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

Rate compatible joint source-channel coding for point-to-point and multiple access channels.

In this Thesis we consider high-throughput rate compatible Joint Source-Channel Coding (JSCC) schemes based on Rate Compatible Modulation (RCM) codes. These codes achieve JSCC capabilities by embedding source compression into modulation through the generation of multi-level symbols from weighted linear combinations of the input bits. The smooth rate adaptation is achieved seamlessly by varying the number of generated symbols. These two properties make them advantageous over conventional Adaptive Coded Modulation (ACM) techniques, which usually rely on unrealistic instant and accurate channel estimations, and a limited set of coding and modulation combinations to choose from. The main drawback of RCM codes is that they experience performance degradation due to the presence of error floors at high Signal-to-Noise Ratios (SNRs). These error floors can be substantially improved by substituting a few RCM symbols by LDGM coded bits, forming an hybrid coding scheme in which the LDGM symbols correct residual errors produced by the RCM. This work investigates new applications and design techniques of these family of codes for point-to-point and multi-user communications. For the point-to-point case, we propose an EXIT chart analysis and a bit error rate prediction procedure suitable for implementing RCM-LDGM codes. The developed EXIT charts speed up the design method of good codes, which otherwise requires the use of time-consuming simulations. We continue by considering the problem of implementing high-throughput JSCC schemes for the transmission of binary sources with memory over AWGN channels, for which we propose a coding scheme that makes use of the Burrows-Wheeler Transform (BWT) and the rate compatible RCM-LDGM codes. Finally, for the first time in the literature, we propose the use of RCM-LDGM codes for additive impulsive noise channels. For multi-user communications we begin by considering that the information sources are uncorrelated and propose a new coding scheme based on the use of an irregular RCM encoder for each user. By properly designing the encoders and taking advantage of the additive nature of the MAC, 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. In the last part of the Thesis, we tackle the multi-user communication scenario in which the transmitted information sources are spatially correlated and also extend the use of LDGM codes in parallel with the proposed RCM systems in the MAC.Esta Tesis estudia esquemas de comunicación con tasas de transmisión altas y adaptables basados en códigos RCM y cuya codificación de fuente y canal es conjunta. La compresión de fuente se incorpora en la modulación mediante la generación de símbolos multi-nivel a partir de combinaciones lineales ponderadas de los bits de entrada, mientras que la adaptación de la tasa de transmisión se logra variando el número de símbolos generados. Estas dos propiedades son ventajosas frente las técnicas convencionales de modulación codificada adaptativa, que generalmente se basan en estimaciones precisas e instantáneas del canal, lo cual, es poco realista. Además, estas técnicas tienen un conjunto limitado de combinaciones de codificación y modulación para elegir. El principal inconveniente de los códigos RCM es que experimentan una degradación del rendimiento debido a la presencia de altos suelos de error. Una solución consiste en sustituir algunos símbolos RCM por LDGM, formando un esquema de codificación híbrido en el que los símbolos LDGM corrigen errores residuales producidos por los RCM. En concreto, en esta Tesis buscamos nuevas técnicas de diseño y aplicaciones para esta familia de códigos tanto en comunicaciones punto a punto como en comunicaciones multi-usuario. Para el caso punto a punto, proponemos un análisis llamado EXIT chart y un procedimiento de predicción de la tasa de error. Las técnicas desarrolladas aceleran el diseño de buenos códigos, ahorrando simulaciones que requieren de mucho tiempo. A continuación, consideramos la transmisión de fuentes binarias con memoria sobre canales AWGN, para lo cual proponemos un esquema de codificación que hace uso de la Transformada de Burrows-Wheeler y los códigos RCM-LDGM. Finalmente, por primera vez en la literatura, proponemos el uso de estos códigos para canales de ruido impulsivo aditivo. Para las comunicaciones multi-usuario empezamos considerando que las fuentes de información a transmitir por los usuarios son independientes y proponemos un nuevo esquema de codificación basado en el uso de un codificador RCM irregular para cada usuario. Al diseñar apropiadamente los codificadores individuales y aprovechando la naturaleza aditiva del canal, el esquema propuesto permite la transmisión simultánea de un gran número de usuarios a altas tasas de transmisión manteniendo la complejidad de decodificación tradicional. En la última parte de la Tesis abordamos el escenario de comunicación multi-usuario en el que las fuentes de información transmitidas están correlacionadas espacialmente y también ampliamos el uso de códigos LDGM en paralelo con los sistemas RCM propuestos para el MAC

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

Analysis of known linear distributed average consensus algorithms on cycles and paths

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 expressions for the convergence time of four known deterministic algorithms and closed-form bounds for the convergence time of two known randomized algorithms on cycles and paths. Moreover, we also compute a closed-form expression for the convergence time of the fastest deterministic algorithm considered on grids

Rate compatible joint source-channel coding for point-to-point and multiple access channels.

In this Thesis we consider high-throughput rate compatible Joint Source-Channel Coding (JSCC) schemes based on Rate Compatible Modulation (RCM) codes. These codes achieve JSCC capabilities by embedding source compression into modulation through the generation of multi-level symbols from weighted linear combinations of the input bits. The smooth rate adaptation is achieved seamlessly by varying the number of generated symbols. These two properties make them advantageous over conventional Adaptive Coded Modulation (ACM) techniques, which usually rely on unrealistic instant and accurate channel estimations, and a limited set of coding and modulation combinations to choose from. The main drawback of RCM codes is that they experience performance degradation due to the presence of error floors at high Signal-to-Noise Ratios (SNRs). These error floors can be substantially improved by substituting a few RCM symbols by LDGM coded bits, forming an hybrid coding scheme in which the LDGM symbols correct residual errors produced by the RCM. This work investigates new applications and design techniques of these family of codes for point-to-point and multi-user communications. For the point-to-point case, we propose an EXIT chart analysis and a bit error rate prediction procedure suitable for implementing RCM-LDGM codes. The developed EXIT charts speed up the design method of good codes, which otherwise requires the use of time-consuming simulations. We continue by considering the problem of implementing high-throughput JSCC schemes for the transmission of binary sources with memory over AWGN channels, for which we propose a coding scheme that makes use of the Burrows-Wheeler Transform (BWT) and the rate compatible RCM-LDGM codes. Finally, for the first time in the literature, we propose the use of RCM-LDGM codes for additive impulsive noise channels. For multi-user communications we begin by considering that the information sources are uncorrelated and propose a new coding scheme based on the use of an irregular RCM encoder for each user. By properly designing the encoders and taking advantage of the additive nature of the MAC, 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. In the last part of the Thesis, we tackle the multi-user communication scenario in which the transmitted information sources are spatially correlated and also extend the use of LDGM codes in parallel with the proposed RCM systems in the MAC.Esta Tesis estudia esquemas de comunicación con tasas de transmisión altas y adaptables basados en códigos RCM y cuya codificación de fuente y canal es conjunta. La compresión de fuente se incorpora en la modulación mediante la generación de símbolos multi-nivel a partir de combinaciones lineales ponderadas de los bits de entrada, mientras que la adaptación de la tasa de transmisión se logra variando el número de símbolos generados. Estas dos propiedades son ventajosas frente las técnicas convencionales de modulación codificada adaptativa, que generalmente se basan en estimaciones precisas e instantáneas del canal, lo cual, es poco realista. Además, estas técnicas tienen un conjunto limitado de combinaciones de codificación y modulación para elegir. El principal inconveniente de los códigos RCM es que experimentan una degradación del rendimiento debido a la presencia de altos suelos de error. Una solución consiste en sustituir algunos símbolos RCM por LDGM, formando un esquema de codificación híbrido en el que los símbolos LDGM corrigen errores residuales producidos por los RCM. En concreto, en esta Tesis buscamos nuevas técnicas de diseño y aplicaciones para esta familia de códigos tanto en comunicaciones punto a punto como en comunicaciones multi-usuario. Para el caso punto a punto, proponemos un análisis llamado EXIT chart y un procedimiento de predicción de la tasa de error. Las técnicas desarrolladas aceleran el diseño de buenos códigos, ahorrando simulaciones que requieren de mucho tiempo. A continuación, consideramos la transmisión de fuentes binarias con memoria sobre canales AWGN, para lo cual proponemos un esquema de codificación que hace uso de la Transformada de Burrows-Wheeler y los códigos RCM-LDGM. Finalmente, por primera vez en la literatura, proponemos el uso de estos códigos para canales de ruido impulsivo aditivo. Para las comunicaciones multi-usuario empezamos considerando que las fuentes de información a transmitir por los usuarios son independientes y proponemos un nuevo esquema de codificación basado en el uso de un codificador RCM irregular para cada usuario. Al diseñar apropiadamente los codificadores individuales y aprovechando la naturaleza aditiva del canal, el esquema propuesto permite la transmisión simultánea de un gran número de usuarios a altas tasas de transmisión manteniendo la complejidad de decodificación tradicional. En la última parte de la Tesis abordamos el escenario de comunicación multi-usuario en el que las fuentes de información transmitidas están correlacionadas espacialmente y también ampliamos el uso de códigos LDGM en paralelo con los sistemas RCM propuestos para el MAC

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

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