Xabier Insausti

• PhD Telecom Engineering, MS Advanced Mathematics
• Researcher at CEIT Centro de Estudios e Investigaciones Técnicas de Gipuzkoa

We present a mathematical model for agri-food industry residual streams flow management, which serves as a decision support tool for optimizing their valorization. The aim is to determine, under a cost-benefit analysis approach, the best strategy at a global level. The proposed mathematical model provides the optimal valorization scenario, namely t...

In their recent paper [], Wan proposed a quantum algorithm to solve systems of linear equations A x = b , where A is an n × n Toeplitz matrix generated by the Fourier coefficients of a continuous, 2 π -periodic, and positive function f . For large enough n , they claimed that the algorithm is valid for all b . In this Comment we prove that, in gene...

In the present article, the differential entropy rate and the rate distortion function (RDF) are computed for certain nonstationary real Gaussian autoregressive moving average (ARMA) vector sources.

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 l...

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...

This paper proposes a mathematical model that studies the fuel consumption of a jet engine aircraft during the climbing and descent flight phases. Such problem is addressed by providing a closed-form formula of the aircraft’s rate-of-climb and rate-of-descent, which then enables obtaining a closed-form formula of the aircraft’s fuel consumption tha...

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 EP...

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...

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 co...

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 compa...

In this paper, we study the asymptotic optimality of a low-complexity coding strategy for Gaussian vector sources. Specifically, we study the convergence speed of the rate of such a coding strategy when it is used to encode the most relevant vector sources, namely wide sense stationary (WSS), moving average (MA), and autoregressive (AR) vector sour...

In this paper, we combine the periodogram method for perturbed block Toeplitz matrices with the Cholesky decomposition to give a parameter estimation method for any perturbed vector autoregressive (VAR) or vector moving average (VMA) process, when we only know a perturbed version of the sequence of correlation matrices of the process. In order to c...

Sensor-based structural health monitoring systems are commonly used to provide real-time information and detect damage in complex structures. In particular, wireless structural health monitoring systems are of low cost but, since wireless sensors are powered with batteries, a low power consumption is critical. A common approach for wireless structu...

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 str...

In this letter we give a low-complexity analog linear coding scheme for transmitting finite-length data blocks of asymptotically wide sense stationary (AWSS) autoregressive (AR) sources through additive white Gaussian noise (AWGN) channels.

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...

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...

In this paper, we give upper bounds for the rate-distortion function (RDF) of any Gaussian vector, and we propose coding strategies to achieve such bounds. We use these strategies to reduce the computational complexity of coding Gaussian asymptotically wide sense stationary (AWSS) autoregressive (AR) sources. Furthermore, we also give sufficient co...

In this paper, we compare six known linear distributed average consensus algorithms on a sensor network in terms of convergence time (and therefore, in terms of the number of transmissions required). The selected network topologies for the analysis (comparison) are the cycle and the path. Specifically, in the present paper, we compute closed-form e...

In this paper, we present upper bounds for the rate distortion function (RDF) of finite-length data blocks of Gaussian wide sense stationary (WSS) sources and we propose coding strategies to achieve such bounds. In order to obtain those bounds, we previously derive new results on the discrete Fourier transform (DFT) of WSS processes.

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...

In the present paper, we obtain a result on the rate-distortion function (RDF) of wide sense stationary (WSS) vector processes that allows us to reduce the complexity of coding those processes. To achieve this result, we propose a sequence of block circulant matrices. In addition, we use the proposed sequence to reduce the complexity of filtering W...

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...

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...

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...

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...

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 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...

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 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...