## 2013 |

Bravo-Santos, Ángel M Polar Codes for Gaussian Degraded Relay Channels Journal Article IEEE Communications Letters, 17 (2), pp. 365–368, 2013, ISSN: 1089-7798. Abstract | Links | BibTeX | Tags: channel capacity, Channel Coding, Decoding, Encoding, Gaussian channels, Gaussian degraded relay channel, Gaussian noise, Gaussian-degraded relay channels, log-likelihood expression, Markov coding, Noise, parity check codes, polar code detector, polar codes, relay-destination link, Relays, Vectors @article{Bravo-Santos2013, title = {Polar Codes for Gaussian Degraded Relay Channels}, author = {Ángel M Bravo-Santos}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6412681}, issn = {1089-7798}, year = {2013}, date = {2013-01-01}, journal = {IEEE Communications Letters}, volume = {17}, number = {2}, pages = {365--368}, publisher = {IEEE}, abstract = {In this paper we apply polar codes for the Gaussian degraded relay channel. We study the conditions to be satisfied by the codes and provide an efficient method for constructing them. The relay-destination link is special because the noise is the sum of two components: the Gaussian noise and the signals from the source. We study this link and provide the log-likelihood expression to be used by the polar code detector. We perform simulations of the channel and the results show that polar codes of high rate and large codeword length are closer to the theoretical limit than other good codes.}, keywords = {channel capacity, Channel Coding, Decoding, Encoding, Gaussian channels, Gaussian degraded relay channel, Gaussian noise, Gaussian-degraded relay channels, log-likelihood expression, Markov coding, Noise, parity check codes, polar code detector, polar codes, relay-destination link, Relays, Vectors}, pubstate = {published}, tppubtype = {article} } In this paper we apply polar codes for the Gaussian degraded relay channel. We study the conditions to be satisfied by the codes and provide an efficient method for constructing them. The relay-destination link is special because the noise is the sum of two components: the Gaussian noise and the signals from the source. We study this link and provide the log-likelihood expression to be used by the polar code detector. We perform simulations of the channel and the results show that polar codes of high rate and large codeword length are closer to the theoretical limit than other good codes. |

## 2009 |

Djuric, Petar M; Bugallo, Monica F; Closas, Pau; Miguez, Joaquin Measuring the Robustness of Sequential Methods Inproceedings 2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop, pp. 29–32, IEEE, Aruba, Dutch Antilles, 2009, ISBN: 978-1-4244-5179-1. Abstract | Links | BibTeX | Tags: Additive noise, cumulative distribution functions, data processing method, extended Kalman filtering, Extraterrestrial measurements, Filtering, Gaussian distribution, Gaussian noise, Kalman filters, Kolmogorov-Smirnov distance, Least squares approximation, Noise robustness, nonlinear filters, robustness, sequential methods, statistical distributions, telecommunication computing @inproceedings{Djuric2009a, title = {Measuring the Robustness of Sequential Methods}, author = {Petar M Djuric and Monica F Bugallo and Pau Closas and Joaquin Miguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5413275}, isbn = {978-1-4244-5179-1}, year = {2009}, date = {2009-01-01}, booktitle = {2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop}, pages = {29--32}, publisher = {IEEE}, address = {Aruba, Dutch Antilles}, abstract = {Whenever we apply methods for processing data, we make a number of model assumptions. In reality, these assumptions are not always correct. Robust methods can withstand model inaccuracies, that is, despite some incorrect assumptions they can still produce good results. We often want to know how robust employed methods are. To that end we need to have a yardstick for measuring robustness. In this paper, we propose an approach for constructing such metrics for sequential methods. These metrics are derived from the Kolmogorov-Smirnov distance between the cumulative distribution functions of the actual observations and the ones based on the assumed model. The use of the proposed metrics is demonstrated with simulation examples.}, keywords = {Additive noise, cumulative distribution functions, data processing method, extended Kalman filtering, Extraterrestrial measurements, Filtering, Gaussian distribution, Gaussian noise, Kalman filters, Kolmogorov-Smirnov distance, Least squares approximation, Noise robustness, nonlinear filters, robustness, sequential methods, statistical distributions, telecommunication computing}, pubstate = {published}, tppubtype = {inproceedings} } Whenever we apply methods for processing data, we make a number of model assumptions. In reality, these assumptions are not always correct. Robust methods can withstand model inaccuracies, that is, despite some incorrect assumptions they can still produce good results. We often want to know how robust employed methods are. To that end we need to have a yardstick for measuring robustness. In this paper, we propose an approach for constructing such metrics for sequential methods. These metrics are derived from the Kolmogorov-Smirnov distance between the cumulative distribution functions of the actual observations and the ones based on the assumed model. The use of the proposed metrics is demonstrated with simulation examples. |

## 2008 |

Rodrigues, Miguel R D; Perez-Cruz, Fernando; Verdu, Sergio Multiple-Input Multiple-Output Gaussian Channels: Optimal Covariance for Non-Gaussian Inputs Inproceedings 2008 IEEE Information Theory Workshop, pp. 445–449, IEEE, Porto, 2008, ISBN: 978-1-4244-2269-2. Abstract | Links | BibTeX | Tags: Binary phase shift keying, covariance matrices, Covariance matrix, deterministic MIMO Gaussian channel, fixed-point equation, Gaussian channels, Gaussian noise, Information rates, intersymbol interference, least mean squares methods, Magnetic recording, mercury-waterfilling power allocation policy, MIMO, MIMO communication, minimum mean-squared error, MMSE, MMSE matrix, multiple-input multiple-output system, Multiple-Input Multiple-Output Systems, Mutual information, Optimal Input Covariance, Optimization, Telecommunications @inproceedings{Rodrigues2008, title = {Multiple-Input Multiple-Output Gaussian Channels: Optimal Covariance for Non-Gaussian Inputs}, author = {Miguel R D Rodrigues and Fernando Perez-Cruz and Sergio Verdu}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4578704}, isbn = {978-1-4244-2269-2}, year = {2008}, date = {2008-01-01}, booktitle = {2008 IEEE Information Theory Workshop}, pages = {445--449}, publisher = {IEEE}, address = {Porto}, abstract = {We investigate the input covariance that maximizes the mutual information of deterministic multiple-input multipleo-utput (MIMO) Gaussian channels with arbitrary (not necessarily Gaussian) input distributions, by capitalizing on the relationship between the gradient of the mutual information and the minimum mean-squared error (MMSE) matrix. We show that the optimal input covariance satisfies a simple fixed-point equation involving key system quantities, including the MMSE matrix. We also specialize the form of the optimal input covariance to the asymptotic regimes of low and high snr. We demonstrate that in the low-snr regime the optimal covariance fully correlates the inputs to better combat noise. In contrast, in the high-snr regime the optimal covariance is diagonal with diagonal elements obeying the generalized mercury/waterfilling power allocation policy. Numerical results illustrate that covariance optimization may lead to significant gains with respect to conventional strategies based on channel diagonalization followed by mercury/waterfilling or waterfilling power allocation, particularly in the regimes of medium and high snr.}, keywords = {Binary phase shift keying, covariance matrices, Covariance matrix, deterministic MIMO Gaussian channel, fixed-point equation, Gaussian channels, Gaussian noise, Information rates, intersymbol interference, least mean squares methods, Magnetic recording, mercury-waterfilling power allocation policy, MIMO, MIMO communication, minimum mean-squared error, MMSE, MMSE matrix, multiple-input multiple-output system, Multiple-Input Multiple-Output Systems, Mutual information, Optimal Input Covariance, Optimization, Telecommunications}, pubstate = {published}, tppubtype = {inproceedings} } We investigate the input covariance that maximizes the mutual information of deterministic multiple-input multipleo-utput (MIMO) Gaussian channels with arbitrary (not necessarily Gaussian) input distributions, by capitalizing on the relationship between the gradient of the mutual information and the minimum mean-squared error (MMSE) matrix. We show that the optimal input covariance satisfies a simple fixed-point equation involving key system quantities, including the MMSE matrix. We also specialize the form of the optimal input covariance to the asymptotic regimes of low and high snr. We demonstrate that in the low-snr regime the optimal covariance fully correlates the inputs to better combat noise. In contrast, in the high-snr regime the optimal covariance is diagonal with diagonal elements obeying the generalized mercury/waterfilling power allocation policy. Numerical results illustrate that covariance optimization may lead to significant gains with respect to conventional strategies based on channel diagonalization followed by mercury/waterfilling or waterfilling power allocation, particularly in the regimes of medium and high snr. |

Vila-Forcen, J E; Artés-Rodríguez, Antonio; Garcia-Frias, J Compressive Sensing Detection of Stochastic Signals Inproceedings 2008 42nd Annual Conference on Information Sciences and Systems, pp. 956–960, IEEE, Princeton, 2008, ISBN: 978-1-4244-2246-3. Abstract | Links | BibTeX | Tags: Additive white noise, AWGN, compressive sensing detection, dimensionality reduction techniques, Distortion measurement, Gaussian noise, matrix algebra, Mutual information, optimized projections, projection matrix, signal detection, Signal processing, signal reconstruction, Stochastic processes, stochastic signals, Support vector machine classification, Support vector machines, SVM @inproceedings{Vila-Forcen2008, title = {Compressive Sensing Detection of Stochastic Signals}, author = {J E Vila-Forcen and Antonio Artés-Rodríguez and J Garcia-Frias}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4558656}, isbn = {978-1-4244-2246-3}, year = {2008}, date = {2008-01-01}, booktitle = {2008 42nd Annual Conference on Information Sciences and Systems}, pages = {956--960}, publisher = {IEEE}, address = {Princeton}, abstract = {Inspired by recent work in compressive sensing, we propose a framework for the detection of stochastic signals from optimized projections. In order to generate a good projection matrix, we use dimensionality reduction techniques based on the maximization of the mutual information between the projected signals and their corresponding class labels. In addition, classification techniques based on support vector machines (SVMs) are applied for the final decision process. Simulation results show that the realizations of the stochastic process are detected with higher accuracy and lower complexity than a scheme performing signal reconstruction first, followed by detection based on the reconstructed signal.}, keywords = {Additive white noise, AWGN, compressive sensing detection, dimensionality reduction techniques, Distortion measurement, Gaussian noise, matrix algebra, Mutual information, optimized projections, projection matrix, signal detection, Signal processing, signal reconstruction, Stochastic processes, stochastic signals, Support vector machine classification, Support vector machines, SVM}, pubstate = {published}, tppubtype = {inproceedings} } Inspired by recent work in compressive sensing, we propose a framework for the detection of stochastic signals from optimized projections. In order to generate a good projection matrix, we use dimensionality reduction techniques based on the maximization of the mutual information between the projected signals and their corresponding class labels. In addition, classification techniques based on support vector machines (SVMs) are applied for the final decision process. Simulation results show that the realizations of the stochastic process are detected with higher accuracy and lower complexity than a scheme performing signal reconstruction first, followed by detection based on the reconstructed signal. |