Leveraging on the reconfigurable intelligent surface (RIS) paradigm for enabling the next Internet of Things (IoT) and 6G era, this paper develops a comprehensive theoretical framework characterizing the performance of RIS-assisted communications in a plethora of propagation environments. We derive unified mathematical models for the outage probability and ergodic capacity of single and multiple-element

Optical nonlinear Fourier transform-based communication systems require an accurate estimation of a signal's nonlinear spectrum, computed usually by piecewise approximation methods on the signal samples. We propose an algorithm, named successive eigenvalue removal, to improve the spectrum estimation of a multi-soliton pulse. It exploits a property of the Darboux transform that allows removing eigenvalues

In this article, we propose an index modulation system suitable for optical communications, where the intensity of the light is modulated along the time, space and frequency dimensions, building a Frequency-Hopping Spatial Multi-Pulse Position Modulation (FH-SMPPM). We analyze its performance from the point of view of its efficiency in power and spectrum, and its implementation complexity and required

Motivated by coding applications,two enumeration problems are considered: the number of distinct divisors of a degree-m polynomial over F = GF(q), and the number of ways a polynomial can be written as a product of two polynomials of degree at most n over F. For the two problems, bounds are obtained on the maximum number of factorizations, and a characterization is presented for polynomials attaining

As a key technology for future wireless networks, massive multiple-input multiple-output (MIMO) can significantly improve the energy efficiency (EE) and spectral efficiency (SE), and the performance is highly dependant on the degree of the available channel state information (CSI). While most existing works on massive MIMO focused on the case where the instantaneous CSI at the transmitter (CSIT) is

This paper proposes a hybrid-relaying scheme empowered by a self-sustainable intelligent reflecting surface (IRS) in a wireless powered communication network (WPCN), to simultaneously improve the performance of downlink energy transfer (ET) from a hybrid access point (HAP) to multiple users and uplink information transmission (IT) from users to the HAP. We propose time-switching (TS) and power-splitting

In group testing, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether any defective item is present. This problem is relevant in areas such as medical testing, data science, communications, and many more. Motivated by physical considerations, we consider a sparsity-based constrained setting (Gandikota {\em et al.}, 2019), in

Recursive Bayesian inference (RBI) provides optimal Bayesian latent variable estimates in real-time settings with streaming noisy observations. Active RBI attempts to effectively select queries that lead to more informative observations to rapidly reduce uncertainty until a confident decision is made. However, typically the optimality objectives of inference and query mechanisms are not jointly selected

A striking result of [Acharya et al. 2017] showed that to estimate symmetric properties of discrete distributions, plugging in the distribution that maximizes the likelihood of observed multiset of frequencies, also known as the profile maximum likelihood (PML) distribution, is competitive compared with any estimators regardless of the symmetric property. Specifically, given $n$ observations from the

Contention-based grant-free transmission is very promising for future massive machine-type communication (mMTC). In contention-based transmission, the random pilot collision is a challenging problem. To solve this problem, multiple pilots scheme is used to reduce the pilot collision probabliltiy. However, the existing work on multiple pilots relies on the low correlation of spatial channels, limiting

We give an overview of several of the mathematical works of Gilles Lachaud and provide a historical context. This is interspersed with some personal anecdotes highlighting many facets of his personality.

In recent years, several integer programming (IP) approaches were developed for maximum-likelihood decoding and minimum distance computation for binary linear codes. Two aspects in particular have been demonstrated to improve the performance of IP solvers as well as adaptive linear programming decoders: the dynamic generation of forbidden-set (FS) inequalities, a family of valid cutting planes, and

In this paper, we investigate comparatively the behaviors of quantum discord and concurrence for Werner states based on two bipartite entangled squeezed states. The maximally entangled squeezed states are regarded as a perfect-Werner states, while the non-maximally entangled squeezed states are called quasi-Werner states. We show that, the behavior of the quantum correlations keep unchanged for these

We previously proposed the first nontrivial examples of a code having support t-designs for all weights obtained from the Assmus-Mattson theorem and having support t'-designs for some weights with some t'>t. This suggests the possibility of generalizing the Assmus-Mattson theorem, which is very important in design and coding theory. In the present paper, we generalize this example as a strengthening

In this paper, we study simultaneous wireless information and power transfer (SWIPT) systems employing practical non-linear energy harvester (EH) circuits. Since the voltage across the reactive elements of realistic EH circuits cannot drop or rise instantaneously, EHs have memory which we model with a Markov decision process (MDP). Moreover, since an analytical model that accurately models all non-linear

In this article, we define an information-theoretic entropy based on the Ihara zeta function of a graph which is called the Ihara entropy. A dynamical system consists of a billiard ball and a set of reflectors correspond to a combinatorial graph. The reflectors are represented by the vertices of the graph. Movement of the billiard ball between two reflectors is represented by the edges. The prime cycles

Generalized concatenated codes were introduced in the 1970s by Zinoviev. There are many types of codes in the literature that are known by other names that can be viewed as generalized concatenated codes. Examples include matrix-product codes, multilevel codes and generalized cascade codes. Decoding algorithms for generalized concatenated codes were developed during the 1970s and 1980s. However, their

Recently, millimeter-wave (mmWave) 5G localization has been shown to be to provide centimeter-level accuracy, lending itself to many location-aware applications, e.g., connected autonomous vehicles (CAVs). One assumption usually made in the investigation of localization methods is that the user equipment (UE), i.e., a CAV, and the base station (BS) are {time} synchronized. In this paper, we remove

We study federated machine learning (ML) at the wireless edge, where power- and bandwidth-limited wireless devices with local datasets carry out distributed stochastic gradient descent (DSGD) with the help of a remote parameter server (PS). Standard approaches assume separate computation and communication, where local gradient estimates are compressed and transmitted to the PS over orthogonal links

While the Euclidean distance characteristics of the Poisson line Cox process (PLCP) have been investigated in the literature, the analytical characterization of the path distances is still an open problem. In this paper, we characterize the length of the shortest path between the typical point and its nearest neighbor in the sense of path distance in a stationary Manhattan Poisson line Cox process

For fixed integers $r\ge 3,e\ge 3,v\ge r+1$, an $r$-uniform hypergraph is called $\mathscr{G}_r(v,e)$-free if the union of any $e$ distinct edges contains at least $v+1$ vertices. Brown, Erd\H{o}s and S\'{o}s showed that the maximum number of edges of such a hypergraph on $n$ vertices, denoted as $f_r(n,v,e)$, satisfies $$\Omega(n^{\frac{er-v}{e-1}})=f_r(n,v,e)=\mathcal{O}(n^{\lceil\frac{er-v}{e-1}\rceil})

A framework for deriving R\'enyi entropy-power inequalities (EPIs) is presented that uses linearization and an inequality of Dembo, Cover, and Thomas. Simple arguments are given to recover the previously known R\'enyi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent $\alpha$ of previous works. An information-theoretic proof of the Dembo-Cover-Thomas

Maximum distance profile (MDP) convolutional codes have the property that their column distances are as large as possible. There exists a well-known criterion to check whether a code is MDP using the generator or parity-check matrix of the code. However, this criterion has only been shown under the assumption that the generator or parity-check matrix is left prime. Proving left primeness of a polynomial

Random attacks that jointly minimize the amount of information acquired by the operator about the state of the grid and the probability of attack detection are presented. The attacks minimize the information acquired by the operator by minimizing the mutual information between the observations and the state variables describing the grid. Simultaneously, the attacker aims to minimize the probability

Fast testing can help mitigate the coronavirus disease 2019 (COVID-19) pandemic. Despite their accuracy for single sample analysis, infectious diseases diagnostic tools, like RT-PCR, require substantial resources to test large populations. We develop a scalable approach for determining the viral status of pooled patient samples. Our approach converts group testing to a linear inverse problem, where

Reconfigurable intelligent surface (RIS)-assisted communications appear as a promising candidate for future wireless systems due to its attractive advantages in terms of implementation cost and end-to-end system performance. In this paper, two new multiple-input multiple-output (MIMO) system designs using RISs are presented to enhance the performance and boost the spectral efficiency of state-of-the-art

We consider the Courtade-Kumar most informative Boolean function conjecture for balanced functions, as well as a conjecture by Li and M\'edard that dictatorship functions also maximize the $L^\alpha$ norm of $T_pf$ for $1\leq\alpha\leq2$ where $T_p$ is the noise operator and $f$ is a balanced Boolean function. By using a result due to Laguerre from the 1880's, we are able to bound how many times an

We study a setting where each agent in a network receives certain private signals generated by an unknown static state that belongs to a finite set of hypotheses. The agents are tasked with collectively identifying the true state. To solve this problem in a communication-efficient manner, we propose an event-triggered distributed learning algorithm that is based on the principle of diffusing low beliefs

Network-connected unmanned aerial vehicle (UAV) communications is a common solution to achieve high-rate image transmission. The broadcast nature of these wireless networks makes this communication vulnerable to eavesdropping. This paper considers the problem of compressed secret image transmission between two nodes, in the presence of a passive eavesdropper. In this paper, we use auto encoder/decoder

We consider the problem of distributed hypothesis testing (or social learning) where a network of agents seeks to identify the true state of the world from a finite set of hypotheses, based on a series of stochastic signals that each agent receives. Prior work on this problem has provided distributed algorithms that guarantee asymptotic learning of the true state, with corresponding efforts to improve

When base stations (BSs) are deployed with multiple antennas, they need to have downlink (DL) channel state information (CSI) to optimize downlink transmissions by beamforming. The DL CSI is usually measured at mobile stations (MSs) through DL training and fed back to the BS in frequency division duplexing (FDD). The DL training and uplink (UL) feedback might become infeasible due to insufficient coherence

In this work, we study the performance of predictor antenna (PA) systems using hybrid automatic repeat request (HARQ). Here, the PA system is referred to as a system with two sets of antennas on the roof of a vehicle. In this setup, the PA positioned in the front of the vehicle can be used to predict the channel state information at the transmitter (CSIT) for data transmission to the receive antenna

Predictor antenna (PA) system is referred to as a system with two sets of antennas on the roof of a vehicle, where the PAs positioned in the front of the vehicle are used to predict the channel state observed by the receive antennas (RAs) that are aligned behind the PAs. In this work, we study the effect of spatial mismatch on the accuracy of channel state information estimation, and analyze the delay-constrained

Non-orthogonal multiple access (NOMA) is an emerging technology for massive connectivity in machine-type communications (MTC). In code-domain NOMA, non-orthogonal spreading sequences are uniquely assigned to all devices, where active ones attempt a grant-free access to a system. In this paper, we study a set of user-specific, non-orthogonal, binary spreading sequences for uplink grant-free NOMA. Based

We propose a construction of lattices from (skew-) polynomial codes, by endowing quotients of some ideals in both number fields and cyclic algebras with a suitable trace form. We give criteria for unimodularity. This yields integral and unimodular lattices with a multiplicative structure. Examples are provided.

Let $G$ be a connected graph on $n$ vertices and $C$ be an $(n,k,d)$ code with $d\ge 2$, defined on the alphabet set $\{0,1\}^m$. Suppose that for $1\le i\le n$, the $i$-th vertex of $G$ holds an input symbol $x_i\in\{0,1\}^m$ and let $\vec{x}=(x_1,\ldots,x_n)\in\{0,1\}^{mn}$ be the input vector formed by those symbols. Assume that each vertex of $G$ can communicate with its neighbors by transmitting

We present double pooling, a simple, easy-to-implement variation on test pooling, that in certain ranges for the a priori probability of a positive test, is significantly more efficient than the standard single pooling approach (the Dorfman method).

Total correlation (`TC') and dual total correlation (`DTC') are two classical way to quantify the correlation among an $n$-tuple of random variables. They both reduce to mutual information when $n=2$. The first part of this paper sets up the theory of TC and DTC for general random variables, not necessarily finite-valued. This generality has not been exposed in the literature before. The second part

Permutation Entropy (PE) has been shown to be a useful tool for time series analysis due to its low computational cost and noise robustness. This has drawn for its successful application in many fields. Some of these include damage detection, disease forecasting, and financial volatility analysis. However, to successfully use PE, an accurate selection of two parameters is needed: the permutation dimension

Consider the following problem: given two arbitrary densities $q_1,q_2$ and a sample-access to an unknown target density $p$, find which of the $q_i$'s is closer to $p$ in total variation. A remarkable result due to Yatracos shows that this problem is tractable in the following sense: there exists an algorithm that uses $O(\epsilon^{-2})$ samples from $p$ and outputs~$q_i$ such that with high probability

Incomplete information allow to deal with data with errors, uncertainty or inconsistencies and have been studied in different application areas such as query answering or data integration. In this paper, we investigate classical functional dependencies in presence of incomplete information. To do so, we associate each attribute with a comparability function which maps every pair of domain values to

We shortly review Bell-diagonal and Werner states of two quantum bits and their characterization, and carry out a detailed experimental study of their generation on the IBM Quantum Experience. To this end we propose new circuits and tomography. One circuit involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. For the first time the entire

A power Hadamard matrix $H(x)$ is a square matrix of dimension $n$ with entries from Laurent polynomial ring $L= \mathbb{Q} [x,x^{-1}]$ such that $H(x)H(x^{-1})^T=nI \mod f(x)$, where $f$ is some Laurent polynomial of degree greater than $0$. In the first part of this work, some new results on power Hadamard matrices are studied, where we mainly entend the work of Craigen and Woodford. In the second

A distributed binary hypothesis testing (HT) problem over a noisy channel studied previously by the authors is investigated from the perspective of the strong converse property. It was shown by Ahlswede and Csisz\'{a}r that a strong converse holds in the above setting when the channel is rate-limited and noiseless. Motivated by this observation, we show that the strong converse continues to hold in

In general coding theory, we often assume that error is observed in transferring or storing encoded symbols, while the process of encoding itself is error-free. Motivated by recent applications of coding theory, we introduce the problem of distributed encoding which comprises of a set of $K \in \mathbb{N}$ isolated source nodes and $N \in \mathbb{N}$ encoding nodes. Each source node has one symbol

In this paper, we discuss a non-orthogonal multiple access (NOMA) scheme to exploit a high diversity gain using repetition, namely repetition-based NOMA. Unlike conventional power-domain NOMA, all the users can have the same transmit power, but different number of repetitions. Thanks to a high diversity gain, a low outage probability can be achieved without instantaneous channel state information (CSI)

In this paper, we discuss a construction method of quantum deletion error-correcting codes. First of all, we define deletion errors for quantum states, an encoder, a decoder, and two conditions which is expressed by only the combinatorial language. Then, we prove that quantum deletion error-correcting codes can be constructed by two sets that satisfy the conditions. In other words, problems that correct

Gopala-Hemachandra codes are a variation of the Fibonacci universal code and have applications in cryptography and data compression. We show that $GH_{a}(n)$ codes always exist for $a=-2,-3$ and $-4$ for any integer $n \geq 1$ and hence are universal codes. We develop two new algorithms to determine whether a GH code exists for a given set of parameters $a$ and $n$. In 2010, Basu and Prasad showed

Consider a channel $W$ along with a given input distribution $P_X$. In certain settings, such as in the construction of polar codes, the output alphabet of $W$ is `too large', and hence we replace $W$ by a channel $Q$ having a smaller output alphabet. We say that $Q$ is upgraded with respect to $W$ if $W$ is obtained from $Q$ by processing its output. In this case, the mutual information $I(P_X,W)$

The research challenge of current Wireless Sensor Networks (WSNs) is to design energy-efficient, low-cost, high-accuracy, self-healing, and scalable systems for applications such as environmental monitoring. Traditional WSNs consist of low density, power-hungry digital motes that are expensive and cannot remain functional for long periods on a single power charge. In order to address these challenges

Deep neural networks (DNN) have shown remarkable success in a variety of machine learning applications. The capacity of these models (i.e., number of parameters), endows them with expressive power and allows them to reach the desired performance. In recent years, there is an increasing interest in deploying DNNs to resource-constrained devices (i.e., mobile devices) with limited energy, memory, and

Hybrid Automatic ReQuest (HARQ) protocol enables reliable communications in wireless systems. Usually, several parallel streams are sent in successive timeslots following a time-sharing approach. Recently, multi-layer HARQ has been proposed by superposing packets within a timeslot. In this paper, we evaluate the potential of this multi-layer HARQ by playing with some design parameters. We show that

We show that the posterior distribution converges weakly to ML-random parameters when the model is consistent and define conditional random set by the inverse of the Bayes estimator to validate consistent theorem in Bayes models for individual ML-random parameters and conditional random sequences.

The paper derives the optimal second-order coding rate for the continuous-time Poisson channel. We also obtain bounds on the third-order coding rate. This is the first instance of a second-order result for a continuous-time channel. The converse proof hinges on a novel construction of an output distribution induced by Wyner's discretized channel and the construction of an appropriate $\epsilon$-net

We show that any $\ell$-controllable complete group system $\mathsf{C}$ can be reduced to a generator group $({\mathcal{U}}_g,\circ)$. The set ${\mathcal{U}}_g$ is defined on a double Cartesian product space, with indices $k$, for $0\le k\le\ell$, and time $t$, for $t\in\mathbf{Z}$. Each index $k$ and time $t$ is associated with a set $G_k^t$ of \glabs\ $g_k^t$. Each $g_k^t$ is the label of a generator

We examine the problem of learning to cooperate in the context of wireless communication. In our setting, two agents must learn modulation schemes that enable them to communicate across a power-constrained additive white Gaussian noise channel. We investigate whether learning is possible under different levels of information sharing between distributed agents which are not necessarily co-designed.

This work studies the problem of estimating a two-dimensional superposition of point sources or spikes from samples of their convolution with a Gaussian kernel. Our results show that minimizing a continuous counterpart of the $\ell_1$ norm exactly recovers the true spikes if they are sufficiently separated, and the samples are sufficiently dense. In addition, we provide numerical evidence that our

This paper investigates intelligent reflecting surface (IRS)-aided multicell wireless networks, where an IRS is deployed to assist the joint processing coordinated multipoint (JP-CoMP) transmission from multiple base stations (BSs) to multiple cell-edge users. By taking into account the fairness among cell-edge users, we aim at maximizing the minimum achievable rate of cell-edge users by jointly optimizing

We prove a Central Limit Theorem (CLT) for Martin-L\"of Random (MLR) sequences. Martin-L\"of randomness attempts to capture what it means for a sequence of bits to be "truly random". By contrast, CLTs do not make assertions about the behavior of a single random sequence, but only on the distributional behavior of a sequence of random variables. Semantically, we usually interpret CLTs as assertions

The determination of the weight distribution of linear codes has been a fascinating problem since the very beginning of coding theory. There has been a lot of research on weight enumerators of special cases, such as self-dual codes and codes with small Singleton's defect. We propose a new set of linear relations that must be satisfied by the coefficients of the weight distribution. From these relations