Minimum power required to achieve a distortion-noise profile, i.e., a function indicating the maximum allowed distortion value for each noise level, is studied for the transmission of Gaussian sources over Gaussian channels under a regime of bandwidth approaching zero. A simple but instrumental lower bound to the minimum required power for a given profile is presented. For an upper bound, a dirty-paper based coding scheme is proposed and its power-distortion tradeoff is analyzed. Finally, upper and lower bounds to the minimum power is analyzed and compared for specific distortion-noise profiles, namely rational profiles with order one and two.

We investigate the framework of privacy amplification by iteration, recently proposed by Feldman et al., from an information-theoretic lens. We demonstrate that differential privacy guarantees of iterative mappings can be determined by a direct application of contraction coefficients derived from strong data processing inequalities for $f$-divergences. In particular, by generalizing the Dobrushin's contraction coefficient for total variation distance to an $f$-divergence known as $E_{\gamma}$-divergence, we derive tighter bounds on the differential privacy parameters of the projected noisy stochastic gradient descent algorithm with hidden intermediate updates.

Applications from finance to epidemiology and cyber-security require accurate forecasts of dynamic phenomena, which are often only partially observed. We demonstrate that a system's predictability degrades as a function of temporal sampling, regardless of the adopted forecasting model. We quantify the loss of predictability due to sampling, and show that it cannot be recovered by using external signals. We validate the generality of our theoretical findings in real-world partially observed systems representing infectious disease outbreaks, online discussions, and software development projects. On a variety of prediction tasks---forecasting new infections, the popularity of topics in online discussions, or interest in cryptocurrency projects---predictability irrecoverably decays as a function of sampling, unveiling fundamental predictability limits in partially observed systems.

Directional transmission patterns (a.k.a. narrow beams) are the key to wireless communications in millimeter wave (mmWave) frequency bands which suffer from high path loss and severe shadowing. In addition, the propagation channel in mmWave frequencies incorporates only a few number of spatial clusters requiring a procedure to align the corresponding narrow beams with the angle of departure (AoD) of the channel clusters. The objective of this procedure, called beam alignment (BA) is to increase the beamforming gain for subsequent data communication. Several prior studies consider optimizing BA procedure to achieve various objectives such as reducing the BA overhead, increasing throughput, and reducing power consumption. While these studies mostly provide optimized BA schemes for scenarios with a single active user, there are often multiple active users in practical networks. Consequently, it is more efficient in terms of BA overhead and delay to design multi-user BA schemes which can perform beam management for multiple users collectively. This paper considers a class of multi-user BA schemes where the base station performs a one shot scan of the angular domain to simultaneously localize multiple users. The objective is to minimize the average of expected width of remaining uncertainty regions (UR) on the AoDs after receiving users' feedbacks. Fundamental bounds on the optimal performance are analyzed using information theoretic tools. Furthermore, a beam design optimization problem is formulated and a practical BA scheme, which provides significant gains compared to the beam sweeping used in 5G standard is proposed.

In this paper, we present an efficiently encodable and decodable code construction that is capable of correction a burst of deletions of length at most $k$. The redundancy of this code is $\log n + k(k+1)/2\log \log n+c_k$ for some constant $c_k$ that only depends on $k$ and thus is scaling-optimal. The code can be split into two main components. First, we impose a constraint that allows to locate the burst of deletions up to an interval of size roughly $\log n$. Then, with the knowledge of the approximate location of the burst, we use several {shifted Varshamov-Tenengolts} codes to correct the burst of deletions, which only requires a small amount of redundancy since the location is already known up to an interval of small size. Finally, we show how to efficiently encode and decode the code.

Reconfigurable Intelligent Surfaces (RIS) or Intelligent Reflecting Surfaces (IRS) are metasurfaces that can be deployed in various places in wireless environments to make these environments controllable and reconfigurable. In this paper, we investigate the problem of using 3D beamforming in RIS-empowered wireless networks and propose a new scheme that provides more degrees of freedom in designing and deploying the RIS-based networks. In the proposed scheme, a base station (BS) equipped with a full dimensional array of antennas optimizes its radiation pattern in the three-dimensional space to maximize the received signal to noise ratio at a target user. We also study the effect of angle of incidence of the received signal by the RIS on its reflecting properties and find a relation between this angle and the BS antenna array's tilt and elevation angles. The user receives the signal from a reflected path from the RIS as well as from a direct path from the BS which both depend on the BS antenna array's tilt and elevation angles. These angles and also the RIS element's phase shifts are jointly numerically optimized. Our simulation results show that using RIS-assisted 3D beamforming with optimized phase shifts and radiation angles can considerably improve the performance of wireless networks.

The Gray and Wyner lossy source coding for a simple network for sources that generate a tuple of jointly Gaussian random variables (RVs) $X_1 : \Omega \rightarrow {\mathbb R}^{p_1}$ and $X_2 : \Omega \rightarrow {\mathbb R}^{p_2}$, with respect to square-error distortion at the two decoders is re-examined using (1) Hotelling's geometric approach of Gaussian RVs-the canonical variable form, and (2) van Putten's and van Schuppen's parametrization of joint distributions ${\bf P}_{X_1, X_2, W}$ by Gaussian RVs $W : \Omega \rightarrow {\mathbb R}^n $ which make $(X_1,X_2)$ conditionally independent, and the weak stochastic realization of $(X_1, X_2)$. Item (2) is used to parametrize the lossy rate region of the Gray and Wyner source coding problem for joint decoding with mean-square error distortions ${\bf E}\big\{||X_i-\hat{X}_i||_{{\mathbb R}^{p_i}}^2 \big\}\leq \Delta_i \in [0,\infty], i=1,2$, by the covariance matrix of RV $W$. From this then follows Wyner's common information $C_W(X_1,X_2)$ (information definition) is achieved by $W$ with identity covariance matrix, while a formula for Wyner's lossy common information (operational definition) is derived, given by $C_{WL}(X_1,X_2)=C_W(X_1,X_2) = \frac{1}{2} \sum_{j=1}^n \ln \left( \frac{1+d_j}{1-d_j} \right),$ for the distortion region $ 0\leq \Delta_1 \leq \sum_{j=1}^n(1-d_j)$, $0\leq \Delta_2 \leq \sum_{j=1}^n(1-d_j)$, and where $1 > d_1 \geq d_2 \geq \ldots \geq d_n>0$ in $(0,1)$ are {\em the canonical correlation coefficients} computed from the canonical variable form of the tuple $(X_1, X_2)$. The methods are of fundamental importance to other problems of multi-user communication, where conditional independence is imposed as a constraint.

This paper studies the tradeoff in privacy and utility in a single-trial multi-terminal guessing (estimation) framework using a system model that is inspired by index coding. There are $n$ independent discrete sources at a data curator. There are $m$ legitimate users and one adversary, each with some side information about the sources. The data curator broadcasts a distorted function of sources to legitimate users, which is also overheard by the adversary. In terms of utility, each legitimate user wishes to perfectly reconstruct some of the unknown sources and attain a certain gain in the estimation correctness for the remaining unknown sources. In terms of privacy, the data curator wishes to minimize the maximal leakage: the worst-case guessing gain of the adversary in estimating any target function of its unknown sources after receiving the broadcast data. Given the system settings, we derive fundamental performance lower bounds on the maximal leakage to the adversary, which are inspired by the notion of confusion graph and performance bounds for the index coding problem. We also detail a greedy privacy enhancing mechanism, which is inspired by the agglomerative clustering algorithms in the information bottleneck and privacy funnel problems.

There is a growing interest in analysing the freshness of data in networked systems. Age of Information (AoI) has emerged as a popular metric to quantify this freshness at a given destination. There has been a significant research effort in optimizing this metric in communication and networking systems under different settings. In contrast to previous works, we are interested in a fundamental question, what is the minimum achievable AoI in any single-server-single-source queuing system for a given service-time distribution? To address this question, we study a problem of optimizing AoI under service preemptions. Our main result is on the characterization of the minimum achievable average peak AoI (PAoI). We obtain this result by showing that a fixed-threshold policy is optimal in the set of all randomized-threshold causal policies. We use the characterization to provide necessary and sufficient conditions for the service-time distributions under which preemptions are beneficial.

Recently, the use of intelligent reflecting surface (IRS) has gained considerable attention in wireless communications. By intelligently adjusting the passive reflection angle, IRS is able to assist the base station (BS) to extend the coverage and improve spectral efficiency. This paper considers a joint symbol-level precoding (SLP) and IRS reflecting design to minimize the symbol-error probability (SEP) of the intended users in an IRS-aided multiuser MISO downlink. We formulate the SEP minimization problems to pursue uniformly good performance for all users for both QAM and PSK constellations. The resulting problem is non-convex and we resort to alternating minimization to obtain a stationary solution. Simulation results demonstrate that under the aid of IRS our proposed design indeed enhances the bit-error rate performance. In particular, the performance improvement is significant when the number of IRS elements is large.

We consider a fully-loaded ground wireless network supporting unmanned aerial vehicle (UAV) transmission services. To enable the overload transmissions to a ground user (GU) and a UAV, two transmission schemes are employed, namely non-orthogonal multiple access (NOMA) and relaying, depending on whether or not the GU and UAV are served simultaneously. Under the assumption of the system operating with infinite blocklength (IBL) codes, the IBL throughputs of both the GU and the UAV are derived under the two schemes. More importantly, we also consider the scenario in which data packets are transmitted via finite blocklength (FBL) codes, i.e., data transmission to both the UAV and the GU is performed under low-latency and high reliability constraints. In this setting, the FBL throughputs are characterized again considering the two schemes of NOMA and relaying. Following the IBL and FBL throughput characterizations, optimal resource allocation designs are subsequently proposed to maximize the UAV throughput while guaranteeing the throughput of the cellular user.Moreover, we prove that the relaying scheme is able to provide transmission service to the UAV while improving the GU's performance, and that the relaying scheme potentially offers a higher throughput to the UAV in the FBL regime than in the IBL regime. On the other hand, the NOMA scheme provides a higher UAV throughput (than relaying) by slightly sacrificing the GU's performance.

Recent works have considered the ability of transmitter Alice to communicate reliably to receiver Bob without being detected by warden Willie. These works generally assume a standard discrete-time model. But the assumption of a discrete-time model in standard communication scenarios is often predicated on its equivalence to a continuous-time model, which has not been established for the covert communications problem. Here, we consider the continuous-time channel directly and study if efficient covert communication can still be achieved. We assume that an uninformed jammer is present to assist Alice, and we consider additive white Gaussian noise (AWGN) channels between all parties. For a channel with approximate bandwidth W, we establish constructions such that O(WT) information bits can be transmitted covertly and reliably from Alice to Bob in T seconds for two separate scenarios: 1) when the path-loss between Alice and Willie is known; and 2) when the path-loss between Alice and Willie is unknown.

Overwhelming theoretical and empirical evidence shows that mildly overparametrized neural networks -- those with more connections than the size of the training data -- are often able to memorize the training data with $100\%$ accuracy. This was rigorously proved for networks with sigmoid activation functions and, very recently, for ReLU activations. Addressing a 1988 open question of Baum, we prove that this phenomenon holds for general multilayered perceptrons, i.e. neural networks with threshold activation functions, or with any mix of threshold and ReLU activations. Our construction is probabilistic and exploits sparsity.

Quantitative aspects of computation are related to the use of both physical and mathematical quantities, including time, performance metrics, probability, and measures for reliability and security. They are essential in characterizing the behaviour of many critical systems and in estimating their properties. Hence, they need to be integrated both at the level of system modeling and within the verification methodologies and tools. Along the last two decades a variety of theoretical achievements and automated techniques have contributed to make quantitative modeling and verification mainstream in the research community. In the same period, they represented the central theme of the series of workshops entitled Quantitative Aspects of Programming Languages and Systems (QAPL) and born in 2001. The aim of this survey is to revisit such achievements and results from the standpoint of QAPL and its community.

The proliferation of connected vehicles along with the high demand for rich multimedia services constitute key challenges for the emerging 5G-enabled vehicular networks. These challenges include, but are not limited to, high spectral efficiency and low latency requirements. Recently, the integration of cache-enabled networks with non-orthogonal multiple access (NOMA) has been shown to reduce the content delivery time and traffic congestion in wireless networks. Ac-cordingly, in this article, we envisage cache-aided NOMA as a technology facilitator for 5G-enabled vehicular networks. In particular, we present a cache-aided NOMA architecture, which can address some of the aforementioned challenges in these networks. We demonstrate that the spectral efficiency gain of the proposed architecture, which depends largely on the cached contents, significantly outperforms that of conventional vehicular networks. Finally, we provide deep insights into the challenges, opportunities, and future research trends that will enable the practical realization of cache-aided NOMA in 5G-enabled vehicular networks.

Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is studied. It is assumed that a collection of random vectors is produced based on an arbitrary joint distribution, and the vectors undergo a permutation operation. The joint typicality of the resulting permuted vectors with respect to the original distribution is investigated. As an initial step, permutations of pairs of correlated random vectors are considered. It is shown that the probability of joint typicality of the permuted vectors depends only on the number and length of the disjoint cycles of the permutation. Consequently, it suffices to study typicality for a class of permutations called 'standard permutations', for which, upper-bounds on the probability of joint typicality are derived. The notion of standard permutations is extended to a class of permutation vectors called 'Bell permutation vectors'. By investigating Bell permutation vectors, upper-bounds on the probability of joint typicality of permutations of arbitrary collections of random sequences are derived.

The problem of finding the sparsest vector (direction) in a low dimensional subspace can be considered as a homogeneous variant of the sparse recovery problem, which finds applications in robust subspace recovery, dictionary learning, sparse blind deconvolution, and many other problems in signal processing and machine learning. However, in contrast to the classical sparse recovery problem, the most natural formulation for finding the sparsest vector in a subspace is usually nonconvex. In this paper, we overview recent advances on global nonconvex optimization theory for solving this problem, ranging from geometric analysis of its optimization landscapes, to efficient optimization algorithms for solving the associated nonconvex optimization problem, to applications in machine intelligence, representation learning, and imaging sciences. Finally, we conclude this review by pointing out several interesting open problems for future research.

Consider a centralized caching network with a single server and $K$ users. The server has a database of $N$ files with each file being divided into $F$ packets ($F$ is known as subpacketization), and each user owns a local cache that can store $\frac{M}{N}$ fraction of the $N$ files. We construct a family of centralized coded caching schemes with polynomial subpacketization. Specifically, given $M$, $N$ and an integer $n\geq 0$, we construct a family of coded caching schemes for any $(K,M,N)$ caching system with $F=O(K^{n+1})$. More generally, for any $t\in\{1,2,\cdots,K-2\}$ and any integer $n$ such that $0\leq n\leq t$, we construct a coded caching scheme with $\frac{M}{N}=\frac{t}{K}$ and $F\leq K\binom{\left(1-\frac{M}{N}\right)K+n}{n}$.

A growing number of works have, in recent years, been concerned with in-vivo DNA as medium for data storage. This paper extends the concept of reconstruction codes for uniform-tandem-duplication noise to the model of associative memory, by finding the uncertainty associated with $m>2$ strings (where a previous paper considered $m=2$). That uncertainty is found as an asymptotic expression assuming code-words belong to a typical set of strings, consisting a growing fraction of the space size, converging to $1$. Our findings show that this uncertainty scales polynomially in the message length.

A new computational private information retrieval (PIR) scheme based on random linear codes is presented. A matrix of messages from a McEliece scheme is used to query the server with carefully chosen errors. The server responds with the sum of the scalar multiple of the rows of the query matrix and the files. The user recovers the desired file by erasure decoding the response. Contrary to code-based cryptographic systems, the scheme presented here enables to use truly random codes, not only codes disguised as such. Further, we show the relation to the so-called error subspace search problem and quotient error search problem, which we assume to be difficult, and show that the scheme is secure against attacks based on solving these problems.

The goal of physical layer security (PLS) is to make use of the properties of the physical layer, including the wireless communication medium and the transceiver hardware, to enable critical aspects of secure communications. In particular, PLS can be employed to provide i) node authentication, ii) message authentication, and, iii) message confidentiality. Unlike the corresponding classical cryptographic approaches which are all based on computational security, PLS's added strength is that it is based on information theoretic security, in which no limitation with respect to the opponent's computational power is assumed and is therefore inherently quantum resistant. In this survey, we review the aforementioned fundamental aspects of PLS, starting with node authentication, moving to the information theoretic characterization of message integrity, and finally, discussing message confidentiality both in the secret key generation from shared randomness and from the wiretap channel point of view. The aim of this review is to provide a comprehensive roadmap on important relevant results by the authors and other contributors and discuss open issues on the applicability of PLS in sixth generation systems.

Recently Reed-Solomon (RS) codes were shown to possess a repair scheme that supports repair of failed nodes with optimal repair bandwidth. In this paper, we extend this result in two directions. First, we propose a new repair scheme for the RS codes constructed in [Tamo-Ye-Barg, {\em IEEE Transactions on Information Theory}, vol. 65, May 2019] and show that our new scheme is robust to erroneous information provided by the helper nodes while maintaining the optimal repair bandwidth. Second, we construct a new family of RS codes with optimal access for the repair of any single failed node. We also show that the constructed codes can accommodate both features, supporting optimal-access repair with optimal error-correction capability. Going beyond RS codes, we also prove that any scalar MDS code with optimal repair bandwidth allows for a repair scheme with optimal access property.

In the last decade there has been a great interest in extending results for codes equipped with the Hamming metric to analogous results for codes endowed with the rank metric. This work follows this thread of research and studies the characterization of systematic generator matrices (encoders) of codes with maximum rank distance. In the context of Hamming distance these codes are the so-called Maximum Distance Separable (MDS) codes and systematic encoders have been fully investigated. In this paper we investigate the algebraic properties and representation of encoders in systematic form of Maximum Rank Distance (MRD) codes and Maximum Sum Rank Distance (MSRD) codes. We address both block codes and convolutional codes separately and present necessary and sufficient conditions for an encoder in systematic form to generate a code with maximum (sum) rank distance. These characterizations are given in terms of certain matrices that must be superregular in a extension field and that preserve superregularity after some transformations performed over the base field. We conclude the work presenting some examples of Maximum Sum Rank convolutional codes over small fields. For the given parameters the examples obtained are over smaller fields than the examples obtained by other authors.

Polynomial coding has been proposed as a solution to the straggler mitigation problem in distributed matrix multiplication. Previous works in the literature employ univariate polynomials to encode matrix partitions. Such schemes greatly improve the speed of distributed computing systems by making the task completion time to depend only on the fastest workers. However, the work done by the slowest workers, which fails to finish the task assigned to them, is completely ignored. In order to exploit the partial computations of the slower workers, we further decompose the overall matrix multiplication task into even smaller subtasks to better fit workers' storage and computation capacities. In this work, we show that univariate schemes fail to make an efficient use of the storage capacity and we propose bivariate polynomial codes. We show that bivariate polynomial codes are a more natural choice to accommodate the additional decomposition of subtasks, as well as, heterogeneous storage and computation resources at workers. However, in contrast to univariate polynomial decoding, for multivariate interpolation guarantying decodability is much harder. We propose two bivartiate polynomial schemes. The first scheme exploits the fact that bivariate interpolation is always possible for rectangular grid of points. We obtain the rectangular grid of points at the cost of allowing some redundant computations. For the second scheme, we relax the decoding constraint, and require decodability for almost all choices of evaluation points. We present interpolation sets satisfying the almost decodability conditions for certain storage configurations of workers. Our numerical results show that bivariate polynomial coding considerably reduces the completion time of distributed matrix multiplication.

Index coding is concerned with efficient broadcast of a set of messages to receivers in the presence of receiver side information. In this paper, we study the secure index coding problem with security constraints on the receivers themselves. That is, for each receiver there is a single legitimate message it needs to decode and a prohibited message list, none of which should be decoded by that receiver. To this end, our contributions are threefold. We first introduce a secure linear coding scheme, which is an extended version of the fractional local partial clique covering scheme that was originally devised for non-secure index coding. We then develop two information-theoretic bounds on the performance of any valid secure index code, namely secure polymatroidal outer bound (on the capacity region) and secure maximum acyclic induced subgraph lower bound (on the broadcast rate). The structure of these bounds leads us to further develop two necessary conditions for a given index coding problem to be securely feasible (i.e., to have nonzero rates).

This paper proposes a new three dimensional (3D) networking architecture enabled by aerial intelligent reflecting surface (AIRS) to achieve panoramic signal reflection from the sky. Compared to the conventional terrestrial IRS, AIRS not only enjoys higher deployment flexibility, but also is able to achieve 360$^\circ$ panoramic full-angle reflection and requires fewer reflections in general due to its higher likelihood of having line of sight (LoS) links with the ground nodes. We focus on the problem to maximize the worst-case signal-to-noise ratio (SNR) in a given coverage area by jointly optimizing the transmit beamforming, AIRS placement and phase shifts. The formulated problem is non-convex and the optimization variables are coupled with each other in an intricate manner. To tackle this problem, we first consider the special case of single-location SNR maximization to gain useful insights, for which the optimal solution is obtained in closed-form. Then for the general case of area coverage, an efficient suboptimal solution is proposed by exploiting the similarity between phase shifts optimization for IRS and analog beamforming for the conventional phase array. Numerical results show that the proposed design can achieve significant performance gain than heuristic AIRS deployment schemes.

Coordinated multi-point (CoMP) transmission is a cooperating technique among base stations (BSs) in a cellular network, with outstanding capability at inter-cell interference (ICI) mitigation. ICI is a dominant source of error, and has detrimental effects on system performance if not managed properly. Based on the theory of Poisson-Delaunay triangulation, this paper proposes a novel analytical model for CoMP operation in cellular networks. Unlike the conventional CoMP operation that is dynamic and needs on-line updating occasionally, the proposed approach enables the cooperating BS set of a user equipment (UE) to be fixed and off-line determined according to the location information of BSs. By using the theory of stochastic geometry, the coverage probability and spectral efficiency of a typical UE are analyzed, and simulation results corroborate the effectiveness of the proposed CoMP scheme and the developed performance analysis.

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.

In 2008, a class of binary sequences of period $N=4(2^k-1)(2^k+1)$ with optimal autocorrelation magnitude has been presented by Yu and Gong based on an $m$-sequence, the perfect sequence $(0,1,1,1)$ of period $4$ and interleaving technique. In this paper, we study the 2-adic complexities of these sequences. Our results show that they are larger than $N-2\lceil\mathrm{log}_2N\rceil$ (which is far larger than $N/2$) and could attain the maximum value $N$ if suitable parameters are chosen, i.e., the 2-adic complexity of this class of interleaved sequences is large enough to resist the Rational Approximation Algorithm.

Cell-free massive MIMO communications is an emerging network technology for 5G wireless communications wherein distributed multi-antenna access points (APs) serve many users simultaneously. Most prior work on cell-free massive MIMO systems assume time-division duplexing mode, although frequency-division duplexing (FDD) systems dominate current wireless standards. The key challenges in FDD massive MIMO systems are channel-state information (CSI) acquisition and feedback overhead. To address these challenges, we exploit the so-called angle reciprocity of multipath components in the uplink and downlink, so that the required CSI acquisition overhead scales only with the number of served users, and not the number of AP antennas nor APs. We propose a low complexity multipath component estimation technique and present linear angle-of-arrival (AoA)-based beamforming/combining schemes for FDD-based cell-free massive MIMO systems. We analyze the performance of these schemes by deriving closed-form expressions for the mean-square-error of the estimated multipath components, as well as expressions for the uplink and downlink spectral efficiency. Using semi-definite programming, we solve a max-min power allocation problem that maximizes the minimum user rate under per-user power constraints. Furthermore, we present a user-centric (UC) AP selection scheme in which each user chooses a subset of APs to improve the overall energy efficiency of the system. Simulation results demonstrate that the proposed multipath component estimation technique outperforms conventional subspace-based and gradient-descent based techniques. We also show that the proposed beamforming and combining techniques along with the proposed power control scheme substantially enhance the spectral and energy efficiencies with an adequate number of antennas at the APs.

We consider near maximum-likelihood (ML) decoding of short linear block codes based on neural belief propagation (BP) decoding recently introduced by Nachmani et al.. While this method significantly outperforms conventional BP decoding, the underlying parity-check matrix may still limit the overall performance. In this paper, we introduce a method to tailor an overcomplete parity-check matrix to (neural) BP decoding using machine learning. We consider the weights in the Tanner graph as an indication of the importance of the connected check nodes (CNs) to decoding and use them to prune unimportant CNs. As the pruning is not tied over iterations, the final decoder uses a different parity-check matrix in each iteration. For Reed-Muller and short low-density parity-check codes, we achieve performance within 0.27 dB and 1.5 dB of the ML performance while reducing the complexity of the decoder.

In this paper, the capacity of the oversampled Wiener phase noise (OWPN) channel is investigated. The OWPN channel is a discrete-time point-to-point channel with a multi-sample receiver in which the channel output is affected by both additive and multiplicative noise. The additive noise is a white standard Gaussian process while the multiplicative noise is a Wiener phase noise process. This channel generalizes a number of channel models previously studied in the literature which investigate the effects of phase noise on the channel capacity, such as the Wiener phase noise channel and the non-coherent channel. We derive upper and inner bounds to the capacity of OWPN channel: (i) an upper bound is derived through the I-MMSE relationship by bounding the Fisher information when estimating a phase noise sample given the past channel outputs and phase noise realizations, then (ii) two inner bounds are shown: one relying on coherent combining of the oversampled channel outputs and one relying on non-coherent combining of the samples. After capacity, we study generalized degrees of freedom (GDoF) of the OWPN channel for the case in which the oversampling factor grows with the average transmit power $P$ as $P$? and the frequency noise variance as $P^{\alpha}$?. Using our new capacity bounds, we derive the GDoF region in three regimes: regime (i) in which the GDoF region equals that of the classic additive white Gaussian noise (for $\beta \leq 1$), one (ii) in which GDoF region reduces to that of the non-coherent channel (for $\beta \geq \min \{\alpha,1\}$) and, finally, one in which partially-coherent combining of the over-samples is asymptotically optimal (for $2 \alpha-1\leq \beta \leq 1$). Overall, our results are the first to identify the regimes in which different oversampling strategies are asymptotically optimal.

Inexpensive cloud services, such as serverless computing, are often vulnerable to straggling nodes that increase end-to-end latency for distributed computation. We propose and implement simple yet principled approaches for straggler mitigation in serverless systems for matrix multiplication and evaluate them on several common applications from machine learning and high-performance computing. The proposed schemes are inspired by error-correcting codes and employ parallel encoding and decoding over the data stored in the cloud using serverless workers. This creates a fully distributed computing framework without using a master node to conduct encoding or decoding, which removes the computation, communication and storage bottleneck at the master. On the theory side, we establish that our proposed scheme is asymptotically optimal in terms of decoding time and provide a lower bound on the number of stragglers it can tolerate with high probability. Through extensive experiments, we show that our scheme outperforms existing schemes such as speculative execution and other coding theoretic methods by at least 25%.

The polarization theory of non-stationary channels and the code construction of secure polar codes for non-stationary cases are considered in this paper. The channel transformation of Ar{\i}kan channel polarization theory is modified to non-stationary channels. As proven, the sequence of non-stationary channels can be polarized the into full noise channels and noiseless channels by the modified non-stationary channel transformation. Also it is proven that the rate of non-stationary polarization can achieve the average capacity of the initial non-stationary channels. Then for non-stationary wiretap channel model, a secure polar coding scheme is constructed by applying the non-stationary polarization. It is proven that the secure polar coding scheme achieves the average secrecy capacity of non-stationary wiretap channel model with both reliability and strong security. For wiretap channel model with non-stationary blocks, virtual bit blocks are constructed, on which a time-bit secure polar coding scheme is constructed by applying the non-stationary polarization. It is proven that the time-bit secure polar coding scheme achieves the average secrecy capacity with both reliability and strong security.

In this paper, we investigate the secure coding issue for a wiretap channel model with fixed main channel and varying wiretap channel, by assuming that legitimate parties can obtain the wiretapping channel state information (CSI) after some time delay. For the symmetric degraded delay CSI case, we present an explicit weak security scheme by constructing secure polar codes on a one-time pad chaining structure, and prove its weak security, reliability and capability of approaching the secrecy capacity of perfect CSI case with delay CSI assumption. Further for the symmetric no-degraded delay CSI case, we present a modified multi-block chaining structure in which the original subset of frozen bit is designed for conveying functional random bits securely. Then we combine this modified multi-block chaining structure with the weak security scheme to construct an explicit strong security polar coding scheme, and prove its strong security, reliability and also the capability of approaching the secrecy capacity of perfect CSI case with delay CSI assumption. At last, we carry out stimulations to prove the performance of both secure schemes.

We propose a general greedy algorithm for binary de Bruijn sequences, called Generalized Prefer-Opposite (GPO) Algorithm, and its modifications. By identifying specific feedback functions and initial states, we demonstrate that most previously-known greedy algorithms that generate binary de Bruijn sequences are particular cases of our new algorithm.

Group codes are right or left ideals in a group algebra of a finite group over a finite field. Following ideas of Bazzi and Mitter on group codes over the binary field, we prove that group codes over finite fields of any characteristic are asymptotically good.

A multi-cell Fog-Radio Access Network (F-RAN) architecture is considered in which Internet of Things (IoT) devices periodically make noisy observations of a Quantity of Interest (QoI) and transmit using grant-free access in the uplink. The devices in each cell are connected to an Edge Node (EN), which may also have a finite-capacity fronthaul link to a central processor. In contrast to conventional information-agnostic protocols, the devices transmit using a Type-Based Multiple Access (TBMA) protocol that is tailored to enable the estimate of the field of correlated QoIs in each cell based on the measurements received from IoT devices. In this paper, this form of information-centric radio access is studied for the first time in a multi-cell F-RAN model with edge or cloud detection. Edge and cloud detection are designed and compared for a multi-cell system. Optimal model-based detectors are introduced and the resulting asymptotic behavior of the probability of error at cloud and edge is derived. Then, for the scenario in which a statistical model is not available, data-driven edge and cloud detectors are discussed and evaluated in numerical results.

This paper considers an unmanned aerial vehicle enabled-up link non-orthogonal multiple-access system, where multiple mobile users on the ground send independent messages to a unmanned aerial vehicle in the sky via non-orthogonal multiple-access transmission. Our objective is to design the unmanned aerial vehicle dynamic maneuver for maximizing the sum-rate throughput of all mobile ground users over a finite time horizon.

We proved that the phaseless sampling (PLS) in the linear-phase modulated shift-invariant space (SIS) $V(e^{\textbf{i}\alpha \cdot}\varphi), \alpha\neq0,$ is impossible even though the real-valued function $\varphi$ enjoys the full spark property (so does $e^{\textbf{i}\alpha \cdot}\varphi$). Stated another way, the PLS in the complex-generated SISs is essentially different from that in the real-generated ones. Motivated by this, we first establish the condition on the complex-valued generator $\phi$ such that the PLS of nonseparable causal (NC) signals in $V(\phi)$ can be achieved by random sampling. The condition is established from the generalized Haar condition (GHC) perspective. Based on the proposed reconstruction approach, it is proved that if the GHC holds then with probability $1$, the random sampling density (SD) $=3$ is sufficient for the PLS of NC signals in the complex-generated SISs. For the real-valued case we also prove that, if the GHC holds then with probability $1$, the random SD $=2$ is sufficient for the PLS of real-valued NC signals in the real-generated SISs. For the local reconstruction of highly oscillatory signals such as chirps, a great number of deterministic samples are required.Compared with deterministic sampling, the proposed random approach enjoys not only the greater sampling flexibility but the much smaller number of samples.To verify our results, numerical simulations were conducted to reconstruct highly oscillatory NC signals in the chirp-modulated SISs.

\textit{Why does the literature consider the channel-state-information (CSI) as a 2/3-D image? What are the pros-and-cons of this consideration for accuracy-complexity trade-off?} Next generations of wireless communications require innumerable disciplines according to which a low-latency, low-traffic, high-throughput, high spectral-efficiency and low energy-consumption are guaranteed. Towards this end, the principle of massive multi-input multi-output (MaMIMO) is emerging which is conveniently deployed for millimeter wave (mmWave) bands. However, practical and realistic MaMIMO transceivers suffer from a huge range of challenging bottlenecks in design the majority of which belong to the issue of channel-estimation. Channel modeling and prediction in MaMIMO particularly suffer from computational complexity due to a high number of antenna sets and supported users. This complexity lies dominantly upon the feedback-overhead which even degrades the pilot-data trade-off in the uplink (UL)/downlink (DL) design. This comprehensive survey studies the novel deep-learning (DLg) driven techniques recently proposed in the literature which tackle the challenges discussed-above - which is for the first time. In addition, we consequently propose 7 open trends e.g. in the context of the lack of Q-learning in MaMIMO detection - for which we talk about a possible solution to the saddle-point in the 2-D pilot-data axis for a \textit{Stackelberg game} based scenario.

Let $p$ be an odd prime number. In this paper, we construct $2(2p-3)$ classes of codes over the ring $R=\Bbb F_p+u\Bbb F_p,u^2=0$, which are associated with down sets. We compute the Lee weight distributions of the $2(2p-3)$ classes of codes when the down sets are generated by a single maximal element. Moreover, by using the Gray map of the linear codes over $R$, we find out $2(p-1)$ classes of $p$-ary distance optimal linear codes. Two of them meet the Griesmer bound.

In this paper, a proposal to improve the reliability of a downlink multiuser (MU) MIMO transmission scheme is investigated with the use of a new approach in orthogonal space-time block codes (OSTBC) and network coding with a superposition modulated system and side information. With the new encoded OSTBC approach, diversity is offered where each user receives all other users' symbols, which allows the recovery of symbols in several ways. In addition, multiple users can be accommodated with the same resource, which is quite useful in a wireless system where resources are always restricted. By employing superposition modulation, the side information needed for error recovery can be transmitted over the same resource used for the normal information frame. In addition, the proposed system exploits diversity through a novel technique of sub-constellation alignment-based signal combining for efficient side information dissemination. A detailed analysis of the new OSTBC approach is carried out. It is shown that the performance of the MU-MIMO system can be improved significantly in terms of block and frame error rates (BLER, FER) considered as reliability measures. By accommodating a reasonable number of multiple users, high reliability is achieved at the expense of the rate. To compensate for the low rate, conventional OSTBC can be considered and simulation results are shown, where, as a penalty to pay, multiple orthogonal resources are required.

End-to-end learning of a communications system using the deep learning-based autoencoder concept has drawn interest in recent research due to its simplicity, flexibility and its potential of adapting to complex channel models and practical system imperfections. In this paper, we have compared the bit error rate (BER) performance of autoencoder based systems and conventional channel coded systems with convolutional coding (CC), in order to understand the potential of deep learning-based systems as alternatives to conventional systems. From the simulations, autoencoder implementation was observed to have a better BER in 0-5 dB $E_{b}/N_{0}$ range than its equivalent half-rate convolutional coded BPSK with hard decision decoding, and to have only less than 1 dB gap at a BER of $10^{-5}$. Furthermore, we have also proposed a novel low complexity autoencoder architecture to implement end-to-end learning of coded systems in which we have shown better BER performance than the baseline implementation. The newly proposed low complexity autoencoder was capable of achieving a better BER performance than half-rate 16-QAM with hard decision decoding over the full 0-10 dB $E_{b}/N_{0}$ range and a better BER performance than the soft decision decoding in 0-4 dB $E_{b}/N_{0}$ range.

Secure sketch produces public information of its input $w$ without revealing it, yet, allows the exact recovery of $w$ given another value $w'$ that is close to $w$. Therefore, it can be used to reliably reproduce any error-prone secret (i.e., biometrics) stored in secret storage. However, some sources have lower entropy compared to the error itself, formally called "more error than entropy", a standard secure sketch cannot show its security promise perfectly to these kind of sources. This paper focuses on secure sketch. We propose a concrete construction for secure sketch. We show security to all noisy sources, including the trivial source with zero min-entropy. In addition, our construction comes with efficient recovery algorithm operates in polynomial time in the sketch size, which can tolerate high number of error rate arbitrary close to 1/2. Above result acts in conjunction to our derivation on the solution to two NP-complete coding problems, suggesting P=NP.

In the high-throughput screening (HTS) campaigns, the Z'-factor and strictly standardized mean difference (SSMD) are commonly used to assess the quality of assays and to select hits. However, these measures are vulnerable to outliers and their performances are highly sensitive to background distributions. Here, we propose an alternative measure for assay quality assessment and hit selection. The proposed method is a non-parametric generalized variant of SSMD (GSSMD). In this paper, we have shown that the proposed method provides more robust and intuitive way of assay quality assessment and hit selection.

We consider the problem of secure distributed matrix multiplication in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We show that if the user is only concerned in optimizing the download rate, a common assumption in the literature, then the problem can be converted into a simple private information retrieval problem by means of a scheme we call Private Oracle Querying. However, this comes at large upload and computational costs for both the user and the servers. In contrast, we show that for the right choice of parameters, polynomial codes can lower the computational time of the system, e.g. if the computational time complexity of an operation in $\mathbb{F}_q$ is at most $\mathcal{Z}_q$ and the computational time complexity of multiplying two $n\times n$ matrices is $\mathcal{O}(n^\omega \mathcal{Z}_q)$ then the user together with the servers can compute the multiplication in $\mathcal{O}(n^{4-\frac{6}{\omega+1}} \mathcal{Z}_q)$ time.

This paper studies the problem of reconstructing a word given several of its noisy copies. This setup is motivated by several applications, among them is reconstructing strands in DNA-based storage systems. Under this paradigm, a word is transmitted over some fixed number of identical independent channels and the goal of the decoder is to output the transmitted word or some close approximation. The main focus of this paper is the case of two deletion channels and studying the error probability of the maximum-likelihood (ML) decoder under this setup. First, it is discussed how the ML decoder operates. Then, we observe that the dominant error patterns are deletions in the same run or errors resulting from alternating sequences. Based on these observations, it is derived that the error probability of the ML decoder is roughly $\frac{3q-1}{q-1}p^2$, when the transmitted word is any $q$-ary sequence and $p$ is the channel's deletion probability. We also study the cases when the transmitted word belongs to the Varshamov Tenengolts (VT) code or the shifted VT code. Lastly, the insertion channel is studied as well. These theoretical results are verified by corresponding simulations.

Millimeter wave (mmWave) bands are considered a powerful key enabler for next generation (5G) mobile networks by providing multi-Gbps data rates. However, their severe pathloss and sensitivity to blockage present challenges in practical implementation. One effective way to mitigate these effects and to increase communication range is beamforming in combination with relaying. In this paper, we focus on two typical mmWave relay networks and for each network, we propose three beam scheduling methods to approach the network information theoretic capacity. The proposed beam scheduling methods include the deterministic horizontal continuous edge coloring (HC-EC) scheduler, the adaptive back pressure (BP) scheduler and the adaptive low-delay new back pressure (newBP) scheduler. With the aid of computer simulations, we show that within the network capacity range, the proposed schedulers provide good guarantees for the network stability, meanwhile achieve very low packet end-to-end delay.

Each agent in a network makes a local observation that is linearly related to a set of public and private parameters. The agents send their observations to a fusion center to allow it to estimate the public parameters. To prevent leakage of the private parameters, each agent first sanitizes its local observation using a local privacy mechanism before transmitting it to the fusion center. We investigate the utility-privacy trade-off in terms of the Cram\'er-Rao lower bounds for estimating the public and private parameters. We study the class of privacy mechanisms given by linear compression and noise perturbation, and derive necessary and sufficient conditions for achieving arbitrarily strong utility-privacy trade-off in a decentralized agent network for both the cases where prior information is available and unavailable, respectively. We also provide a method to find the maximum estimation privacy achievable without compromising the utility and propose an alternating algorithm to optimize the utility-privacy trade-off in the case where arbitrarily strong utility-privacy trade-off is not achievable.

For a discrete memoryless channel with finite input and output alphabets, we prove convergence of iterative computation of the optimal correct-decoding exponent as a function of communication rate, for a fixed rate and for a fixed slope.

Federated edge learning (FEEL) is a popular framework for model training at an edge server using data distributed at edge devices (e.g., smart-phones and sensors) without compromising their privacy. In the FEEL framework, edge devices periodically transmit high-dimensional stochastic gradients to the edge server, where these gradients are aggregated and used to update a global model. When the edge devices share the same communication medium, the multiple access channel from the devices to the edge server induces a communication bottleneck. To overcome this bottleneck, an efficient broadband analog transmission scheme has been recently proposed, featuring the aggregation of analog modulated gradients (or local models) via the waveform-superposition property of the wireless medium. However, the assumed linear analog modulation makes it difficult to deploy this technique in modern wireless systems that exclusively use digital modulation. To address this issue, we propose in this work a novel digital version of broadband over-the-air aggregation, called one-bit broadband digital aggregation (OBDA). The new scheme features one-bit gradient quantization followed by digital modulation at the edge devices and a majority-voting based decoding at the edge server. We develop a comprehensive analysis framework for quantifying the effects of wireless channel hostilities (channel noise, fading, and channel estimation errors) on the convergence rate. The analysis shows that the hostilities slow down the convergence of the learning process by introducing a scaling factor and a bias term into the gradient norm. However, we show that all the negative effects vanish as the number of participating devices grows, but at a different rate for each type of channel hostility.

We determine the semantic security capacity for quantum wiretap channels. We extend methods for classical channels to quantum channels to demonstrate that a strongly secure code guarantees a semantically secure code with the same secrecy rate. Furthermore, we show how to transform a non-secure code into a semantically secure code by means of biregular irreducible functions (BRI functions). We analyze semantic security for classical quantum channels and for quantum channels.

Reconfigurable intelligent surface (RIS) is considered to be an energy-efficient approach to reshape the wireless environment for improved throughput. Its passive feature greatly reduces the energy consumption, which makes RIS a promising technique for enabling the future smart city. Existing beamforming designs for RIS mainly focus on optimizing the spectral efficiency for single carrier systems. To avoid the complicated bit allocation on different spatial domain subchannels in MIMO systems, in this paper, we propose a geometric mean decomposition-based beamforming for RIS-assisted millimeter wave (mmWave) hybrid MIMO systems so that multiple parallel data streams in the spatial domain can be considered to have the same channel gain. Specifically, by exploiting the common angular-domain sparsity of mmWave massive MIMO channels over different subcarriers, a simultaneous orthogonal match pursuit algorithm is utilized to obtain the optimal multiple beams from an oversampling 2D-DFT codebook. Moreover, by only leveraging the angle of arrival and angle of departure associated with the line of sight (LoS) channels, we further design the phase shifters for RIS by maximizing the array gain for LoS channel. Simulation results show that the proposed scheme can achieve better BER performance than conventional approaches. Our work is an initial attempt to discuss the broadband hybrid beamforming for RIS-assisted mmWave hybrid MIMO systems.

Coded caching is an information theoretic scheme to reduce high peak hours traffic by partially prefetching files in the users local storage during low peak hours. This paper considers heterogeneous decentralized caching systems where cache of users and content library files may have distinct sizes. The server communicates with the users through a Gaussian broadcast channel. The main contribution of this paper is a novel modulation strategy to map the multicast messages generated in the coded caching delivery phase to the symbols of a signal constellation, such that users can leverage their cached content to demodulate the desired symbols with higher reliability. For the sake of simplicity, in this paper we focus only on uncoded modulation and symbol-by-symbol error probability. However, our scheme in conjunction with multilevel coded modulation can be extended to channel coding over a larger block lengths.

This paper investigates the extended weight enumerators for the number-theoretic insertion/deletion correcting codes. As a special case, this paper provides the Hamming weight enumerators and cardinalities of the non-binary VT codes.

We use prefix-free code distribution matching (PCDM) for rate matching (RM) in some 5G New Radio (NR) deployment scenarios, realizing a wide range of information rates from 1.4 to 6.0 bit/symbol in fine granularity of 0.2 bit/symbol. We study the performance and implementation of the PCDM-based RM, in comparison with the low-density parity-check (LDPC)-based RM, as defined in the 5G NR standard. Simulations in the additive white Gaussian noise channel show that up to 2.16 dB gain in the signal-to-noise ratio can be obtained with the PCDM-based RM at a block error rate of 10-2 when compared to LDPC-based RM in the tested scenarios, potentially at a smaller hardware cost.

In the classical private information retrieval (PIR) setup, a user wants to retrieve a file from a database or a distributed storage system (DSS) without revealing the file identity to the servers holding the data. In the quantum PIR (QPIR) setting, a user privately retrieves a classical file by downloading quantum systems from the servers. The QPIR problem has been treated by Song \emph{et al.} in the case of replicated servers, both without collusion and with all but one servers colluding. In this paper, the QPIR setting is extended to account for MDS-coded servers. The proposed protocol works for any [n,k]-MDS code and t-collusion with t = n - k. Similarly to the previous cases, the rates achieved are better than those known or conjectured in the classical counterparts.

We present new efficient recursive decoders for the Barnes-Wall lattices based on their squaring construction. The analysis of the new decoders reveals a quasi-quadratic complexity in the lattice dimension. The error rate is shown to be close to the universal lower bound in dimensions 64 and 128.

In this work, we study the generalized degrees-of-freedom (GDoF) of downlink and uplink cellular networks, modeled as Gaussian interfering broadcast channels (IBC) and Gaussian interfering multiple access channels (IMAC), respectively. We focus on regimes of low inter-cell interference, where single-cell transmission with power control and treating inter-cell interference as noise (mc-TIN) is GDoF optimal. Recent works have identified two relevant regimes in this context: one in which the GDoF region achieved through mc-TIN for both the IBC and IMAC is a convex polyhedron without the need for time-sharing (mc-CTIN regime), and a smaller (sub)regime where mc-TIN is GDoF optimal for both the IBC and IMAC (mc-TIN regime). In this work, we extend the mc-TIN framework to cellular scenarios where channel state information at the transmitters (CSIT) is limited to finite precision. We show that in this case, the GDoF optimality of mc-TIN extends to the entire mc-CTIN regime, where GDoF benefits due to interference alignment (IA) are lost. Our result constitutes yet another successful application of robust outer bounds based on the aligned images (AI) approach.