2013
Olmos, Pablo M; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando
Tree-Structure Expectation Propagation for LDPC Decoding Over the BEC Artículo de revista
En: IEEE Transactions on Information Theory, vol. 59, no 6, pp. 3354–3377, 2013, ISSN: 0018-9448.
Resumen | Enlaces | BibTeX | Etiquetas: Algorithm design and analysis, Approximation algorithms, Approximation methods, BEC, belief propagation, Belief-propagation (BP), binary erasure channel, Complexity theory, decode low-density parity-check codes, Decoding, discrete memoryless channels, expectation propagation, finite-length analysis, LDPC codes, LDPC decoding, parity check codes, peeling-type algorithm, Probability density function, random graph evolution, Tanner graph, tree-structure expectation propagation
@article{Olmos2013b,
title = {Tree-Structure Expectation Propagation for LDPC Decoding Over the BEC},
author = {Pablo M Olmos and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6451276},
issn = {0018-9448},
year = {2013},
date = {2013-01-01},
journal = {IEEE Transactions on Information Theory},
volume = {59},
number = {6},
pages = {3354--3377},
abstract = {We present the tree-structure expectation propagation (Tree-EP) algorithm to decode low-density parity-check (LDPC) codes over discrete memoryless channels (DMCs). Expectation propagation generalizes belief propagation (BP) in two ways. First, it can be used with any exponential family distribution over the cliques in the graph. Second, it can impose additional constraints on the marginal distributions. We use this second property to impose pairwise marginal constraints over pairs of variables connected to a check node of the LDPC code's Tanner graph. Thanks to these additional constraints, the Tree-EP marginal estimates for each variable in the graph are more accurate than those provided by BP. We also reformulate the Tree-EP algorithm for the binary erasure channel (BEC) as a peeling-type algorithm (TEP) and we show that the algorithm has the same computational complexity as BP and it decodes a higher fraction of errors. We describe the TEP decoding process by a set of differential equations that represents the expected residual graph evolution as a function of the code parameters. The solution of these equations is used to predict the TEP decoder performance in both the asymptotic regime and the finite-length regimes over the BEC. While the asymptotic threshold of the TEP decoder is the same as the BP decoder for regular and optimized codes, we propose a scaling law for finite-length LDPC codes, which accurately approximates the TEP improved performance and facilitates its optimization.},
keywords = {Algorithm design and analysis, Approximation algorithms, Approximation methods, BEC, belief propagation, Belief-propagation (BP), binary erasure channel, Complexity theory, decode low-density parity-check codes, Decoding, discrete memoryless channels, expectation propagation, finite-length analysis, LDPC codes, LDPC decoding, parity check codes, peeling-type algorithm, Probability density function, random graph evolution, Tanner graph, tree-structure expectation propagation},
pubstate = {published},
tppubtype = {article}
}
We present the tree-structure expectation propagation (Tree-EP) algorithm to decode low-density parity-check (LDPC) codes over discrete memoryless channels (DMCs). Expectation propagation generalizes belief propagation (BP) in two ways. First, it can be used with any exponential family distribution over the cliques in the graph. Second, it can impose additional constraints on the marginal distributions. We use this second property to impose pairwise marginal constraints over pairs of variables connected to a check node of the LDPC code's Tanner graph. Thanks to these additional constraints, the Tree-EP marginal estimates for each variable in the graph are more accurate than those provided by BP. We also reformulate the Tree-EP algorithm for the binary erasure channel (BEC) as a peeling-type algorithm (TEP) and we show that the algorithm has the same computational complexity as BP and it decodes a higher fraction of errors. We describe the TEP decoding process by a set of differential equations that represents the expected residual graph evolution as a function of the code parameters. The solution of these equations is used to predict the TEP decoder performance in both the asymptotic regime and the finite-length regimes over the BEC. While the asymptotic threshold of the TEP decoder is the same as the BP decoder for regular and optimized codes, we propose a scaling law for finite-length LDPC codes, which accurately approximates the TEP improved performance and facilitates its optimization.
2012
Monzon, Sandra; Trigano, Tom; Luengo, David; Artés-Rodríguez, Antonio
Sparse Spectral Analysis of Atrial Fibrillation Electrograms. Proceedings Article
En: 2012 IEEE International Workshop on Machine Learning for Signal Processing, pp. 1–6, IEEE, Santander, 2012, ISSN: 1551-2541.
Resumen | Enlaces | BibTeX | Etiquetas: Algorithm design and analysis, atrial fibrillation, atrial fibrillation electrogram, biomedical signal processing, dominant frequency, Doped fiber amplifiers, electrocardiography, Harmonic analysis, Heart, heart disorder, Indexes, Mathematical model, medical signal processing, multiple foci, multiple uncoordinated activation foci, signal processing technique, sparse spectral analysis, sparsity-aware learning, sparsity-aware learning technique, spectral analysis, spike train
@inproceedings{Monzon2012,
title = {Sparse Spectral Analysis of Atrial Fibrillation Electrograms.},
author = {Sandra Monzon and Tom Trigano and David Luengo and Antonio Art\'{e}s-Rodr\'{i}guez},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6349721},
issn = {1551-2541},
year = {2012},
date = {2012-01-01},
booktitle = {2012 IEEE International Workshop on Machine Learning for Signal Processing},
pages = {1--6},
publisher = {IEEE},
address = {Santander},
abstract = {Atrial fibrillation (AF) is a common heart disorder. One of the most prominent hypothesis about its initiation and maintenance considers multiple uncoordinated activation foci inside the atrium. However, the implicit assumption behind all the signal processing techniques used for AF, such as dominant frequency and organization analysis, is the existence of a single regular component in the observed signals. In this paper we take into account the existence of multiple foci, performing a spectral analysis to detect their number and frequencies. In order to obtain a cleaner signal on which the spectral analysis can be performed, we introduce sparsity-aware learning techniques to infer the spike trains corresponding to the activations. The good performance of the proposed algorithm is demonstrated both on synthetic and real data.},
keywords = {Algorithm design and analysis, atrial fibrillation, atrial fibrillation electrogram, biomedical signal processing, dominant frequency, Doped fiber amplifiers, electrocardiography, Harmonic analysis, Heart, heart disorder, Indexes, Mathematical model, medical signal processing, multiple foci, multiple uncoordinated activation foci, signal processing technique, sparse spectral analysis, sparsity-aware learning, sparsity-aware learning technique, spectral analysis, spike train},
pubstate = {published},
tppubtype = {inproceedings}
}
Atrial fibrillation (AF) is a common heart disorder. One of the most prominent hypothesis about its initiation and maintenance considers multiple uncoordinated activation foci inside the atrium. However, the implicit assumption behind all the signal processing techniques used for AF, such as dominant frequency and organization analysis, is the existence of a single regular component in the observed signals. In this paper we take into account the existence of multiple foci, performing a spectral analysis to detect their number and frequencies. In order to obtain a cleaner signal on which the spectral analysis can be performed, we introduce sparsity-aware learning techniques to infer the spike trains corresponding to the activations. The good performance of the proposed algorithm is demonstrated both on synthetic and real data.