The machinery of industrial environments was connected to the Internet years ago with the scope of increasing their performance. However, this change made such environments vulnerable against cyber-attacks that can compromise their correct functioning resulting in economic or social problems. Moreover, implementing cryptosystems in the communications between operational technology (OT) devices is a more challenging task than for information technology (IT) environments since the OT networks are generally composed of legacy elements, characterized by low-computational capabilities. Consequently, implementing cryptosystems in industrial communication networks faces a tradeoff between the security of the communications and the amortization of the industrial infrastructure. Critical infrastructure (CI) refers to the industries which provide key resources for the daily social and economical development, e.g., electricity. Furthermore, a new threat to cybersecurity has arisen with the theoretical proposal of quantum computers, due to their potential ability of breaking state-of-the-art cryptography protocols, such as RSA or elliptic curve cryptography. Many global agents have become aware that transitioning their secure communications to a quantum secure paradigm is a priority that should be established before the arrival of fault-tolerance. In this article, we aim to describe the problematic of implementing post-quantum cryptography (PQC) to CI environments. For doing so, we describe the requirements for these scenarios and how they differ against IT. We also introduce classical cryptography and how quantum computers pose a threat to such security protocols. Furthermore, we introduce state-of-the-art proposals of PQC protocols and present their characteristics. We conclude by discussing the problematic of integrating PQC in industrial environments.

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.

Using some recent results on asymptotically equivalent sequences of matrices, we present in this paper, a new derivation of the capacity formula given by Brandenburg and Wyner for a discrete-time Gaussian multiple-input-multiple-output channel with memory. In this paper, we tackle not only the case considered by them, where the number of channel inputs and the number of channel outputs are the same, but also when both numbers are different.

The wide availability of power distribution cables provides an interesting no-new-wires communication channel. However, its electrical characteristics make it a harsh environment for the data transmission purpose and prevent the deployment of services with high reliability requirements. This paper proposes and implements an OSI-Layer2 network coding-based cooperative scheme with the aim of improving communication reliability in indoor narrowband powerline channels. The proposed scheme uses random linear network coding with a sliding window and relaying. We use network coding to replace the retransmissions triggered by legacy subsequent repeat request (ARQ) schemes. We evaluate the performance of our approach in terms of throughput and delay. Regarding the throughput achieved in harsh environments, we show that our scheme often more than doubles the throughput of existing legacy ARQ schemes. At the same time, and even under the large variation of traffic characteristics, it is shown that the delay is likely to be upper bounded by a few seconds, a bound that cannot be guaranteed in other existing transmission techniques.

This paper proposes a low-complexity coding strategy for the flat fading Gaussian Multiple Access Channel (MAC) based on the concept of Compute-and-Forward. To assess the performance of the proposed coding scheme, we compare the block error probability of a particular code implementation with that of an optimal Gaussian MAC code with the same rates, when applied to our slow fading Gaussian MAC. We show by simulation that even using very short codewords, our strategy beats standard Successive Interference Cancellation techniques by obtaining a good performance with low coding and decoding complexity.

In this paper we propose a coding and decoding strategy for computing modulo M sums in a Multiple Access Channel over Additive White Gaussian Noise based on linear codes in FM. The complexity of our strategy is the same as the complexity of the linear code and we show that when there are 2 users in the network and M = 2, our strategy is close to the theoretical limit. We also provide some figures in which it is possible to appreciate that good codes in a point to point scenario are also good codes for computing modulo M sums.

In this paper, an interactive tool for learning the fundamental concepts of communications systems from an information theory point of view is presented. This tool is composed of two parts: a C++ library and a Graphical User Interface application in Matlab. The C++ library is designed following an object-oriented structure and is fully scalable (it is open for future updates). The Matlab-GUI application is a friendly interface that aids undergraduate students to understand the theory. Some of the tool's capabilities are illustrated through classroom examples. In addition, this tool is designed to improve the students' theoretical knowledge of information theory.

In this paper we prove the asymptotic formula that has been recently used as a numerical integration method to approximate the relative entropy (or Kullback-Leibler distance) between two probability density functions with bounded support in terms of functions of Hermitian Toeplitz matrices. To prove that asymptotic formula we use the Gray concept of asymptotically equivalent sequences of matrices.

In this paper, we propose a Decode-and-Forward (DF) relaying scheme for the multihop transmission in wireless networks, where the information generated by an independent source has to be sent to a far destination based on multiplerelay cooperation. The proposed DF scheme blends together convolutional channel coding with linear combination of blocks of data over a finite field. The performance of the proposed system is compared with reference schemes previously proposed in the literature. We provide simulation results showing that using blocks of K = 13 information bits, our scheme clearly outperforms these reference schemes that use blocks of K = 1500 information bits. Moreover, we show that the proposed DF scheme is suitable for large multi-hop networks with relays that share their resources with other networks since: 1) a negligible performance degradation is obtained for adding more hops; and 2) most of the iterative gain at the decoding is achieved in less than 10 iterations.

This paper proposes a novel joint non-binary network-channel code for the Time-Division Decode-and-Forward Multiple Access Relay Channel (TD-DF-MARC), where the relay linearly combines — over a non-binary finite field — the coded sequences from the source nodes. A method based on an EXIT chart analysis is derived for selecting the best coefficients of the linear combination. Moreover, it is shown that for different setups of the system, different coefficients should be chosen in order to improve the performance. This conclusion contrasts with previous works where a random selection was considered. Monte Carlo simulations show that the proposed scheme outperforms, in terms of its gap to the outage probabilities, the previously published joint network-channel coding approaches. Besides, this gain is achieved by using very short-length codewords, which makes the scheme particularly attractive for low-latency applications.

An extended analog joint source-channel coding (JSCC) multiple description (MD) scheme is introduced. This new scheme extends a previously presented analog JSCC-MD scheme in order to work at different bandwidth ratios. This scheme is suitable for transmissions through parallel AWGN on-off channels and parallel slow-fading channels. The strengths of the proposed scheme in comparison with other coding alternatives are its coding/decoding simplicity and low delay, and its optimality in terms of distortion exponent in the fading parallel channels.

In this paper, we develop a new power-efficient algorithm for Wireless Sensor Networks (WSN) in order to obtain, in a distributed manner, the Projection of an observed sampled spatial field on a subspace of lower dimension. This is an important problem that is motivated in various applications where there are well defined subspaces of interest (e.g. spectral maps in cognitive radios). As opposed to traditional Gossip Algorithms used for subspace projection assuming separation of channel coding and computation, our algorithm combines Computational Coding and a modification of existing Gossip Algorithms, achieving important savings in convergence time and yielding an exponential decrease in energy consumption as the size of the network increases.

In this paper, we develop a novel strategy to compute the transition matrix for the projection problem in a distributed fashion through gossiping in Wireless Sensor Networks. So far, the transition matrix had to be computed off-line by a third party and then provided to the network. The Subspace Projection Problem is useful in various application scenarios (e.g. spectral spatial maps in cognitive radios) and consists of projecting the observed sampled spatial field into a subspace of interest with lower dimension. Although the actual exact computation of the optimal transition matrix is not feasible in a distributed way, we develop an algorithm that is based on well known results from linear algebra and a distributed genetic algorithm in order to compute an approximation of the optimal matrix to a desired precision.

In this paper, we describe an innovative queue management mechanism in order to achieve an optimal use of shared communication resources. The target scenario contemplates different data flows sharing the same network resources at the same time. The main challenge over this scenario is to achieve the required QoS (Quality of Service) to redistribute real-time and high constraints services. The described queue management algorithm, proposes an innovative queue utilization method based on the combination of the data flows to be redistributed, providing a more efficient use of the network resources, and inducing important improvements in the caused delay and jitter. Present work describes the design of a mechanism based on Network Coding that achieves new QoS up-bound limits and reduces the queue occupancy that cannot be achieved with store-and-forward mechanisms. Finally, we describe the very promising preliminary results obtained by the simulation of a still open study, and discover a new potential future research field.

We propose a low complexity analog joint source channel coding Multiple Description (MD) scheme for transmitting the symbols of a Gaussian source across a pair of independent AWGN channels. The outputs of these channels have each a separated receiver, whereas a third receiver has both outputs available. At the transmitter side, a pair of bandwidth-reduction analog mappings are used for joint source-channel coding. The presented scheme has the inherent advantage over digital MD schemes based on separation, that coding and decoding can be performed by using a single-letter (or symbol), a strategy that is very suitable for applications where latency originated by the digital compression and the error correcting coding can not be tolerated. Our scheme achieves a performance that is competitive as compared to the optimal region while having a very low complexity and delay.

In this paper, we propose a novel decode-combine-forward scheme for the multi-hop transmission in ad-hoc wireless networks, where the information generated by two independent sources has to be sent to a common destination based on multiple-relay cooperation. The proposed scheme blends together LDPC channel coding with linear combination of blocks of data over a finite field. The performance of the proposed system is compared with two reference schemes previously proposed on the literature. We provide simulation results which show that our scheme clearly outperforms these reference systems.

In this paper we present a novel joint network-channel coding scheme for the time-division Multiple Access Relay Channel (MARC), which combines Bit-Interleaved Coded Modulation with iterative decoding (BICM-ID) based on nonbinary Low-Density Parity Check (LDPC) codes, along with the linear combination of blocks of data at the relay. The common receiver iteratively exchanges soft information between a joint soft demapper and the LDPC decoder associated to the transmitting nodes. The performance of the proposed system is compared, in terms of Frame Error Rate (FER) and through intensive Monte Carlo simulations, with the corresponding theoretical outage rate for different values of the spectral efficiency of the overall setup. Two main conclusions are drawn: 1) small FER degradation is obtained as the spectral efficiency increases; and 2) no diversity is lost with respect to the theoretical outage rate.

The present paper considers a special class of vector random processes that we call multivariate asymptotically wide sense stationary (WSS) processes. A multivariate random process is said to be asymptotically WSS if it has constant mean and the sequence of its autocorrelation matrices is asymptotically equivalent (a.e.) to the sequence of autocorrelation matrices of some multivariate WSS process. It is shown that this class of processes contains meaningful processes other than multivariate WSS processes. In particular, we give sufficient conditions for multivariate moving average (MA) processes, multivariate autoregressive (AR) processes and multivariate autoregressive moving average (ARMA) processes to be asymptotically WSS. Furthermore, in order to solve multiple-input-multiple-output (MIMO) problems in communications and signal processing involving this kind of processes, we extend the Gray definition of a.e. sequences of matrices and his main results on these sequences to non-square matrices. As an example, the derived results on a.e. sequences of non-square matrices are applied to compute the differential entropy rate and the minimum mean square error (MMSE) for a linear predictor of a multivariate asymptotically WSS process.

The Burrows-Wheeler Transform (BWT) [1] is a block sorting algorithm which has been proven to be useful in compressing text data [2]. More recently, schemes based on the BWT have been proposed for lossless data compression using LDPC [3]-[5] and Fountain [6] codes, as well as for joint source-channel coding of sources with memory [7],[8]. In this paper we propose a source-controlled Turbo coding scheme for the transmission of sources with memory over AWGN channels also based on the Burrows-Wheeler Transform. Our approach combines the BWT with a Turbo code and employs different energy allocation techniques for the encoded symbols before their transmission. Simulation results show that the performance of the designed scheme is close (within 1.5 dB) to the theoretical Shannon limit.

For the engineering community, Gray's tutorial monograph on Toeplitz and circulant matrices has been, and remains, the best elementary introduction to the Szego theory on large Toeplitz matrices. In this paper, the most important results of the cited monograph are generalized to block Toeplitz (BT) matrices by maintaining the same mathematical tools used by Gray, that is, by using asymptotically equivalent sequences of matrices. As applications of these results, the geometric minimum mean square error (MMSE) for both an infinite-length multivariate linear predictor and an infinite-length decision feedback equalizer (DFE) for multiple-input-multiple-output (MIMO) channels, are obtained as a limit of the corresponding finite-length cases. Similarly, a short derivation of the well-known capacity of a time-invariant MIMO Gaussian channel with intersymbol interference (ISI) and fixed input covariance matrix is also presented.

Given an AWGN channel, we look at the problem of designing a source controlled binary antipodal signaling system for transmitting blocks of binary symbols generated either by a Markov chain source (MC) or by a hidden Markov model source (HMM). The goal is to minimize the average SNR required for any given block error rate. The particular case where the binary source is memoryless with nonuniform symbol probabilities has been studied in I. Korn et al. (2003) by optimally allocating the signal energies. In this paper we extend the previous work to include the important case of sources with memory. The proposed system integrates the block sorting burrows wheeler transform (BWT) with an optimal energy allocation scheme based on the first order probabilities of the transformed symbols. This method is compared with standard communication techniques for the transmission of sources with memory.

Toeplitz matrices and functions of Toeplitz matrices (such as the inverse of a Toeplitz matrix, powers of a Toeplitz matrix or the exponential of a Toeplitz matrix) arise in many different theoretical and applied fields. They can be found in the mathematical modelling of problems where some kind of shift invariance occurs in terms of space or time. For the engineering community, R. M. Gray's tutorial monograph on Toeplitz and circulant matrices has been, and remains, the best elementary introduction to the Szego distribution theory on the asymptotic behavior of continuous functions of Toeplitz matrices. His asymptotic results, widely used in engineering due to the simplicity of its mathematical proofs, do not concern individual entries of these matrices but rather, they describe an "average" behavior. However, there are important applications where the asymptotic expressions of interest are directly related to the convergence of a single entry of a continuous function of a Toeplitz matrix. To gain insight into the solutions of this sort of problems, the present paper introduces new theoretical results regarding the convergence of these entries, that can be derived by using similar mathematical tools.

As data rates are increasing continuously in wireless networks, additional ways of improving system performance and providing higher rates is needed. One scheme that has recently attracted a lot of attention, is using relays in order to provide additional diversity, especially in scenarios that use of multiple antennas may not be practical at transmit or receive sites. In this paper, we will present a novel channel assignment scheme at the relay which will provide full diversity for the case in which two non-cooperative independent users communicate with their destination through a single relay and by using only two frequency channels. As the simulation results show, through use of this approach, significant performance improvement is achieved in comparison with the case in which each user and its corresponding relay use an independent channel for transmission. In addition, the proposed scheme is applied to two main relay-based transmission systems, namely amplify and forward (AF) and decode and forward (DF). As the results show, the performance of DF algorithms is especially superior in scenarios in which the relay is closer to the receiver.

Toeplitz matrices and functions of Toeplitz matrices (such as the inverse of a Toeplitz matrix, powers of a Toeplitz matrix or the exponential of a Toeplitz matrix) arise in many different theoretical and applied fields. They can be found in the mathematical modeling of problems where some kind of shift invariance occurs in terms of space or time. R. M. Gray's excellent tutorial monograph on Toeplitz and circulant matrices has been, and remains, the best elementary introduction to the Szegö distribution theory on the asymptotic behavior of continuous functions of Toeplitz matrices. His asymptotic results, widely used in engineering due to the simplicity of its mathematical proofs, do not concern individual entries of these matrices but rather, they describe an “average” behavior. However, there are important applications where the asymptotic expressions of interest are directly related to the convergence of a single entry of a continuous function of a Toeplitz matrix. Using similar mathematical tools and to gain insight into the solutions of this sort of problems, the present correspondence derives new theoretical results regarding the convergence of these entries.

Abstract In this paper, we investigate how to increase the capacity of GSM (Global System for Mobile communications) radio interfaces in subway tunnel environments by means of antenna arrays and Space–Time (ST) receivers. We address the modeling, both theoretically and experimentally, of the multiple‐antenna wireless channels encountered in subway tunnels. We demonstrate that propagation is conveniently modeled by a flat‐fading channel, but there exist strong spatial correlations among channel components that decrease capacity and affect receivers' performance. Different space–time GSM receiving strategies have also been investigated. We first consider ST equalization techniques that only account for the noise and the controlled Intersymbol Interference (ISI) introduced by the modulation format employed in GSM. Then, we analyze the performance of receivers that incorporate ST coding capabilities and show the superior performance of iterative MAP (Maximum a Posteriori) receivers that interchange soft information among the equalizer and the ST decoder. All receivers are evaluated with experimental channels measured in the subway of Paris. Copyright © 2002 John Wiley & Sons, Ltd.

This letter presents the main statistical characterization of the underlying error process obtained in the case of the Digital European Cordless Telecommunications (DECT) radio system. By simulation of the transmission Link, error sequences are generated for different channel parameters. Relevant statistics are then computed for the purpose of efficient channel coding design and evaluation.

An alternative code-division multiple-access (CDMA) scheme to spread spectrum (SS), called spread time (ST) is proposed for bandlimited multiple-access channels. ST-CDMA can be considered the time-frequency dual of SS-CDMA. In ST-CDMA pseudorandom (PN) sequences are assigned to each user, and the Fourier transform of the transmitted pulse for a given user is determined by modulating the phase of the desired transmitted spectrum by the user's PN-sequence. The transmitted data for a particular user can be recovered by sampling the output of a filter matched to the user's pulse. Implementations are described in which surface acoustic wave devices are used to perform the matched filtering or Fourier transformation. Averaged signal-to-interference plus noise ratio (SIR) and spectral efficiency are computed for both asynchronous ST and direct-sequence SS-CDMA systems, assuming an arbitrary channel transfer function H(f), which is the same between all pairs of users. The results are the same for SS and ST provided that the magnitude of the Fourier transform of the chip shape in the SS system is the same as the magnitude of the Fourier transform of the ST pulse shape. The main advantage of the ST technique Is the flexibility with which the transmitted spectrum can be selected. We derive the transmitted spectrum that maximizes the SIR subject to an average power constraint.>

Full-duplex data communication over a multi-input/multi-output linear time-invariant channel is considered. The minimum mean square error (MMSE) linear equalizer is derived in the presence of both near- and far-end crosstalk and independent additive noise. The MMSE equalizer is completely specified in terms of the channel and crosstalk transfer functions by using a generalization of previous work due to Salz (1985). Conditions are given under which the equalizer can completely eliminate both near- and far-end crosstalk and intersymbol interference. The MMSE transmitter filter, subject to a transmitted power constraint, is specified when the channel and crosstalk transfer functions are bandlimited to the Nyquist frequency. Also considered is the design of MMSE transmitter and receiver filters when the data signals are arbitrary wide-sense stationary continuous or discrete-time signals, corresponding to the situation where the crosstalk is not phase-synchronous with the desired signal.>

A decision feedback equalizer (DFE) containing a feedback filter with both poles and zeros is proposed for high-speed digital communications over the subscriber loop. The feedback filter is composed of a relatively short FIR filter that cancels the initial part of the channel impulse response, which may contain rapid variations due to bridge taps, and a pole-zero, or IIR, filter that cancels the smoothly decaying tail of the impulse response. Modifications of an adaptive IIR algorithm, based on the Steiglitz-McBride (1965) identification scheme, are proposed to adapt the feedback filter. A measured subscriber loop impulse response is used to compare the performance of the adaptive pole-zero DFE, assuming a two-pole feedback filter, with a conventional DFE having the same number of coefficients. Results show that the pole-zero DFE offers a significant improvement in mean squared error relative to the conventional DFE. The speed convergence of the adaptive pole-zero DFE is comparable to that of the conventional DFE using the standard least mean square (LMS) adaptive algorithm.>

An innovative digital timing recovery method for synchronous digital receivers is described. This method is based on estimating the impulse response of the channel and then choosing an optimal sampling phase from this estimate. The method uses an adaptive transversal filter (TF), operating at the baud rate and driven by a decision-directed reference, to cancel the sampled received far-end signal. This timing recovery technique connects, in a natural way, with receivers using decision feedback equalizers (DFEs). A 30-tap DFE receiver incorporating this timing recovery scheme has been simulated and implemented in real time on a single DSP (digital signal processor).>