The minimum weight perfect matching (MWPM) decoder is the standard decoding strategy for quantum surface codes. However, it suffers a harsh decrease in performance when subjected to biased or nonidentical quantum noise. In this work, we modify the conventional MWPM decoder so that it considers the biases, the nonuniformities, and the relationship between X, Y, and Z errors of the constituent qubits of a given surface code. Our modified approach, which we refer to as the recursive MWPM decoder, obtains an 18% improvement in the probability threshold p(th) under depolarizing noise. We also obtain significant performance improvements when considering biased noise and independent nonidentically distributed (i.ni.d.) error models derived from measurements performed on state-of-the-art quantum processors. In fact, when subjected to i.ni.d. noise, the recursive MWPM decoder yields a performance improvement of 105.5% over the conventional MWPM strategy, and in some cases, it even surpasses the performance obtained over the well-known depolarizing channel.

Structural health monitoring (SHM) using wireless sensor networks (WSN) has become a popular implementation, due to low maintenance and installation costs. These networks commonly use a centralized approach and battery-powered sensors, leading to energy consumption limitations, in both the central unit and the sensors. Therefore, it is of interest to consider the use of passive sensors and distributed processing in the network. In this letter, we present a distributed algorithm for SHM using wireless passive sensor networks (WPSNs) that allows any passive sensor in the network to obtain the distance to its neighbours via backscattering, and hence to detect and signal changes in the monitored structure.

As the correlation matrices of stationary vector processes are block Toeplitz, autoregressive (AR) vector processes are non-stationary. However, in the literature, an AR vector process of finite order is said to be stationary if it satisfies the so-called stationarity condition (i.e., if the spectral radius of the associated companion matrix is less than one). Since the term stationary is used for such an AR vector process, its correlation matrices should somehow approach the correlation matrices of a stationary vector process, but the meaning of somehow approach has not been mathematically established in the literature. In the present paper we give necessary and sufficient conditions for AR vector processes to be stationary. These conditions show in which sense the correlation matrices of an AR stationary vector process asymptotically behave like block Toeplitz matrices. Applications in information theory and in statistical signal processing of these necessary and sufficient conditions are also given.

Time-varying quantum channels (TVQCs) have been proposed as a model to include fluctuations of the relaxation (T1) and dephasing times (T2). In previous works, realizations of multiqubit TVQCs have been assumed to be equal for all the qubits of an error correction block, implying that the random variables that describe the fluctuations of T1 and T2 are block-to-block uncorrelated but qubit-wise perfectly correlated for the same block. In this article, we perform a correlation analysis of the fluctuations of the relaxation times of five multiqubit quantum processors. Our results show that it is reasonable to assume that the fluctuations of the relaxation and dephasing times of superconducting qubits are local to each of the qubits of the system. Based on these results, we discuss the multiqubit TVQCs when the fluctuations of the decoherence parameters for an error correction block are qubit-wise uncorrelated (as well as from block-to-block), a scenario we have named the fast time-varying quantum channel (FTVQC). Furthermore, we lower-bound the quantum capacity of general FTVQCs based on a quantity we refer to as the ergodic quantum capacity. Finally, we use numerical simulations to study the performance of quantum error correction codes when they operate over FTVQCs.

Surface codes are generally studied based on the assumption that each of the qubits that make up the surface code lattice suffers noise that is independent and identically distributed (i.i.d.). However, real benchmarks of the individual relaxation (T1) and dephasing (T2) times of the constituent qubits of state-of-the-art quantum processors have recently shown that the decoherence effects suffered by each particular qubit actually vary in intensity. In consequence, in this paper we introduce the independent nonidentically distributed (i.n.i.d.) noise model, a decoherence model that accounts for the nonuniform behavior of the decoherence parameters of qubits. Additionally, we use the i.n.i.d. model to study how it affects the performance of a specific family of quantum error correction codes known as planar codes. For this purpose we employ data from four state-of-the-art superconducting processors: ibmq_brooklyn, ibm_washington, Zuchongzhi, and Rigetti Aspen-M-1. Our results show that the i.i.d. noise assumption overestimates the performance of surface codes, which can suffer up to 95% performance decrements in terms of the code pseudothreshold when they are subjected to the i.n.i.d. noise model. Furthermore, we consider and describe two methods which enhance the performance of planar codes under i.n.i.d. noise. The first method involves a so-called reweighting process of the conventional minimum weight perfect matching (MWPM) decoder, while the second one exploits the relationship that exists between code performance and qubit arrangement in the surface code lattice. The optimum qubit configuration derived through the combination of the previous two methods can yield planar code pseudothreshold values that are up to 650% higher than for the traditional MWPM decoder under i.n.i.d. noise.

We have presented a method to detect degenerate errors in sparse quantum codes in a computationally efficient manner. We have also shown how this method is less complex than other existing strategies to compute the logical error rate of sparse CSS quantum codes. Making use of our scheme, we have shown how sparse quantum codes have a significant percentage of degenerate errors. This means that the discrepancy between the logical error rate and the physical error rate is exacerbated for sparse quantum codes. Our results show that, for specific families of QLDPC codes, performance may be up to 20% better than would be expected from previous results in the literature that are based on the physical error rate. In addition, these simulation outcomes serve to show how performance may be improved by constructing degenerate quantum codes, and they also speak toward the positive impact that modified decoding strategies can have on the performance of sparse quantum codes.

Recent experimental studies have shown that the relaxation time T-1 and the dephasing time T-2 of superconducting qubits fluctuate considerably over time. Time-varying quantum channel (TVQC) models have been proposed in order to consider the time-varying nature of the parameters that define qubit decoherence. This dynamic nature of quantum channels causes a degradation of the performance of quantum error correction codes (QECCs) that is portrayed as a flattening of their error rate curves. In this article we introduce the concepts of quantum outage probability and quantum hashing outage probability as asymptotically achievable error rates by a QECC with the quantum rate RQ operating over a TVQC. We derive closed-form expressions for the family of time-varying amplitude damping channels and study their behavior for different scenarios. We quantify the impact of time variation as a function of the relative variation of T-1 around its mean. We conclude that the performance of QECCs is limited in many cases by the inherent fluctuations of their decoherence parameters and corroborate that parameter stability is crucial to maintain the excellent performance observed over static quantum channels.

In recent years, various forecasters have been developed to decrease the uncertainty related to the intermittent nature of photovoltaic generation. While the vast majority of these forecasters are usually just focused on deterministic or probabilistic prediction points, few studies have been carried out in relation to prediction intervals. In increasing the reliability of photovoltaic generators, being able to set a confidence level is as important as the forecaster's accuracy. For instance, changes in ambient temperature or solar irradiation produce variations in photovoltaic generators' output power as well as in control parameters such as cell temperature and open voltage circuit. Therefore, the aim of this paper is to develop a new mathematical model to quantify the confidence interval of ambient temperature in the next 10 min. Several error metrics, such as the prediction interval coverage percentage, the Winkler score and the Skill score, are calculated for 95%, 90% and 85% confidence levels to analyse the reliability of the developed model. In all cases, the prediction interval coverage percentage is higher than the selected confidence interval, which means that the estimation model is valid for practical photovoltaic applications.

In the era of the Internet of Things, there are many applications where numerous devices are deployed to acquire information and send it to analyse the data and make informed decisions. In these applications, the power consumption and price of the devices are often an issue. In this work, analog coding schemes are considered, so that an ADC is not needed, allowing the size and power consumption of the devices to be reduced. In addition, linear and DFT-based transmission schemes are proposed, so that the complexity of the operations involved is lowered, thus reducing the requirements in terms of processing capacity and the price of the hardware. The proposed schemes are proved to be asymptotically optimal among the linear ones for WSS, MA, AR and ARMA sources.

Aircraft manufacturers aim to decrease the fuel consumption based on reducing weight and increasing the subsystem efficiency. Hence, the electric power system (EPS) acquires great relevance because it must be efficient and lightweight. Any change in the EPS must not affect the aircraft's electrical safety, which under a traditional decentralized EPS strategy is ensured by redundancy. Recently, several decentralized EPS strategies based on the introduction of multiport power converters have arisen. Such strategies meet the established safety goals since the aforementioned devices make it possible to recalculate the path to continue powering the loads in case of failure. However, the literature does not address how to connect such multiport power converters. The main contribution of this article is to present a low-complexity algorithm that minimizing the redundancy of wiring, provides a fault-tolerant power transmission network. This is done under a decentralized EPS strategy where multiport power converters are used. The proposed strategy is evaluated on Boeing 787 aircraft, where we compare the length of the cables both under a traditional decentralized network configuration (where the redundancy option is used to ensure the safety of operation) and in the network provided by our algorithm. A saving of 66.6% is obtained.

In this paper we propose a mathematical model for the fuel consumption analysis during aircraft cruise. A closed-form formula that expresses the aircraft's weight variation over time, and hence, the fuel flow rate, is obtained as a result. Furthermore, a closed-form expression of the aircraft's main performance parameters is also obtained. We compare the values of such parameters computed by using the Piano-X software and computed by using our mathematical model. Simulation results confirm that our mathematical model provides results very close to reality. Finally, the closed-form formula of the fuel flow rate provided by our model is used to improve the calculation of the carbon dioxide emissions for four example routes, which, unlike here, are usually obtained under the assumption of a constant value of the fuel flow rate.

In this paper we consider the problem of transmitting spatially Correlated Information Sources (CIS) over the Additive White Gaussian Noise (AWGN) Multiple Access Channel (MAC) with transmitted energy constraint. It is well known that the system performance is optimized if the codewords are designed to take advantage of the correlation among sources in the multiple access channel. To that end, we make use of Rate Compatible Modulation (RCM) codes, whose sparse nature is advantageous to preserve the source correlation in the MAC. In order to exploit the source correlation, the proposed RCM-CIS system is comprised of a set of RCM codes that share the same random structure but with each code having its own weight values that are jointly designed. At the receiver, non-binary decoding is applied to avoid short length cycles that arise in the factor graph, which is obtained by jointly considering the source correlation and the RCM codes. Simulation results show that for high throughput transmission rate RCM-CIS has good performance in terms of the BER vs SNR, attaining values below the Shannon limit if source-channel separation is assumed. As shown by the numerical results, the proposed RCM system inherits the high error floors encountered in point-to-point RCM codes. In order to lower the error floor, we propose the use of a Low Density Generation Matrix (LDGM) code in parallel with the proposed RCM structure. The LDGM system transmits a small fraction of the total coded sequence, and it is capable of correcting the residual errors produced by the RCM-CIS system.

The well-documented capacity-approaching performance of sparse codes in the realm of classical communications has inspired the search for their quantum counterparts. Sparse quantum codes are generally built as the amalgamation of two robust classical codes and are decoded via classical decoding algorithms. However, the quantum paradigm presents phenomena that act in a deleterious manner on sparse quantum codes when they are decoded based on classical methodologies. One such phenomenon is known as degeneracy, and it is a major contributor to why sparse quantum codes do not entirely evoke the stupendous error correcting abilities of their classical counterparts. In this paper, we adopt a group theoretical approach to discuss the issue of degeneracy as it relates to sparse quantum codes. Furthermore, we compare the decoding process of sparse quantum codes with that of sparse classical codes, illustrating the challenges that appear in the quantum domain. Finally, we provide a detailed example to illustrate the effects of degeneracy on sparse quantum codes and the challenges of designing an optimum decoder for these schemes.

The decoherence effects experienced by the qubits of a quantum processor are generally characterized using the amplitude damping time (T-1) and the dephasing time (T-2). Quantum channel models that exist at the time of writing assume that these parameters are fixed and invariant. However, recent experimental studies have shown that they exhibit a time-varying (TV) behaviour. These time-dependant fluctuations of T-1 and T-2, which become even more pronounced in the case of superconducting qubits, imply that conventional static quantum channel models do not capture the noise dynamics experienced by realistic qubits with sufficient precision. In this article, we study how the fluctuations of T-1 and T-2 can be included in quantum channel models. We propose the idea of time-varying quantum channel (TVQC) models, and we show how they provide a more realistic portrayal of decoherence effects than static models in some instances. We also discuss the divergence that exists between TVQCs and their static counterparts by means of a metric known as the diamond norm. In many circumstances this divergence can be significant, which indicates that the time-dependent nature of decoherence must be considered, in order to construct models that capture the real nature of quantum devices

Quantum low-density-generator-matrix (QLDGM) codes are known to exhibit great error correction capabilities, surpassing existing quantum low-density-parity-check (QLDPC) codes and other sparse-graph schemes over the depolarizing channel. Most of the research on QLDPC codes and quantum error correction (QEC) is conducted for the symmetric instance of the generic Pauli channel, which incurs bit flips, phase flips, or a combination of both with the same probability. However, due to the behavior of the materials they are built from, some quantum devices must be modelled using a different channel model capable of accurately representing asymmetric scenarios in which the likelihood of a phase flip is higher than that of a bit flip. In this work, we study the design of QLDGM CSS codes for such Pauli channels. We show how codes tailored to the depolarizing channel are not well suited to these asymmetric environments and we derive methods to aptly design QLDGM CSS codes for this paradigm.

The COVID-19 pandemic has had severe consequences on the global economy, mainly due to indiscriminate geographical lockdowns. Moreover, the digital tracking tools developed to survey the spread of the virus have generated serious privacy concerns. In this paper, we present an algorithm that adaptively groups individuals according to their social contacts and their risk level of severe illness from COVID-19, instead of geographical criteria. The algorithm is fully distributed and therefore, individuals do not know any information about the group they belong to. Thus, we present a distributed clustering algorithm for adaptive pandemic control.

We propose a new Non-Orthogonal Multiple Access (NOMA) coding scheme based on the use of a Rate Compatible Modulation (RCM) encoder for each user. By properly designing the encoders and taking advantage of the additive nature of the Multiple Access Channel (MAC), the joint decoder from the inputs of all the users can be represented by a bipartite graph corresponding to a standard point-to-point RCM structure with certain constraints. Decoding is performed over this bipartite graph utilizing the sum-product algorithm. The proposed scheme allows the simultaneous transmission of a large number of uncorrelated users at high rates, while the decoding complexity is the same as that of standard point-to-point RCM schemes. When Rayleigh fast fading channels are considered, the BER vs SNR performance improves as the number of simultaneous users increases, as a result of the averaging effect.

Industry 4.0 applications foster new business opportunities, but they also pose new and challenging requirements, such as low latency communications and highly reliable systems. They would likely exploit novel wireless technologies (5G), but it would also become crucial using architectures that appropriately support them. In this sense, the combination of fog and cloud computing represents a potential solution, since it can dynamically allocate the workload depending on the specific needs of each application. In this paper, our main goal is to provide a highly reliable and dynamic architecture, which minimizes the time that an end node or user, spends in downloading the required data. In order to achieve this, we have developed an optimal distribution algorithm that decides the amount of information that should be stored at, or retrieved from, each node, to minimize the overall data download time. Our scheme is based on various parameters and it exploits Network Coding (NC) as a tool for data distribution, as a key enabler of the proposed solution. We compare the performance of the proposed scheme with other alternative solutions, and the results show that there is a clear gain in terms of the download time.

Quantum information is prone to suffer from errors caused by the so-called decoherence, which describes the loss in coherence of quantum states associated to their interactions with the surrounding environment. This decoherence phenomenon is present in every quantum information task, be it transmission, processing or even storage of quantum information. Consequently, the protection of quantum information via quantum error correction codes (QECC) is of paramount importance to construct fully operational quantum computers. Understanding environmental decoherence processes and the way they are modeled is fundamental in order to construct effective error correction methods capable of protecting quantum information. Moreover, quantum channel models that are efficiently implementable and manageable on classical computers are required in order to design and simulate such error correction schemes. In this article, we present a survey of decoherence models, reviewing the manner in which these models can be approximated into quantum Pauli channel models, which can be efficiently implemented on classical computers. We also explain how certain families of quantum error correction codes can be entirely simulated in the classical domain, without the explicit need of a quantum computer. A quantum error correction code for the approximated channel is also a correctable code for the original channel, and its performance can be obtained by Monte Carlo simulations on a classical computer.

Quantum low-density generator matrix (QLDGM) codes based on Calderbank-Steane-Shor (CSS) con-structions have shown unprecedented error correction capabilities, displaying much improved performance in comparison to other sparse-graph codes. However, the nature of CSS designs and the manner in which they must be decoded limit the performance that is attainable with codes that are based on this construction. This motivates the search for quantum code design strategies capable of avoiding the drawbacks associated with CSS codes. In this article, we introduce non-CSS quantum code constructions based on classical LDGM codes. The proposed codes are derived from CSS QLDGM designs by performing specific row operations on their quantum parity check matrices to modify the associated decoding graphs. The application of this method results in performance improvements in comparison to CSS QLDGM codes, while also allowing for greater flexibility in the design process. The proposed non-CSS QLDGM scheme outperforms the best quantum low-density parity check codes that have appeared in the literature.

In this paper, we present a low-complexity coding strategy to encode (compress) finite-length data blocks of Gaussian vector sources. We show that for large enough data blocks of a Gaussian asymptotically wide sense stationary (AWSS) vector source, the rate of the coding strategy tends to the lowest possible rate. Besides being a low-complexity strategy it does not require the knowledge of the correlation matrix of such data blocks. We also show that this coding strategy is appropriate to encode the most relevant Gaussian vector sources, namely, wide sense stationary (WSS), moving average (MA), autoregressive (AR), and ARMA vector sources.

The introduction of the Internet of Things (IoT) is creating manifold new services and opportunities. This new technological trend enables the connection of a massive number of devices among them and with the Internet. The integration of IoT with cloud platforms also provides large storage and computing capabilities, enabling Big Data analytics and bidirectional communication between devices and users. Novel research directions are showing that Network Coding (NC) can increase the robustness and throughput of wireless networks, as well as that Homomorphic Encryption (HE) can be used to perform computations in the cloud while maintaining data privacy. In this paper, we overview the benefits of NC and HE along the entire vertical of cloud-based IoT architectures. By merging both technologies, the architecture may offer manifold advantages: First, it provides end-to-end data privacy, from end-devices to end-users. Second, sensitive data can be stored in public cloud platforms without concern about their privacy. In addition, clouds can perform advanced operations in a confidential manner, without the need to access actual data. Finally, latency can be reduced and the reliability of the system is increased. We show state-of-the-art works that demonstrate the role of both technologies in this type of architectures on a review basis. Furthermore, we describe the main characteristics of NC and HE and also discuss their benefits and limitations, as well as the emerging open challenge

Quantum turbo codes (QTC) have shown excellent error Corrección capabilities in the setting of quantum communication, achieving a performance less than 1 dB away from their corresponding hashing bounds. Existing QTCs have been constructed using uniform random interleavers. However, interleaver design plays an important role in the optimization of classical turbo codes. Consequently, inspired by the widely used classical-to-quantum isomorphism, this paper studies the integration of classical interleaving design methods into the paradigm of quantum turbo coding. Simulations results demonstrate that error floors in QTCs can be lowered significantly, while decreasing memory consumption, by proper interleaving design without increasing the overall decoding complexity of the system.

Quantum turbo codes (QTC) have shown excellent error correction capabilities in the setting of quantum communication, achieving a performance less than 1 dB away from their corresponding hashing bounds. Decoding for QTCs typically assumes that perfect knowledge about the channel is available at the decoder. However, in realistic systems, such information must be estimated, and thus, there exists a mismatch between the true channel information and the estimated one. In this article, we first heuristically study the sensitivity of QTCs to such mismatch. Then, existing estimation protocols for the depolarizing channel are presented and applied in an off-line manner to provide bounds on how the use of off-line estimation techniques affects the error correction capabilities of QTCs. Finally, we present an on-line estimation method for the depolarizing probability, which, different from off-line estimation techniques, neither requires extra qubits, nor increases the latency. The application of the proposed method results in a performance similar to that obtained with QTCs using perfect channel information, while requiring less stringent conditions on the variability of the channel than off-line estimation techniques.

In this paper, we look at the problem of implementing high-throughput Joint Source- Channel (JSC) coding schemes for the transmission of binary sources with memory over AWGN channels. The sources are modeled either by a Markov chain (MC) or a hidden Markov model (HMM). We propose a coding scheme based on the Burrows-Wheeler Transform (BWT) and the parallel concatenation of Rate-Compatible Modulation and Low-Density Generator Matrix (RCM-LDGM) codes. The proposed scheme uses the BWT to convert the original source with memory into a set of independent non-uniform Discrete Memoryless (DMS) binary sources, which are then separately encoded, with optimal rates, using RCM-LDGM codes.

This paper proposes a novel scheme for the slow block fading Gaussian multiple access relay channel inspired by the compute-and-forward (CoF) relaying strategy. The CoF relaying strategy exploits interference to obtain significantly higher rates between users in a network by decoding linear functions of the transmitted messages. Unlike other approaches in the literature, our approach is valid for any number of transmitters and, most importantly, it only requires channel state information at the receiver side, while it still attains similar or higher rates than the other approaches found in the literature.

This paper proposes an extrinsic information transfer (EXIT) chart analysis and an asymptotic bit error rate (BER) prediction method to speed up the design of high rate RCM-LDGM hybrid codes over AWGN and fast Rayleigh channels. These codes are based on a parallel concatenation of a rate compatible modulation (RCM) code with a low-density generator matrix (LDGM) code. The decoder uses the iterative sum-product algorithm to exchange information between the variable nodes (VNs) and the two types of constituent check nodes: RCM-CN and LDGM-CN. The novelty of the proposed EXIT chart procedure lies on the fact that it mixes together the analog RCM check nodes with the digital LDGM check nodes, something not possible in previous multi-edge EXIT charts proposed in the literature.

The adoption of both Cyber¿Physical Systems (CPSs) and the Internet-of-Things (IoT) has enabled the evolution towards the so-called Industry 4.0. These technologies, together with cloud computing and artificial intelligence, foster new business opportunities. Besides, several industrial applications need immediate decision making and fog computing is emerging as a promising solution to address such requirement. In order to achieve a cost-efficient system, we propose taking advantage from spot instances, a new service offered by cloud providers, which provide resources at lower prices. The main downside of these instances is that they do not ensure service continuity and they might suffer from interruptions. An architecture that combines fog and multi-cloud deployments along with Network Coding (NC) techniques, guarantees the needed fault-tolerance for the cloud environment, and also reduces the required amount of redundant data to provide reliable services. In this paper we analyze how NC can actually help to reduce the storage cost and improve the resource efficiency for industrial applications, based on a multi-cloud infrastructure. The cost analysis has been carried out using both real AWS EC2 spot instance prices and, to complement them, prices obtained from a model based on a finite Markov chain, derived from real measurements. We have analyzed the overall system cost, depending on different parameters, showing that configurations that seek to minimize the storage yield a higher cost reduction, due to the strong impact of storage cost

This paper focuses on the modeling, simulation, and experimental verification of wideband single-input single-output (SISO) mobile fading channels for indoor propagation environments. The indoor reference channel model is derived from a geometrical rectangle scattering model, which consists of an infinite number of scatterers. It is assumed that the scatterers are exponentially distributed over the two-dimensional (2D) horizontal plane of a rectangular room. Analytical expressions are derived for the probability density function (PDF) of the angle of arrival (AOA), the PDF of the propagation path length, the power delay profile (PDP), and the frequency correlation function (FCF). An efficient sum-of-cisoids (SOC) channel simulator is derived from the nonrealizable reference model by employing the SOC principle. It is shown that the SOC channel simulator approximates closely the reference model with respect to the FCF. The SOC channel simulator enables the performance evaluation of wideband indoor wireless communication systems with reduced realization expenditure. Moreover, the rationality and usefulness of the derived indoor channel model is confirmed by various measurements at 2.4, 5, and 60¿GHz.

Non-circular or improper Gaussian signaling has proven beneficial in several interference-limited wireless networks. However, all implementable coding schemes are based on finite discrete constellations rather than Gaussian signals. In this paper, we propose a new family of improper constellations generated by widely linear processing of a square M-QAM (quadrature amplitude modulation) signal. This family of discrete constellations is parameterized by , the circularity coefficient and a phase phi. For uncoded communication systems, this phase should be optimized as phi * to maximize the minimum Euclidean distance between points of the improper constellation, therefore minimizing the bit error rate (BER). For the more relevant case of coded communications, where the coded symbols are constrained to be in this family of improper constellations using phi*, it is shown theoretically and further corroborated by simulations that, except for a shaping loss of 1.53 dB encountered at a high signal-to-noise ratio (snr), there is no rate loss with respect to the improper Gaussian capacity. In this sense, the proposed family of constellations can be viewed as the improper counterpart of the standard proper M-QAM constellations widely used in coded communication systems.