A Low-Complexity and Asymptotically Optimal Coding Strategy for Gaussian Vector Sources

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

On the asymptotic optimality of a low-complexity coding strategy for WSS, MA, and AR vector sources

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 sources. We also study how the coding strategy considered performs when it is used to encode perturbed versions of those relevant sources. More precisely, we give a sufficient condition for such perturbed versions so that the convergence speed of the rate remains unaltered

Rate-distortion function upper bounds for Gaussian vectors and their applications in coding AR sources

source coding; rate-distortion function (RDF); Gaussian vector; autoregressive (AR) source; discrete Fourier transform (DFT

Necessary and sufficient conditions for AR vector processes to be stationary: Applications in information theory and in statistical signal processing

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

On the topology design of large wireless sensor networks for distributed consensus with low power consumption

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 structural health monitoring is to use a distributed computation strategy, which is usually based on consensus algorithms. Power consumption in such wireless consensus networks depends on the number of connections of the network. If sensors are randomly connected, there is no control on the power consumption. In this article, we present a novel strategy to connect a large number of wireless sensors for distributed consensus with low power consumption by combining small networks with basic topologies using the Kronecker product

Rate Distortion Function of Gaussian Asymptotically WSS Vector Processes

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

An Assessment of the Impact of Social Networks on Collaborative Learning at College Level

This study considers the effect of the usage of a social network site (www.grouply.com) for a class related group project on the development of individual abilities and performance in group work. Data were collected from three sections of an intermediate macroeconomic class at a Spanish university and groups were randomly assigned to work (or not) using the social network. Findings suggest that, although students are in general attracted by the idea of using SNS in class-related team work, the introduction of a tool they are not familiar with may hamper their self-perceived level of competence in a number of skills

Applications of the periodogram method for perturbed block toeplitz satrices in statistical signal processing

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 combine the periodogram method for perturbed block Toeplitz matrices with the Cholesky decomposition, we first need to generalize a known result on the Cholesky decomposition of Toeplitz matrices to perturbed block Toeplitz matrices

In-Network Computation of the Optimal Weighting Matrix for Distributed Consensus on Wireless Sensor Networks

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 such an optimal weighting matrix

Rate-Distortion Function Upper Bounds for Gaussian Vectors and Their Applications in Coding AR Sources

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 conditions for AR processes to be AWSS