Pedro M. Crespo

• MSc. Appl. Math, PhD. EE (USC)
• Head of Department at TECNUN-Universidad de Navarra

Quantum channel capacity is a fundamental quantity in order to understand how well quantum information can be transmitted or corrected when subjected to noise. However, it is generally not known how to compute such quantities since the quantum channel coherent information is not additive for all channels, implying that it must be maximized over an...

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 b...

Quantum technologies have the potential to solve computationally hard problems that are intractable via classical means. Unfortunately, the unstable nature of quantum information makes it prone to errors. For this reason, quantum error correction is an invaluable tool to make quantum information reliable and enable the ultimate goal of fault-tolera...

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...

Quantum channel capacity is a fundamental quantity in order to understand how good can quantum information be transmitted or corrected when subjected to noise. However, it is generally not known how to compute such quantities, since the quantum channel coherent information is not additive for all channels, implying that it must be maximized over an...

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 non-identical quantum noise. In this work, we modify the conventional MWPM decoder so that it considers the biases and non-uniformities of the constituent qub...

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 re...

Recent experimental studies have shown that the relaxation time ($T_1$) and the dephasing time ($T_2$) of superconducting qubits fluctuate considerably over time. To appropriately consider this time-varying nature of the $T_1$ and $T_2$ parameters, a new class of quantum channels, known as Time-Varying Quantum Channels (TVQCs), has been proposed. I...

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 ($T_1$) and dephasing ($T_2$) times of the constituent qubits of state-of-the-art quantum processors h...

Recent experimental studies have shown that the relaxation time T1 and the dephasing time T2 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 c...

The quantum paradigm presents a phenomenon known as degeneracy that can potentially improve the performance of quantum error correcting codes. However, the effects of this mechanism are sometimes ignored when evaluating the performance of sparse quantum codes and the logical error rate is not always correctly reported. In this article, we discuss p...

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...

The quantum paradigm presents a phenomenon known as degeneracy that should improve the performance of quantum error correcting codes. However, the effects of this mechanism are generally ignored when employing sparse quantum codes because of the computational complexity associated to the detection of degenerate error events. In this paper, we deriv...

The decoherence effects experienced by the qubits of a quantum processor are generally characterized using the amplitude damping time (T1) and the dephasing time (T2). 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 tim...

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 phe...

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 source...

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 o...

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 g...

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 informa...

In this paper, we tackle the channel estimation problem for Pauli channels. Online estimation methods for the depolarizing channel have been proposed in previous literature. However, realistic quantum devices often exhibit an asymmetric behaviour not captured by the symmetric depolarizing model, implying that the estimation method used by Quantum T...

—QuantumLowDensityGeneratorMatrix(QLDGM) codes based on Calderbank-Steane-Shor (CSS) constructions have shown unprecedented error correction capabilities in the paradigm of quantum communication. Recently, a strategy based on non-CSS quantum codes derived from QLDGM CSS codes has been shown to surpass other Quantum Low Density Parity Check (QLDPC)...

Quantum Low Density Generator Matrix (QLDGM) codes based on Calderbank-Steane-Shor (CSS) constructions 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 a...

ndustry 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 combinat...

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 enable to exploit novel wireless technologies (5G), but it would also be crucial to rely on architectures that appropriately support them. Thus, the combination of fog...

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 infor...

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...

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. Existing QTCs have been constructed using uniform random interleavers. However, interleaver design plays an important role in the optimization of c...

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...

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...

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 approa...

Abstract 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...

In this paper, we obtain an integral formula for the rate distortion function (RDF) of any Gaussian asymptotically wide sense stationary (AWSS) vector process. Applying this result, we also obtain an integral formula for the RDF of Gaussian moving average (MA) vector processes and of Gaussian autoregressive MA (ARMA) AWSS vector processes.

In this letter we design a low latency, low complexity, and low transmission power analog linear coding scheme to estimate finite-length data blocks under a mean-square error (distortion) criterion. The proposed scheme is based on analog linear coding and on the discrete Fourier transform (DFT). A remarkable feature of our scheme is that it does no...

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 th...

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...

In a network, a distributed consensus algorithm is fully characterized by its weighting matrix. Although there exist numerical methods for obtaining the optimal weighting matrix, we have not found an in-network implementation of any of these methods that works for all network topologies. In this paper, we propose an in-network algorithm for finding...

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 (MIMO) channel with memory. In the present paper we tackle not only the case considered by them where the number of...

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 codin...

This paper proposes a Decode-and-Forward (DF) relaying scheme for the multi-hop transmission in wireless networks, where the information generated by an independent source has to be sent to a far destination based on multiple-relay cooperation. The proposed DF scheme blends together convolutional channel coding with linear combination of blocks of...

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...

Multimedia services distribution is very dependent on the quality of the communications link. Due to the nature of the related services, these are usually very sensitive to packet loss, delay and jitter, and hence service quality is immediately worsen in harsh scenarios. This paper proposes an OSI-Layer2 cooperative link layer scheme (known as Gala...

We consider analog multiple description joint source-channel schemes for the transmission of a Gaussian source over two independent AWGN parallel channels under a quadratic error distortion criteria. For such systems, Lines mapping was proved to be a simple and efficient mapping when MMSE decoding is used. However, MMSE decoding presents a high com...

Joint source-channel coding schemes based on analog mappings for point to point channels have recently gained attention for their simplicity and low delay. In this work, these schemes are extended either to scenarios with or without side information at the decoders to transmit multiple descriptions of a Gaussian source over independent parallel cha...

This paper proposes a Decode-and-Forward (DF) relaying scheme for the multi-hop transmission in wireless networks, where the information generated by an independent source has to be sent to a far destination based on multiple-relay cooperation. The proposed DF scheme blends together convolutional channel coding with linear combination of blocks of...

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 th...

Due to its wide availability narrowband powerline networks provide an interesting no-new-wires communication channel. Nevertheless, as powerline was not designed for data communication, its electrical characteristics make it a harsh environment for data transmission and prevents the deployment of services with high reliability requirements. This pa...

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 of bounded support in terms of functions of Hermitian Toeplitz matrices. To prove that asymptotic formula we use the Gray concept of...

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...

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 coefficien...

The multimedia content distribution is very sensitive to packet loss, immediately reducing the service quality at receiver nodes. However, a realistic wireless scenario must take into account existing different wireless propagation effects, as well as receivers mobility and the existence of interfering nodes.

In this paper, we present a fundamental study on the stationarity and ergodicity of eight classes of sum-of-cisoids (SOC) processes for the modeling and simulation of frequency-nonselective mobile Rayleigh fading channels. The purpose of this study is to determine which classes of SOC models enable the design of channel simulators that accurately r...

In this paper, we design a practical 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...

One of the most challenging research fields in which research community has taken a very active role is focused on trying to bring the features of wireless networks into line with the traditional wired solutions. Given the noisy and lossy nature of the wireless medium, it is more difficult to provide a comparable Quality of Service (QoS) and Reliab...

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...

In this article, we present a cross-layer adaptive algorithm that dynamically maximizes the average utility function. A per stage utility function is defined for each link of a carrier sense multiple access-based wireless network as a weighted concave function of energy consumption, smoothed rate, and smoothed queue size. Hence, by selecting weight...

The complexity and delay introduced by efficient digital coding strategies may be a barrier in some real-time communications. In this sense, these last years, joint source-channel coding schemes based on analog mappings have gained prominence precisely for their simplicity and their implicit low delay. In this work, analog mappings originally desig...

In this paper' we have studied some important statistical properties of error sequences of M-ary orthogonal frequency-shift keying (FSK) modulation schemes over Nakagami-m fading channels. We have derived the joint probability density function (PDF) of error sequences of arbitrary length. From the joint PDF' we have found an analytical solution for...

This letter introduces a novel channel coding design framework for short-length codewords that permits balancing the tradeoff between the bit error rate floor and waterfall region by modifying a single real-valued parameter. The proposed approach is based on combining convolutional coding with a $q$-ary linear combination and unequal energy allocat...

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...

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 s...

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...

Recently, the joint source-channel coding schemes based on analog mappings have gained prominence. Their simplicity and low delay compared to other coding strategies make them more suitable for real-time applications. In this work, we propose a novel joint source-channel coding scheme, based also on analog mappings, for a point-to-point communicati...

With the purpose of reducing the coding complexity and delay of the separation-based schemes, an analog joint source-channel coding scheme is proposed for transmissions through parallel AWGN channels with side information at the receiver. This scheme divides the bidimensional source space into a set of hexagons and transmits the relative position o...

In this paper we use a gossip algorithm to obtain the projection of the observed signal into a subspace of lower dimension. Gossip algorithms allow distributed, fast and efficient computations on a Wireless Sensor Network and they can be properly modified to evaluate the sought projection. By combining computation coding with gossip algorithms we p...

This paper focuses on the data fusion scenario where N nodes sense and transmit the data generated by a source S to a common destination, which estimates the original information from S more accurately than in the case of a single sensor. This work joins the upsurge of research interest in this topic by addressing the setup where the sensed informa...

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 re...

In the absence of observation noise, it is known that it is possible to develop exact sampling schemes for a large class of parametric non-bandlimited signals, namely, certain signals of finite rate of innovation (FRI signals), either periodic or aperiodic, such as streams of Diracs, nonuniform splines or piecewise polynomials. A common feature of...

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 autocorr...

Present paper describes the design of a new Queue Management Mechanism that allows the optimization in the use of shared network resources by different flows with high QoS constraints. The new real-time multimedia interactive services require network devices whose behavior complies with high time constraints. Hence, the proposed queue management me...

Complex biological networks are commonly represented as graphs, where nodes represent biological entities and edges interactions between such entities. An important topological property of such graphs is the connectivity between any pair of nodes, as well as, if connected, their underlying minimum distance, which overall restricts the global behavi...

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-...

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 non- binary Low-Density Parity Check (LDPC) codes, along with the linear combination of blocks of data at the relay. The common r...

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 o...

The present monograph studies the asymptotic behaviour of eigenvalues, products and functions of block Toeplitz matrices generated by the Fourier coefficients of a continuous matrix-valued function. This study is based on the concept of asymptotically equivalent sequences of non-square matrices. The asymptotic results on block Toeplitz matrices obt...

In this paper, we design a new energy allocation strategy for non-uniform binary memoryless sources encoded by Low-Density Parity-Check (LDPC) codes and sent over Additive White Gaussian Noise (AWGN) channels. The new approach estimates the a priori probabilities of the encoded symbols, and uses this information to allocate more energy to the trans...

One of the applications of wireless sensor networks currently undergoing active research focuses on the scenario where the information generated by a data source S is simultaneously sensed by N nodes and therefrom transmitted to a common receiver. Based on the received information from such N nodes, such receiver infers the original information fro...

With the XXIst century, a new mathematical flow emerges from the Information Theory field with the aim of reaching new up-bound limits in the use of data networks resources, in order to maximize the transmitted information. Mentioned research field has been named as Network Coding, and provides innovative mechanisms for the provision of Quality of...

The Burrows-Wheeler Transform (BWT) is a block sorting algorithm which has been proven to be useful in compressing text data . More recently, schemes based on the BWT have been proposed for lossless data compression using LDPC and Fountain codes, as well as for joint source-channel coding of sources with memory. In this paper we propose a source-co...

This letter proposes a novel one-layer coding/ shaping scheme with single-level codes and sigma-mapping for the bandwidth-limited regime. Specifically, we consider nonuniform memoryless sources sent over AWGN channels. At the transmitter, binary data are encoded by a Turbo code composed of two identical RSC (Recursive Systematic Convolutional) enco...

Antenna arrays that incorporate MIMO technology for indoor–outdoor network interconnection on the same terminal, i.e., for DCS 1800, PCS 1900, WCDMA, 3G, 802.11a/b/g, Bluetooth®, ZigBee®, WiMAX™, and UWB standards, are proposed. Staircase profile printed circuit antennas, monopoles (PCM), and slots (PCS) with VSWR < 2 bandwidth mainly from 1.12 to...

Recent contributions have shown that, by switching frequency bands at intermediate relay nodes, enhanced diversity can be attained in two-user wireless frequency division relay networks at a minimum computational cost. This paper elaborates on the design of frequency-switching patterns for more involved relay scenarios. We conclude that in general,...

Erratum to "serially-concatenated LDGM codes for correlated sources over Gaussian broadcast channels"

The last decade, some signals with finite rate of innovation have been proved to be recoverable from the samples of their filtered versions. Different contributions have also been made to reduce the reconstruction error with noisy samples. In this work a new reconstruction method for aperiodic streams of Diracs is introduced, which reduces the comp...

In this paper, we present a decentralized algorithm to find minimum cost quality of service (QoS) flow subgraphs in network coded multicast schemes. The main objective is to find minimum cost subgraphs that also satisfy user-specified QoS con- straints, specifically with respect to rate and delay demands. We consider networks with multiple multicas...

In early 2000, it was shown that it is possible to develop exact sampling schemes for a large class of parametric non-bandlimited noiseless signals, namely certain signals of finite rate of innovation. In particular, signals x(t) that are linear combinations of a finite number of Diracs per unit of time can be acquired by linear filtering followed...

In this paper we propose a novel one-layer coding/shaping transmission system for the bandwidth-limited regime based on single-level codes and sigma-mapping [1]. Specifically, we focus on cycle- stationary information sources with independent symbols. High spectral efficiencies can be achieved by combine at the transmitter a Turbo code with a sigma...

This paper proposes a low-complexity signal shaping scheme for the transmission of non-binary symbols generated by sources with memory over the AWGN channel. It is based on using the Burrows-Wheeler Transform (BWT) [1] and standard two dimensional (QAM) constellations. The constellation points are driven based on the first order probabilities of th...

We propose a superposition scheme, based on the use of serially-concatenated LDGM codes, for the transmission of spatially correlated sources over Gaussian broadcast channels. The messages intended for each receiver are independently encoded using the same code. In this manner, a strong degree of correlation is kept between the encoded sequences, w...

In this work, a new technique for the estimation of the Shannon's entropy and the Kullback-Leibler (KL) di- vergence for one dimensional data is presented. The estimator is based on the Szego's theorem for sequences of Toeplitz matrices, which deals with the asymptotic behavior of the eigenvalues of those matrices, and the analogy between a probabi...

This paper addresses the sensor network scenario where several nodes sense a common information source S. When such sensors forward their correlated observations to a common shared receiver, it is necessary to combine the received information in order to obtain an estimation of S with high reliability. In this manuscript we propose the use of low-c...

Focusing on densely deployed wireless sensor networks, this paper presents a novel method for joint source-channel-network coding of distributed correlated sources through multiple access relay channels. In such networks, the role of intermediate sensors as relay nodes permits to achieve enhanced end-to-end error performance and increased spatial d...

Works in the last decades have shown that a large class of parametric non-bandlimited signals can be exactly re-constructed from samples of their filtered versions. In particular, signals x(t) that are linear combinations of a finite number of Diracs per unit of time can be acquired by linear filtering followed by uniform sampling. Nevertheless, wh...

In this paper, we present a decentralized algorithm that computes minimum cost QoS flow subgraphs in network coded multicast networks. These subgraphs are minimum cost solutions that also satisfy user-specified QoS constraints, specifically handling elastic rate and delay demands. Although earlier network coding algorithms in this area have only de...

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 tool...