2016
Nazábal, Alfredo; Garcia-Moreno, Pablo; Artés-Rodríguez, Antonio; Ghahramani, Zoubin
Human Activity Recognition by Combining a Small Number of Classifiers. Artículo de revista
En: IEEE journal of biomedical and health informatics, vol. 20, no 5, pp. 1342 – 1351, 2016, ISSN: 2168-2208.
Resumen | Enlaces | BibTeX | Etiquetas: Bayes methods, Bayesian inference, Biological system modeling, Classifier combination, Databases, Estimation, Hidden Markov models, Journal, Sensor systems
@article{Nazabal2016b,
title = {Human Activity Recognition by Combining a Small Number of Classifiers.},
author = {Alfredo Naz\'{a}bal and Pablo Garcia-Moreno and Antonio Art\'{e}s-Rodr\'{i}guez and Zoubin Ghahramani},
url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7161292},
doi = {10.1109/JBHI.2015.2458274},
issn = {2168-2208},
year = {2016},
date = {2016-09-01},
journal = {IEEE journal of biomedical and health informatics},
volume = {20},
number = {5},
pages = {1342 -- 1351},
publisher = {IEEE},
abstract = {We consider the problem of daily Human Activity Recognition (HAR) using multiple wireless inertial sensors and, specifically, HAR systems with a very low number of sensors, each one providing an estimation of the performed activities. We propose new Bayesian models to combine the output of the sensors. The models are based on a soft outputs combination of individual classifiers to deal with the small number of sensors. We also incorporate the dynamic nature of human activities as a first order homogeneous Markov chain. We develop both inductive and transductive inference methods for each model to be employed in supervised and semi-supervised situations, respectively. Using different real HAR databases, we compare our classifiers combination models against a single classifier that employs all the signals from the sensors. Our models exhibit consistently a reduction of the error rate and an increase of robustness against sensor failures. Our models also outperform other classifiers combination models that do not consider soft outputs and a Markovian structure of the human activities.},
keywords = {Bayes methods, Bayesian inference, Biological system modeling, Classifier combination, Databases, Estimation, Hidden Markov models, Journal, Sensor systems},
pubstate = {published},
tppubtype = {article}
}
We consider the problem of daily Human Activity Recognition (HAR) using multiple wireless inertial sensors and, specifically, HAR systems with a very low number of sensors, each one providing an estimation of the performed activities. We propose new Bayesian models to combine the output of the sensors. The models are based on a soft outputs combination of individual classifiers to deal with the small number of sensors. We also incorporate the dynamic nature of human activities as a first order homogeneous Markov chain. We develop both inductive and transductive inference methods for each model to be employed in supervised and semi-supervised situations, respectively. Using different real HAR databases, we compare our classifiers combination models against a single classifier that employs all the signals from the sensors. Our models exhibit consistently a reduction of the error rate and an increase of robustness against sensor failures. Our models also outperform other classifiers combination models that do not consider soft outputs and a Markovian structure of the human activities.
Valera, Isabel; Ruiz, Francisco J R; Perez-Cruz, Fernando
Infinite Factorial Unbounded-State Hidden Markov Model Artículo de revista
En: IEEE transactions on pattern analysis and machine intelligence, vol. 38, no 9, pp. 1816 – 1828, 2016, ISSN: 1939-3539.
Resumen | Enlaces | BibTeX | Etiquetas: Bayes methods, Bayesian nonparametrics, CASI CAM CM, Computational modeling, GAMMA-L+ UC3M, Gibbs sampling, Hidden Markov models, Inference algorithms, Journal, Markov processes, Probability distribution, reversible jump Markov chain Monte Carlo, slice sampling, Time series, variational inference, Yttrium
@article{Valera2016b,
title = {Infinite Factorial Unbounded-State Hidden Markov Model},
author = {Isabel Valera and Francisco J R Ruiz and Fernando Perez-Cruz},
url = {http://www.ncbi.nlm.nih.gov/pubmed/26571511 http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true\&arnumber=7322279},
doi = {10.1109/TPAMI.2015.2498931},
issn = {1939-3539},
year = {2016},
date = {2016-09-01},
journal = {IEEE transactions on pattern analysis and machine intelligence},
volume = {38},
number = {9},
pages = {1816 -- 1828},
abstract = {There are many scenarios in artificial intelligence, signal processing or medicine, in which a temporal sequence consists of several unknown overlapping independent causes, and we are interested in accurately recovering those canonical causes. Factorial hidden Markov models (FHMMs) present the versatility to provide a good fit to these scenarios. However, in some scenarios, the number of causes or the number of states of the FHMM cannot be known or limited a priori. In this paper, we propose an infinite factorial unbounded-state hidden Markov model (IFUHMM), in which the number of parallel hidden Markov models (HMMs) and states in each HMM are potentially unbounded. We rely on a Bayesian nonparametric (BNP) prior over integer-valued matrices, in which the columns represent the Markov chains, the rows the time indexes, and the integers the state for each chain and time instant. First, we extend the existent infinite factorial binary-state HMM to allow for any number of states. Then, we modify this model to allow for an unbounded number of states and derive an MCMC-based inference algorithm that properly deals with the trade-off between the unbounded number of states and chains. We illustrate the performance of our proposed models in the power disaggregation problem.},
keywords = {Bayes methods, Bayesian nonparametrics, CASI CAM CM, Computational modeling, GAMMA-L+ UC3M, Gibbs sampling, Hidden Markov models, Inference algorithms, Journal, Markov processes, Probability distribution, reversible jump Markov chain Monte Carlo, slice sampling, Time series, variational inference, Yttrium},
pubstate = {published},
tppubtype = {article}
}
There are many scenarios in artificial intelligence, signal processing or medicine, in which a temporal sequence consists of several unknown overlapping independent causes, and we are interested in accurately recovering those canonical causes. Factorial hidden Markov models (FHMMs) present the versatility to provide a good fit to these scenarios. However, in some scenarios, the number of causes or the number of states of the FHMM cannot be known or limited a priori. In this paper, we propose an infinite factorial unbounded-state hidden Markov model (IFUHMM), in which the number of parallel hidden Markov models (HMMs) and states in each HMM are potentially unbounded. We rely on a Bayesian nonparametric (BNP) prior over integer-valued matrices, in which the columns represent the Markov chains, the rows the time indexes, and the integers the state for each chain and time instant. First, we extend the existent infinite factorial binary-state HMM to allow for any number of states. Then, we modify this model to allow for an unbounded number of states and derive an MCMC-based inference algorithm that properly deals with the trade-off between the unbounded number of states and chains. We illustrate the performance of our proposed models in the power disaggregation problem.
Vazquez-Vilar, Gonzalo; Campo, Adria Tauste; i Fabregas, Albert Guillen; Martinez, Alfonso
Bayesian M-Ary Hypothesis Testing: The Meta-Converse and Verdú-Han Bounds Are Tight Artículo de revista
En: IEEE Transactions on Information Theory, vol. 62, no 5, pp. 2324–2333, 2016, ISSN: 0018-9448.
Resumen | Enlaces | BibTeX | Etiquetas: Bayes methods, Channel Coding, Electronic mail, error probability, Journal, Random variables, Testing
@article{Vazquez-Vilar2016,
title = {Bayesian M-Ary Hypothesis Testing: The Meta-Converse and Verd\'{u}-Han Bounds Are Tight},
author = {Gonzalo Vazquez-Vilar and Adria Tauste Campo and Albert Guillen i Fabregas and Alfonso Martinez},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7434042},
doi = {10.1109/TIT.2016.2542080},
issn = {0018-9448},
year = {2016},
date = {2016-05-01},
journal = {IEEE Transactions on Information Theory},
volume = {62},
number = {5},
pages = {2324--2333},
abstract = {Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy et al.; the second expression is a function of an information-spectrum measure and implies the tightness of a generalized Verd\'{u}-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose.},
keywords = {Bayes methods, Channel Coding, Electronic mail, error probability, Journal, Random variables, Testing},
pubstate = {published},
tppubtype = {article}
}
Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy et al.; the second expression is a function of an information-spectrum measure and implies the tightness of a generalized Verdú-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose.
Valera, Isabel; Ruiz, Francisco J R; Perez-Cruz, Fernando
Infinite Factorial Unbounded-State Hidden Markov Model Artículo de revista
En: IEEE transactions on pattern analysis and machine intelligence, vol. To appear, no 99, pp. 1, 2016, ISSN: 1939-3539.
Resumen | Enlaces | BibTeX | Etiquetas: Bayes methods, Bayesian nonparametrics, CASI CAM CM, Computational modeling, GAMMA-L+ UC3M, Gibbs sampling, Hidden Markov models, Inference algorithms, Markov processes, Probability distribution, reversible jump Markov chain Monte Carlo, slice sampling, Time series, variational inference, Yttrium
@article{Valera2016c,
title = {Infinite Factorial Unbounded-State Hidden Markov Model},
author = {Isabel Valera and Francisco J R Ruiz and Fernando Perez-Cruz},
url = {http://www.ncbi.nlm.nih.gov/pubmed/26571511 http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true\&arnumber=7322279},
doi = {10.1109/TPAMI.2015.2498931},
issn = {1939-3539},
year = {2016},
date = {2016-01-01},
journal = {IEEE transactions on pattern analysis and machine intelligence},
volume = {To appear},
number = {99},
pages = {1},
abstract = {There are many scenarios in artificial intelligence, signal processing or medicine, in which a temporal sequence consists of several unknown overlapping independent causes, and we are interested in accurately recovering those canonical causes. Factorial hidden Markov models (FHMMs) present the versatility to provide a good fit to these scenarios. However, in some scenarios, the number of causes or the number of states of the FHMM cannot be known or limited a priori. In this paper, we propose an infinite factorial unbounded-state hidden Markov model (IFUHMM), in which the number of parallel hidden Markov models (HMMs) and states in each HMM are potentially unbounded. We rely on a Bayesian nonparametric (BNP) prior over integer-valued matrices, in which the columns represent the Markov chains, the rows the time indexes, and the integers the state for each chain and time instant. First, we extend the existent infinite factorial binary-state HMM to allow for any number of states. Then, we modify this model to allow for an unbounded number of states and derive an MCMC-based inference algorithm that properly deals with the trade-off between the unbounded number of states and chains. We illustrate the performance of our proposed models in the power disaggregation problem.},
keywords = {Bayes methods, Bayesian nonparametrics, CASI CAM CM, Computational modeling, GAMMA-L+ UC3M, Gibbs sampling, Hidden Markov models, Inference algorithms, Markov processes, Probability distribution, reversible jump Markov chain Monte Carlo, slice sampling, Time series, variational inference, Yttrium},
pubstate = {published},
tppubtype = {article}
}
There are many scenarios in artificial intelligence, signal processing or medicine, in which a temporal sequence consists of several unknown overlapping independent causes, and we are interested in accurately recovering those canonical causes. Factorial hidden Markov models (FHMMs) present the versatility to provide a good fit to these scenarios. However, in some scenarios, the number of causes or the number of states of the FHMM cannot be known or limited a priori. In this paper, we propose an infinite factorial unbounded-state hidden Markov model (IFUHMM), in which the number of parallel hidden Markov models (HMMs) and states in each HMM are potentially unbounded. We rely on a Bayesian nonparametric (BNP) prior over integer-valued matrices, in which the columns represent the Markov chains, the rows the time indexes, and the integers the state for each chain and time instant. First, we extend the existent infinite factorial binary-state HMM to allow for any number of states. Then, we modify this model to allow for an unbounded number of states and derive an MCMC-based inference algorithm that properly deals with the trade-off between the unbounded number of states and chains. We illustrate the performance of our proposed models in the power disaggregation problem.
Nazabal, Alfredo; Garcia-Moreno, Pablo; Artes-Rodriguez, Antonio; Ghahramani, Zoubin
Human Activity Recognition by Combining a Small Number of Classifiers Artículo de revista
En: IEEE journal of biomedical and health informatics, vol. To appear, 2016, ISSN: 2168-2208.
Resumen | Enlaces | BibTeX | Etiquetas: Bayes methods, Bayesian inference, Biological system modeling, Classifier combination, Databases, Estimation, Hidden Markov models, Sensor systems
@article{Nazabal2016bb,
title = {Human Activity Recognition by Combining a Small Number of Classifiers},
author = {Alfredo Nazabal and Pablo Garcia-Moreno and Antonio Artes-Rodriguez and Zoubin Ghahramani},
url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7161292},
doi = {10.1109/JBHI.2015.2458274},
issn = {2168-2208},
year = {2016},
date = {2016-01-01},
journal = {IEEE journal of biomedical and health informatics},
volume = {To appear},
publisher = {IEEE},
abstract = {We consider the problem of daily Human Activity Recognition (HAR) using multiple wireless inertial sensors and, specifically, HAR systems with a very low number of sensors, each one providing an estimation of the performed activities. We propose new Bayesian models to combine the output of the sensors. The models are based on a soft outputs combination of individual classifiers to deal with the small number of sensors. We also incorporate the dynamic nature of human activities as a first order homogeneous Markov chain. We develop both inductive and transductive inference methods for each model to be employed in supervised and semi-supervised situations, respectively. Using different real HAR databases, we compare our classifiers combination models against a single classifier that employs all the signals from the sensors. Our models exhibit consistently a reduction of the error rate and an increase of robustness against sensor failures. Our models also outperform other classifiers combination models that do not consider soft outputs and a Markovian structure of the human activities.},
keywords = {Bayes methods, Bayesian inference, Biological system modeling, Classifier combination, Databases, Estimation, Hidden Markov models, Sensor systems},
pubstate = {published},
tppubtype = {article}
}
We consider the problem of daily Human Activity Recognition (HAR) using multiple wireless inertial sensors and, specifically, HAR systems with a very low number of sensors, each one providing an estimation of the performed activities. We propose new Bayesian models to combine the output of the sensors. The models are based on a soft outputs combination of individual classifiers to deal with the small number of sensors. We also incorporate the dynamic nature of human activities as a first order homogeneous Markov chain. We develop both inductive and transductive inference methods for each model to be employed in supervised and semi-supervised situations, respectively. Using different real HAR databases, we compare our classifiers combination models against a single classifier that employs all the signals from the sensors. Our models exhibit consistently a reduction of the error rate and an increase of robustness against sensor failures. Our models also outperform other classifiers combination models that do not consider soft outputs and a Markovian structure of the human activities.
2014
Read, Jesse; Bielza, Concha; Larranaga, Pedro
Multi-Dimensional Classification with Super-Classes Artículo de revista
En: IEEE Transactions on Knowledge and Data Engineering, vol. 26, no 7, pp. 1720–1733, 2014, ISSN: 1041-4347.
Resumen | Enlaces | BibTeX | Etiquetas: Accuracy, Bayes methods, Classification, COMPRHENSION, conditional dependence, Context, core goals, data instance, evaluation metrics, Integrated circuit modeling, modeling class dependencies, multi-dimensional, Multi-dimensional classification, multidimensional classification problem, multidimensional datasets, multidimensional learners, multilabel classification, multilabel research, multiple class variables, ordinary class, pattern classification, problem transformation, recently-popularized task, super classes, super-class partitions, tractable running time, Training, Vectors
@article{Read2014bb,
title = {Multi-Dimensional Classification with Super-Classes},
author = {Jesse Read and Concha Bielza and Pedro Larranaga},
url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6648319},
issn = {1041-4347},
year = {2014},
date = {2014-01-01},
journal = {IEEE Transactions on Knowledge and Data Engineering},
volume = {26},
number = {7},
pages = {1720--1733},
publisher = {IEEE},
abstract = {The multi-dimensional classification problem is a generalisation of the recently-popularised task of multi-label classification, where each data instance is associated with multiple class variables. There has been relatively little research carried out specific to multi-dimensional classification and, although one of the core goals is similar (modelling dependencies among classes), there are important differences; namely a higher number of possible classifications. In this paper we present method for multi-dimensional classification, drawing from the most relevant multi-label research, and combining it with important novel developments. Using a fast method to model the conditional dependence between class variables, we form super-class partitions and use them to build multi-dimensional learners, learning each super-class as an ordinary class, and thus explicitly modelling class dependencies. Additionally, we present a mechanism to deal with the many class values inherent to super-classes, and thus make learning efficient. To investigate the effectiveness of this approach we carry out an empirical evaluation on a range of multi-dimensional datasets, under different evaluation metrics, and in comparison with high-performing existing multi-dimensional approaches from the literature. Analysis of results shows that our approach offers important performance gains over competing methods, while also exhibiting tractable running time.},
keywords = {Accuracy, Bayes methods, Classification, COMPRHENSION, conditional dependence, Context, core goals, data instance, evaluation metrics, Integrated circuit modeling, modeling class dependencies, multi-dimensional, Multi-dimensional classification, multidimensional classification problem, multidimensional datasets, multidimensional learners, multilabel classification, multilabel research, multiple class variables, ordinary class, pattern classification, problem transformation, recently-popularized task, super classes, super-class partitions, tractable running time, Training, Vectors},
pubstate = {published},
tppubtype = {article}
}
The multi-dimensional classification problem is a generalisation of the recently-popularised task of multi-label classification, where each data instance is associated with multiple class variables. There has been relatively little research carried out specific to multi-dimensional classification and, although one of the core goals is similar (modelling dependencies among classes), there are important differences; namely a higher number of possible classifications. In this paper we present method for multi-dimensional classification, drawing from the most relevant multi-label research, and combining it with important novel developments. Using a fast method to model the conditional dependence between class variables, we form super-class partitions and use them to build multi-dimensional learners, learning each super-class as an ordinary class, and thus explicitly modelling class dependencies. Additionally, we present a mechanism to deal with the many class values inherent to super-classes, and thus make learning efficient. To investigate the effectiveness of this approach we carry out an empirical evaluation on a range of multi-dimensional datasets, under different evaluation metrics, and in comparison with high-performing existing multi-dimensional approaches from the literature. Analysis of results shows that our approach offers important performance gains over competing methods, while also exhibiting tractable running time.
2013
Vazquez, Manuel A; Miguez, Joaquin
User Activity Tracking in DS-CDMA Systems Artículo de revista
En: IEEE Transactions on Vehicular Technology, vol. 62, no 7, pp. 3188–3203, 2013, ISSN: 0018-9545.
Resumen | Enlaces | BibTeX | Etiquetas: Activity detection, activity tracking, Bayes methods, Bayesian framework, Channel estimation, code division multiple access, code-division multiple access (CDMA), computer simulations, data detection, direct sequence code division multiple-access, DS-CDMA systems, Equations, joint channel and data estimation, joint channel estimation, Joints, MAP equalizers, Mathematical model, maximum a posteriori, MIMO communication, Multiaccess communication, multiple-input-multiple-output communication chann, multiuser communication systems, per-survivor processing (PSP), radio receivers, Receivers, sequential Monte Carlo (SMC) methods, time-varying number, time-varying parameter, Vectors, wireless channels
@article{Vazquez2013a,
title = {User Activity Tracking in DS-CDMA Systems},
author = {Manuel A Vazquez and Joaquin Miguez},
url = {http://www.tsc.uc3m.es/~jmiguez/papers/P39_2013_User Activity Tracking in DS-CDMA Systems.pdf http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6473922},
issn = {0018-9545},
year = {2013},
date = {2013-01-01},
journal = {IEEE Transactions on Vehicular Technology},
volume = {62},
number = {7},
pages = {3188--3203},
abstract = {In modern multiuser communication systems, users are allowed to enter or leave the system at any given time. Thus, the number of active users is an unknown and time-varying parameter, and the performance of the system depends on how accurately this parameter is estimated over time. The so-called problem of user identification, which consists of determining the number and identities of users transmitting in a communication system, is usually solved prior to, and hence independently of, that posed by the detection of the transmitted data. Since both problems are tightly connected, a joint solution is desirable. In this paper, we focus on direct-sequence (DS) code-division multiple-access (CDMA) systems and derive, within a Bayesian framework, different receivers that cope with an unknown and time-varying number of users while performing joint channel estimation and data detection. The main feature of these receivers, compared with other recently proposed schemes for user activity detection, is that they are natural extensions of existing maximum a posteriori (MAP) equalizers for multiple-input-multiple-output communication channels. We assess the validity of the proposed receivers, including their reliability in detecting the number and identities of active users, by way of computer simulations.},
keywords = {Activity detection, activity tracking, Bayes methods, Bayesian framework, Channel estimation, code division multiple access, code-division multiple access (CDMA), computer simulations, data detection, direct sequence code division multiple-access, DS-CDMA systems, Equations, joint channel and data estimation, joint channel estimation, Joints, MAP equalizers, Mathematical model, maximum a posteriori, MIMO communication, Multiaccess communication, multiple-input-multiple-output communication chann, multiuser communication systems, per-survivor processing (PSP), radio receivers, Receivers, sequential Monte Carlo (SMC) methods, time-varying number, time-varying parameter, Vectors, wireless channels},
pubstate = {published},
tppubtype = {article}
}
In modern multiuser communication systems, users are allowed to enter or leave the system at any given time. Thus, the number of active users is an unknown and time-varying parameter, and the performance of the system depends on how accurately this parameter is estimated over time. The so-called problem of user identification, which consists of determining the number and identities of users transmitting in a communication system, is usually solved prior to, and hence independently of, that posed by the detection of the transmitted data. Since both problems are tightly connected, a joint solution is desirable. In this paper, we focus on direct-sequence (DS) code-division multiple-access (CDMA) systems and derive, within a Bayesian framework, different receivers that cope with an unknown and time-varying number of users while performing joint channel estimation and data detection. The main feature of these receivers, compared with other recently proposed schemes for user activity detection, is that they are natural extensions of existing maximum a posteriori (MAP) equalizers for multiple-input-multiple-output communication channels. We assess the validity of the proposed receivers, including their reliability in detecting the number and identities of active users, by way of computer simulations.
2012
Salamanca, Luis; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando
Bayesian Equalization for LDPC Channel Decoding Artículo de revista
En: IEEE Transactions on Signal Processing, vol. 60, no 5, pp. 2672–2676, 2012, ISSN: 1053-587X.
Resumen | Enlaces | BibTeX | Etiquetas: Approximation methods, Bayes methods, Bayesian equalization, Bayesian estimation problem, Bayesian inference, Bayesian methods, BCJR (Bahl–Cocke–Jelinek–Raviv) algorithm, BCJR algorithm, Channel Coding, channel decoding, channel equalization, channel equalization problem, Channel estimation, channel state information, CSI, Decoding, equalisers, Equalizers, expectation propagation, expectation propagation algorithm, fading channels, graphical model representation, intersymbol interference, Kullback-Leibler divergence, LDPC, LDPC coding, low-density parity-check decoder, Modulation, parity check codes, symbol posterior estimates, Training
@article{Salamanca2012b,
title = {Bayesian Equalization for LDPC Channel Decoding},
author = {Luis Salamanca and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6129544},
issn = {1053-587X},
year = {2012},
date = {2012-01-01},
journal = {IEEE Transactions on Signal Processing},
volume = {60},
number = {5},
pages = {2672--2676},
abstract = {We describe the channel equalization problem, and its prior estimate of the channel state information (CSI), as a joint Bayesian estimation problem to improve each symbol posterior estimates at the input of the channel decoder. Our approach takes into consideration not only the uncertainty due to the noise in the channel, but also the uncertainty in the CSI estimate. However, this solution cannot be computed in linear time, because it depends on all the transmitted symbols. Hence, we also put forward an approximation for each symbol's posterior, using the expectation propagation algorithm, which is optimal from the Kullback-Leibler divergence viewpoint and yields an equalization with a complexity identical to the BCJR algorithm. We also use a graphical model representation of the full posterior, in which the proposed approximation can be readily understood. The proposed posterior estimates are more accurate than those computed using the ML estimate for the CSI. In order to illustrate this point, we measure the error rate at the output of a low-density parity-check decoder, which needs the exact posterior for each symbol to detect the incoming word and it is sensitive to a mismatch in those posterior estimates. For example, for QPSK modulation and a channel with three taps, we can expect gains over 0.5 dB with same computational complexity as the ML receiver.},
keywords = {Approximation methods, Bayes methods, Bayesian equalization, Bayesian estimation problem, Bayesian inference, Bayesian methods, BCJR (Bahl\textendashCocke\textendashJelinek\textendashRaviv) algorithm, BCJR algorithm, Channel Coding, channel decoding, channel equalization, channel equalization problem, Channel estimation, channel state information, CSI, Decoding, equalisers, Equalizers, expectation propagation, expectation propagation algorithm, fading channels, graphical model representation, intersymbol interference, Kullback-Leibler divergence, LDPC, LDPC coding, low-density parity-check decoder, Modulation, parity check codes, symbol posterior estimates, Training},
pubstate = {published},
tppubtype = {article}
}
We describe the channel equalization problem, and its prior estimate of the channel state information (CSI), as a joint Bayesian estimation problem to improve each symbol posterior estimates at the input of the channel decoder. Our approach takes into consideration not only the uncertainty due to the noise in the channel, but also the uncertainty in the CSI estimate. However, this solution cannot be computed in linear time, because it depends on all the transmitted symbols. Hence, we also put forward an approximation for each symbol's posterior, using the expectation propagation algorithm, which is optimal from the Kullback-Leibler divergence viewpoint and yields an equalization with a complexity identical to the BCJR algorithm. We also use a graphical model representation of the full posterior, in which the proposed approximation can be readily understood. The proposed posterior estimates are more accurate than those computed using the ML estimate for the CSI. In order to illustrate this point, we measure the error rate at the output of a low-density parity-check decoder, which needs the exact posterior for each symbol to detect the incoming word and it is sensitive to a mismatch in those posterior estimates. For example, for QPSK modulation and a channel with three taps, we can expect gains over 0.5 dB with same computational complexity as the ML receiver.