial vehicles (UAV). Based on stochastic differential equations, the models offer a unique property of explicitly incorporating the mobility control mechanism and environmental perturbation, while enabling tractable steady state solutions for properties such as position and connectivity. Specifically, motivated by UAV flight data, for a symmetric mobility model with an arbitrary control mechanism, we derive the steady state distribution of the distance from the target position. We provide closed form expressions for the special cases of the Ornstein-Uhlenbeck (OU) process and on-off control (OC). We extend the model to incorporate imperfect positioning and asymmetric control. For a practically relevant scenario of partial symmetry (such as in the x-y plane), we present steady state position results for the OU control. Building on these results, we derive UAV connectivity probability results based on a SNR criterion in a Rayleigh fading environment., Comment: 6 pages, 6 figures, accepted for publication at IEEE PIMRC 2020

In this paper, we propose novel modulation concepts that we call weak composition modulation (WCM) and composition modulation (CM). We use weak and strict compositions of an integer to form codewords of WCM and CM, respectively. For the proposed schemes, we depict a practical model using orthogonal frequency division multiplexing (OFDM). We also analyze the error performance of the proposed schemes. It is shown that the proposed schemes are capable of outperforming conventional OFDM and OFDM with index modulation (OFDM-IM) in terms of error performance., Comment: 5 pages, 2 figures

In this paper, we propose a novel orthogonal frequency division multiplexing with index modulation (OFDM-IM) scheme, which we call Q-ary multi-mode OFDM-IM (Q-MM-OFDM-IM). In the proposed scheme, Q disjoint M-ary constellations are used repeatedly on each subcarrier, and a maximum-distance separable code is applied to the indices of these constellations to achieve the highest number of index symbols. A low-complexity subcarrier-wise detection is shown possible for the proposed scheme. Spectral efficiency (SE) and the error rate performance of the proposed scheme are further analyzed. It is shown that the proposed scheme exhibits a very flexible structure that is capable of encompassing conventional OFDM as a special case. It is also shown that the proposed scheme is capable of considerably outperforming the other OFDM-IM schemes and conventional OFDM in terms of error and SE performance while preserving a low-complexity structure., Comment: 5 pages, 2 figures

In this paper, we propose an enhanced Huffman coded orthogonal frequency-division multiplexing with index modulation (EHC-OFDM-IM) scheme. The proposed scheme is capable of utilizing all legitimate subcarrier activation patterns (SAPs) and adapting the bijective mapping relation between SAPs and leaves on a given Huffman tree according to channel state information (CSI). As a result, a dynamic codebook update mechanism is obtained, which can provide more reliable transmissions. We take the average block error rate (BLER) as the performance evaluation metric and approximate it in closed form when the transmit power allocated to each subcarrier is independent of channel states. Also, we propose two CSI-based power allocation schemes with different requirements for computational complexity to further improve the error performance. Subsequently, we carry out numerical simulations to corroborate the error performance analysis and the proposed dynamic power allocation schemes. By studying the numerical results, we find that the depth of the Huffman tree has a significant impact on the error performance when the SAP-to-leaf mapping relation is optimized based on CSI. Meanwhile, through numerical results, we also discuss the trade-off between error performance and data transmission rate and investigate the impacts of imperfect CSI on the error performance of EHC-OFDM-IM.

In this paper, we derive closed-form expressions for significant statistical properties of the link signal-to-noise ratio (SNR) and the separation distance in mobile ad hoc networks subject to Ornstein-Uhlenbeck (OU) mobility and Rayleigh fading. In these systems, the SNR is a critical parameter as it directly influences link performance. In the absence of signal fading, the distribution of the link SNR depends exclusively on the squared distance between nodes, which is governed by the mobility model. In our analysis, nodes move randomly according to an Ornstein-Uhlenbeck process, using one tuning parameter to control the temporal dependency in the mobility pattern. We derive a complete statistical description of the squared distance and show that it forms a stationary Markov process. Then, we compute closed-form expressions for the probability density function (pdf), the cumulative distribution function (cdf), the bivariate pdf, and the bivariate cdf of the link SNR. Next, we introduce small-scale fading, modelled by a Rayleigh random variable, and evaluate the pdf of the link SNR for rational path loss exponents. The validity of our theoretical analysis is verified by extensive simulation studies. The results presented in this work can be used to quantify link uncertainty and evaluate stability in mobile ad hoc wireless systems.

In this paper, a novel modulation scheme called set partition modulation (SPM) is proposed. In this scheme, set partitioning and ordered subsets in the set partitions are used to form codewords. We define different SPM variants and depict a practical model for using SPM with orthogonal frequency division multiplexing (OFDM). For the OFDM-SPM schemes, different constellations are used to distinguish between different subsets in a set partition. To achieve good distance properties as well as better error performance for the OFDM-SPM codewords, we define a codebook selection problem and formulate such a problem as a clique problem in graph theory. In this regard, we propose a fast and efficient codebook selection algorithm. We analyze error and achievable rate performance of the proposed schemes and provide asymptotic results for the performance. It is shown that the proposed SPM variants are general schemes, which encompass multi-mode OFDM with index modulation (MM-OFDM-IM) and dual-mode OFDM with index modulation (DM-OFDM-IM) as special cases. It is also shown that OFDM-SPM schemes are capable of exhibiting better error performance and improved achievable rate than conventional OFDM, OFDM-IM, DM-OFDM-IM, and MM-OFDM-IM., Comment: 13 pages, 7 figures, journal paper

Assume the communication between a source and a destination is supported by a large reflecting surface (LRS), which consists of an array of reflector elements with adjustable reflection phases. By knowing the phase shifts induced by the composite propagation channels through the LRS, the phases of the reflectors can be configured such that the signals combine coherently at the destination, which improves the communication performance. However, perfect phase estimation or high-precision configuration of the reflection phases is unfeasible. In this paper, we study the transmission through an LRS with phase errors that have a generic distribution. We show that the LRS-based composite channel is equivalent to a point-to-point Nakagami fading channel. This equivalent representation allows for theoretical analysis of the performance and can help the system designer study the interplay between performance, the distribution of phase errors, and the number of reflectors. Numerical evaluation of the error probability for a limited number of reflectors confirms the theoretical prediction and shows that the performance is remarkably robust against the phase errors., Comment: 5 pages, 2 figures

In this paper, we consider the problem of reducing the bit error rate of flash-based solid state drives (SSDs) when cells are subject to inter-cell interference (ICI). By observing that the outputs of adjacent victim cells can be correlated due to common aggressors, we propose a novel channel model to accurately represent the true flash channel. This model, equivalent to a finite-state Markov channel model, allows the use of the sum-product algorithm to calculate more accurate posterior distributions of individual cell inputs given the joint outputs of victim cells. These posteriors can be easily mapped to the log-likelihood ratios that are passed as inputs to the soft LDPC decoder. When the output is available with high precision, our simulation showed that a significant reduction in the bit-error rate can be obtained, reaching $99.99\%$ reduction compared to current methods, when the diagonal coupling is very strong. In the realistic case of low-precision output, our scheme provides less impressive improvements due to information loss in the process of quantization. To improve the performance of the new detector in the quantized case, we propose a new iterative scheme that alternates multiple times between the detector and the decoder. Our simulations showed that the iterative scheme can significantly improve the bit error rate even in the quantized case., Comment: Submitteed To Transactions on Communications

The problem of designing bit-to-pattern mappings and power allocation schemes for orthogonal frequency-division multiplexing (OFDM) systems that employ subcarrier index modulation (IM) is considered. We assume the binary source conveys a stream of independent, uniformly distributed bits to the pattern mapper, which introduces a constraint on the pattern transmission probability distribution that can be quantified using a binary tree formalism. Under this constraint, we undertake the task of maximizing the achievable rate subject to the availability of channel knowledge at the transmitter. The optimization variables are the pattern probability distribution (i.e., the bit-to-pattern mapping) and the transmit powers allocated to active subcarriers. To solve the problem, we first consider the relaxed problem where pattern probabilities are allowed to take any values in the interval [0,1] subject to a sum probability constraint. We develop (approximately) optimal solutions to the relaxed problem by using new bounds and asymptotic results, and then use a novel heuristic algorithm to project the relaxed solution onto a point in the feasible set of the constrained problem. Numerical analysis shows that this approach is capable of achieving the maximum mutual information for the relaxed problem in low and high-SNR regimes and offers noticeable benefits in terms of achievable rate relative to a conventional OFDM-IM benchmark., Comment: 18 pages, 16 figures, 2 tables

The performance of mobile ad hoc networks in general and that of the routing algorithm, in particular, can be heavily affected by the intrinsic dynamic nature of the underlying topology. In this paper, we build a new analytical/numerical framework that characterizes nodes' mobility and the evolution of links between them. This formulation is based on a stationary Markov chain representation of link connectivity. The existence of a link between two nodes depends on their distance, which is governed by the mobility model. In our analysis, nodes move randomly according to an Ornstein-Uhlenbeck process using one tuning parameter to obtain different levels of randomness in the mobility pattern. Finally, we propose an entropy-rate-based metric that quantifies link uncertainty and evaluates its stability. Numerical results show that the proposed approach can accurately reflect the random mobility in the network and fully captures the link dynamics. It may thus be considered a valuable performance metric for the evaluation of the link stability and connectivity in these networks., Comment: 6 pages, 4 figures, Submitted to IEEE International Conference on Communications 2019

In this paper, we present a detailed framework to analyze the evolution of the random topology of a time-varying wireless network via the information theoretic notion of entropy rate. We consider a propagation channel varying over time with random node positions in a closed space and Rayleigh fading affecting the connections between nodes. The existence of an edge between two nodes at given locations is modeled by a Markov chain, enabling memory effects in network dynamics. We then derive a lower and an upper bound on the entropy rate of the spatiotemporal network. The entropy rate measures the shortest per-step description of the stationary stochastic process defining the state of the wireless system and depends both on the maximum Doppler shift and the path loss exponent. It characterizes the topological uncertainty of the wireless network and quantifies how quickly the underlying topology is varying with time., Comment: 6 pages, 6 figures, IEEE Global Communications Conference (GLOBECOM), in press, 2018

Unmanned aerial vehicles (UAVs) have been undergoing fast development for providing broader signal coverage and more extensive surveillance capabilities in military and civilian applications. Due to the broadcast nature of the wireless signal and the openness of the space, UAV eavesdroppers (UEDs) pose a potential threat to ground communications. In this paper, we consider the communications of a legitimate ground link in the presence of friendly jamming and UEDs within a finite area of space. The spatial distribution of the UEDs obeying a uniform binomial point process (BPP) is used to characterize the randomness of the UEDs. The ground link is assumed to experience log-distance path loss and Rayleigh fading, while free space path loss with/without the averaged excess path loss due to the environment is used for the air-to-ground/air-to-air links. A piecewise function is proposed to approximate the line-of-sight (LoS) probability for the air-to-ground links, which provides a better approximation than using the existing sigmoid-based fitting. The analytical expression for the secure connection probability (SCP) of the legitimate ground link in the presence of non-colluding UEDs is derived. The analysis reveals some useful trends in the SCP as a function of the transmit signal to jamming power ratio, the location of the UAV jammer, and the height of UAVs.

We propose a self-organization scheme for cost-effective and load-balanced routing in multi-hop networks. To avoid overloading nodes that provide favourable routing conditions, we assign each node with a cost function that penalizes high loads. Thus, finding routes to sink nodes is formulated as an optimization problem in which the global objective function strikes a balance between route costs and node loads. We apply belief propagation (its min-sum version) to solve the network optimization problem and obtain a distributed algorithm whereby the nodes collectively discover globally optimal routes by performing low-complexity computations and exchanging messages with their neighbours. We prove that the proposed method converges to the global optimum after a finite number of local exchanges of messages. Finally, we demonstrate numerically our framework's efficacy in balancing the node loads and study the trade-off between load reduction and total cost minimization.

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random topology, properties (e.g., connectedness), or Shannon entropy as a measure of the graph's topological uncertainty (or information content). Moreover, the distribution is also relevant for determining average network performance or designing protocols. However, a major impediment in deducing the graph distribution is that it requires the joint probability distribution of the $n(n-1)/2$ distances between $n$ nodes randomly distributed in a bounded domain. As no such result exists in the literature, we make progress by obtaining the joint distribution of the distances between three nodes confined in a disk in $\mathbb{R}^2$. This enables the calculation of the probability distribution and entropy of a three-node graph. For arbitrary $n$, we derive a series of upper bounds on the graph entropy; in particular, the bound involving the entropy of a three-node graph is tighter than the existing bound which assumes distances are independent. Finally, we provide numerical results on graph connectedness and the tightness of the derived entropy bounds., Comment: submitted to the IEEE International Symposium on Information Theory 2018

In this paper, we propose a power allocation strategy for the adaptive orthogonal frequency-division multiplexing (OFDM) index modulation (IM) in cooperative networks. The allocation strategy is based on the Karush-Kuhn-Tucker (KKT) conditions, and aims at maximizing the average network capacity according to the instantaneous channel state information (CSI). As the transmit power at source and relay is constrained separately, we can thus formulate an optimization problem by allocating power to active subcarriers. Compared to the conventional uniform power allocation strategy, the proposed dynamic strategy can lead to a higher average network capacity, especially in the low signal-to-noise ratio (SNR) region. The analysis is also verified by numerical results produced by Monte Carlo simulations. By applying the proposed power allocation strategy, the efficiency of adaptive OFDM IM can be enhanced in practice, which paves the way for its implementation in the future, especially for cell-edge communications.

In this paper, we analyze the outage performance of two multicarrier relay selection schemes, i.e. bulk and per-subcarrier selections, for two-hop orthogonal frequency-division multiplexing (OFDM) systems. To provide a comprehensive analysis, three forwarding protocols: decode-and-forward (DF), fixed-gain (FG) amplify-and-forward (AF) and variable-gain (VG) AF relay systems are considered. We obtain closed-form approximations for the outage probability and closed-form expressions for the asymptotic outage probability in the high signal-to-noise ratio (SNR) region for all cases. Our analysis is verified by Monte Carlo simulations, and provides an analytical framework for multicarrier systems with relay selection.

In this paper, we propose a full-duplex orthogonal frequency-division multiplexing (OFDM) device-to-device (D2D) system in two-hop networks, where multiple full-duplex decode-and-forward (DF) relays assist the transmission from D2D user equipment (DUE) transmitter to DUE receiver. By such a transmission mechanism, the signal transmitted by the DUE transmitter does not need to go through a base station (BS). Meanwhile, due to the adoption of underlay D2D communication protocol, power control mechanisms are thereby necessary to be applied to mitigate the interference to conventional cellular communications. Based on these considerations, we analyze the outage performance of the proposed system, and derive the exact expressions of outage probabilities when bulk and per-subcarrier relay selection criteria are applied. Furthermore, closed-form expressions of outage probabilities are also obtained for special cases when the instantaneous channel state information (CSI) between BS and cellular user equipments (CUEs) is not accessible, so that a static power control mechanism is applied. Subsequently, we also investigate the outage performance optimization problem by coordinating transmit power among DUE transmitter and relays, and provide a suboptimal solution, which is capable of improving the outage performance. All analysis is substantiated by numerical results provided by Monte Carlo simulations. The analytical and numerical results demonstrated in this paper can provide an insight into the full-duplex relay-assisted OFDM D2D systems, and serve as a guideline for its implementation in next generation networks.

In this paper, we analyze the outage performance of different multicarrier relay selection schemes for two-hop orthogonal frequency-division multiplexing (OFDM) systems in a Poisson field of relays. In particular, special emphasis is placed on decode-and-forward (DF) relay systems, equipped with bulk and per-subcarrier selection schemes, respectively. The exact expressions for outage probability are derived in integrals for general cases. In addition, asymptotic expressions for outage probability in the high signal-to-noise ratio (SNR) region in the finite circle relay distribution region are determined in closed forms for both relay selection schemes. Also, the outage probabilities for free space in the infinite relay distribution region are derived in closed forms. Meanwhile, a series of important properties related to cooperative systems in random networks are investigated, including diversity, outage probability ratio of two selection schemes and optimization of the number of subcarriers in terms of system throughput. All analysis is numerically verified by simulations. Finally, a framework for analyzing the outage performance of OFDM systems with spatially random relays is constructed, which can be easily modified to analyze other similar cases with different forwarding protocols, location distributions and/or channel conditions.

The quantum enhanced classical sensor network consists of $K$ clusters of $N_e$ entangled quantum states that have been trialled $r$ times, each feeding into a classical estimation process. Previous literature has shown that each cluster can {ideally} achieve an estimation variance of $1/N_e^2r$ for sufficient $r$. We begin by deriving the optimal values for the minimum mean squared error of this quantum enhanced classical system. We then show that if noise is \emph{absent} in the classical estimation process, the mean estimation error will decay like $\Omega(1/KN_e^2r)$. However, when noise is \emph{present} we find that the mean estimation error will decay like $\Omega(1/K)$, so that \emph{all} the sensing gains obtained from the individual quantum clusters will be lost.

We show that the von Neumann entropy (from herein referred to as the von Neumann index) of a graph's trace normalized combinatorial Laplacian provides structural information about the level of centralization across a graph. This is done by considering the Theil index, which is an established statistical measure used to determine levels of inequality across a system of `agents', e.g., income levels across a population. Here, we establish a Theil index for graphs, which provides us with a macroscopic measure of graph centralization. Concretely, we show that the von Neumann index can be used to bound the graph's Theil index, and thus we provide a direct characterization of graph centralization via the von Neumann index. Because of the algebraic similarities between the bound and the Theil index, we call the bound the von Neumann Theil index. %From an information theoretic perspective, the von Neumann Theil index describes the mutual information between the quantum state corresponding to a graph and the maximally mixed state (which corresponds to the complete graph). We elucidate our ideas by providing examples and a discussion of different $n=7$ vertex graphs. We also discuss how the von Neumann Theil index provides a more comprehensive measure of centralization when compared to traditional centralization measures, and when compared to the graph's classical Theil index. This is because it more accurately accounts for macro-structural changes that occur from micro-structural changes in the graph (e.g., the removal of a vertex). Finally, we provide future direction, showing that the von Neumann Theil index can be generalized by considering the R\'enyi entropy. We then show that this generalization can be used to bound the negative logarithm of the graph's Jain fairness index.

This paper considers secrecy enhancement mechanisms in visible light communication (VLC) systems with spatially distributed passive eavesdroppers (EDs) under the assumption that there are multiple LED transmitters and one legitimate receiver (UE). Based on certain amplitude constraints, we propose an optimal beamforming scheme to optimize secrecy performance. Contrary to the case where null-steering is made possible by using knowledge of the ED locations, we show that the optimal solution when only statistical information about ED locations is available directs the transmission along a particular eigenmode related to the intensity of the ED process and the intended channel. Then, a sub-optimal LED selection scheme is provided to reduce the secrecy outage probability (SOP). An approximate closed-form for the SOP is derived by using secrecy capacity bounds. All analysis is numerically verified by Monte Carlo simulations. The analysis shows that the optimal beamformer yields superior performance to LED selection. However, LED selection is still a highly efficient suboptimal scheme due to the complexity associated with the use of multiple transmitters in the full beamforming approach. These performance trends and exact relations between system parameters can be used to develop a secure VLC system in the presence of randomly distributed EDs., Comment: 27 pages

We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly in space and links formed independently between pairs of nodes with probability given by a specified function (the "pair connection function") of their mutual distance. We consider the general case where randomness arises in node positions as well as pairwise connections (i.e., for a given pair distance, the corresponding edge state is a random variable). Classical random geometric graph and exponential graph models can be recovered in certain limits. We derive a simple bound for the entropy of a spatial network ensemble and calculate the conditional entropy of an ensemble given the node location distribution for hard and soft (probabilistic) pair connection functions. Under this formalism, we derive the connection function that yields maximum entropy under general constraints. Finally, we apply our analytical framework to study two practical examples: ad hoc wireless networks and the US flight network. Through the study of these examples, we illustrate that both exhibit properties that are indicative of nearly maximally entropic ensembles., Comment: 7 pages, 4 figures

In this paper, we propose an adaptive orthogonal frequency-division multiplexing (OFDM) index modulation (IM) scheme for two-hop relay networks. In contrast to the traditional OFDM IM scheme with a deterministic and fixed mapping scheme, in this proposed adaptive OFDM IM scheme, the mapping schemes between a bit stream and indices of active subcarriers for the first and second hops are adaptively selected by a certain criterion. As a result, the active subcarriers for the same bit stream in the first and second hops can be varied in order to combat slow frequency-selective fading. In this way, the system reliability can be enhanced. Additionally, considering the fact that a relay device is normally a simple node, which may not always be able to perform mapping scheme selection due to limited processing capability, we also propose an alternative adaptive methodology in which the mapping scheme selection is only performed at the source and the relay will simply utilize the selected mapping scheme without changing it. The analyses of average outage probability, network capacity and symbol error rate (SER) are given in closed form for decode-and-forward (DF) relaying networks and are substantiated by numerical results generated by Monte Carlo simulations., Comment: 30 pages

In a wide range of complex networks, the links between the nodes are temporal and may sporadically appear and disappear. This temporality is fundamental to analyze the formation of paths within such networks. Moreover, the presence of the links between the nodes is a random process induced by nature in many real-world networks. In this paper, we study random temporal networks at a microscopic level and formulate the \emph{probability of accessibility} from a node \emph{i} to a node \emph{j} after a certain number of discrete time units $T$. While solving the original problem is computationally intractable, we provide an upper and two lower bounds on this probability for a very general case with arbitrary time-varying probabilities of links' existence. Moreover, for a special case where the links have identical probabilities across the network at each time slot, we obtain the exact probability of accessibility between any two nodes. Finally, we discuss scenarios where the information regarding the presence and absence of links is initially available in the form of time duration (of presence or absence intervals) continuous probability distributions rather than discrete probabilities over time slots. We provide a method for transforming such distributions to discrete probabilities which enables us to apply the given bounds in this paper to a broader range of problem settings.

We show that the (normalized) symmetric Laplacian of a simple graph can be obtained from the partial trace over a pure bipartite quantum state that resides in a bipartite Hilbert space (one part corresponding to the vertices, the other corresponding to the edges). This suggests an interpretation of the symmetric Laplacian's Von Neumann entropy as a measure of bipartite entanglement present between the two parts of the state. We then study extreme values for a connected graph's generalized R\'enyi-$p$ entropy. Specifically, we show that (1) the complete graph achieves maximum entropy, (2) the $2$-regular graph: a) achieves minimum R\'enyi-$2$ entropy among all $k$-regular graphs, b) is within $\log 4/3$ of the minimum R\'enyi-$2$ entropy and $\log4\sqrt{2}/3$ of the minimum Von Neumann entropy among all connected graphs, c) achieves a Von Neumann entropy less than the star graph. Point $(2)$ contrasts sharply with similar work applied to (normalized) combinatorial Laplacians, where it has been shown that the star graph almost always achieves minimum Von Neumann entropy. In this work we find that the star graph achieves maximum entropy in the limit as the number of vertices grows without bound. Keywords: Symmetric; Laplacian; Quantum; Entropy; Bounds; R\'enyi.

We analyze the secrecy outage probability in the downlink for wireless networks with spatially (Poisson) distributed eavesdroppers (EDs) under the assumption that the base station employs transmit antenna selection (TAS) to enhance secrecy performance. We compare the cases where the receiving user equipment (UE) operates in half-duplex (HD) mode and full-duplex (FD) mode. In the latter case, the UE simultaneously receives the intended downlink message and transmits a jamming signal to strengthen secrecy. We investigate two models of (semi)passive eavesdropping: (1) EDs act independently and (2) EDs collude to intercept the transmitted message. For both of these models, we obtain expressions for the secrecy outage probability in the downlink for HD and FD UE operation. The expressions for HD systems have very accurate approximate or exact forms in terms of elementary and/or special functions for all path loss exponents. Those related to the FD systems have exact integral forms for general path loss exponents, while exact closed forms are given for specific exponents. A closed-form approximation is also derived for the FD case with colluding EDs. The resulting analysis shows that the reduction in the secrecy outage probability is logarithmic in the number of antennas used for TAS and identifies conditions under which HD operation should be used instead of FD jamming at the UE. These performance trends and exact relations between system parameters can be used to develop adaptive power allocation and duplex operation methods in practice. Examples of such techniques are alluded to herein.