## 2015 |

Santos, Irene; Murillo-Fuentes, Juan Jose; Olmos, Pablo M Block Expectation Propagation Equalization for ISI Channels Inproceedings 2015 23rd European Signal Processing Conference (EUSIPCO), pp. 379–383, IEEE, Nice, 2015, ISBN: 978-0-9928-6263-3. Abstract | Links | BibTeX | Tags: Approximation algorithms, Approximation methods, BCJR algorithm, channel equalization, Complexity theory, Decoding, Equalizers, expectation propagation, ISI, low complexity, Signal processing algorithms @inproceedings{Santos2015, title = {Block Expectation Propagation Equalization for ISI Channels}, author = {Irene Santos and Juan Jose Murillo-Fuentes and Pablo M Olmos}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7362409}, doi = {10.1109/EUSIPCO.2015.7362409}, isbn = {978-0-9928-6263-3}, year = {2015}, date = {2015-08-01}, booktitle = {2015 23rd European Signal Processing Conference (EUSIPCO)}, pages = {379--383}, publisher = {IEEE}, address = {Nice}, abstract = {Actual communications systems use high-order modulations and channels with memory. However, as the memory of the channels and the order of the constellations grow, optimal equalization such as BCJR algorithm is computationally intractable, as their complexity increases exponentially with the number of taps and size of modulation. In this paper, we propose a novel low-complexity hard and soft output equalizer based on the Expectation Propagation (EP) algorithm that provides high-accuracy posterior probability estimations at the input of the channel decoder with similar computational complexity than the linear MMSE. We experimentally show that this quasi-optimal solution outperforms classical solutions reducing the bit error probability with low complexity when LDPC channel decoding is used, avoiding the curse of dimensionality with channel memory and constellation size.}, keywords = {Approximation algorithms, Approximation methods, BCJR algorithm, channel equalization, Complexity theory, Decoding, Equalizers, expectation propagation, ISI, low complexity, Signal processing algorithms}, pubstate = {published}, tppubtype = {inproceedings} } Actual communications systems use high-order modulations and channels with memory. However, as the memory of the channels and the order of the constellations grow, optimal equalization such as BCJR algorithm is computationally intractable, as their complexity increases exponentially with the number of taps and size of modulation. In this paper, we propose a novel low-complexity hard and soft output equalizer based on the Expectation Propagation (EP) algorithm that provides high-accuracy posterior probability estimations at the input of the channel decoder with similar computational complexity than the linear MMSE. We experimentally show that this quasi-optimal solution outperforms classical solutions reducing the bit error probability with low complexity when LDPC channel decoding is used, avoiding the curse of dimensionality with channel memory and constellation size. |

## 2012 |

Salamanca, Luis; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando Bayesian Equalization for LDPC Channel Decoding Journal Article IEEE Transactions on Signal Processing, 60 (5), pp. 2672–2676, 2012, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: 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–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}, 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. |

## 2010 |

Salamanca, Luis; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando Bayesian BCJR for Channel Equalization and Decoding Inproceedings 2010 IEEE International Workshop on Machine Learning for Signal Processing, pp. 53–58, IEEE, Kittila, 2010, ISSN: 1551-2541. Abstract | Links | BibTeX | Tags: a posteriori probability, Bayes methods, Bayesian BCJR, Bayesian methods, Bit error rate, channel decoding, channel estate information, Channel estimation, Decoding, digital communication, digital communications, equalisers, Equalizers, error statistics, Markov processes, Maximum likelihood decoding, maximum likelihood estimation, multipath channel, probabilistic channel equalization, Probability, single input single output model, SISO model, statistical information, Training @inproceedings{Salamanca2010, title = {Bayesian BCJR for Channel Equalization and Decoding}, author = {Luis Salamanca and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5589201}, issn = {1551-2541}, year = {2010}, date = {2010-01-01}, booktitle = {2010 IEEE International Workshop on Machine Learning for Signal Processing}, pages = {53--58}, publisher = {IEEE}, address = {Kittila}, abstract = {In this paper we focus on the probabilistic channel equalization in digital communications. We face the single input single output (SISO) model to show how the statistical information about the multipath channel can be exploited to further improve our estimation of the a posteriori probabilities (APP) during the equalization process. We consider not only the uncertainty due to the noise in the channel, but also in the estimate of the channel estate information (CSI). Thus, we resort to a Bayesian approach for the computation of the APP. This novel algorithm has the same complexity as the BCJR, exhibiting lower bit error rate at the output of the channel decoder than the standard BCJR that considers maximum likelihood (ML) to estimate the CSI.}, keywords = {a posteriori probability, Bayes methods, Bayesian BCJR, Bayesian methods, Bit error rate, channel decoding, channel estate information, Channel estimation, Decoding, digital communication, digital communications, equalisers, Equalizers, error statistics, Markov processes, Maximum likelihood decoding, maximum likelihood estimation, multipath channel, probabilistic channel equalization, Probability, single input single output model, SISO model, statistical information, Training}, pubstate = {published}, tppubtype = {inproceedings} } In this paper we focus on the probabilistic channel equalization in digital communications. We face the single input single output (SISO) model to show how the statistical information about the multipath channel can be exploited to further improve our estimation of the a posteriori probabilities (APP) during the equalization process. We consider not only the uncertainty due to the noise in the channel, but also in the estimate of the channel estate information (CSI). Thus, we resort to a Bayesian approach for the computation of the APP. This novel algorithm has the same complexity as the BCJR, exhibiting lower bit error rate at the output of the channel decoder than the standard BCJR that considers maximum likelihood (ML) to estimate the CSI. |

Salamanca, Luis; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando Channel Decoding with a Bayesian Equalizer Inproceedings 2010 IEEE International Symposium on Information Theory, pp. 1998–2002, IEEE, Austin, TX, 2010, ISBN: 978-1-4244-7892-7. Abstract | Links | BibTeX | Tags: a posteriori probability, Bayesian equalizer, Bayesian methods, BER, Bit error rate, Channel Coding, channel decoding, channel estate information, Communication channels, Decoding, equalisers, Equalizers, error statistics, low-density parity-check decoders, LPDC decoders, Maximum likelihood decoding, maximum likelihood detection, maximum likelihood estimation, Noise reduction, parity check codes, Probability, Uncertainty @inproceedings{Salamanca2010a, title = {Channel Decoding with a Bayesian Equalizer}, author = {Luis Salamanca and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5513348}, isbn = {978-1-4244-7892-7}, year = {2010}, date = {2010-01-01}, booktitle = {2010 IEEE International Symposium on Information Theory}, pages = {1998--2002}, publisher = {IEEE}, address = {Austin, TX}, abstract = {Low-density parity-check (LPDC) decoders assume the channel estate information (CSI) is known and they have the true a posteriori probability (APP) for each transmitted bit. But in most cases of interest, the CSI needs to be estimated with the help of a short training sequence and the LDPC decoder has to decode the received word using faulty APP estimates. In this paper, we study the uncertainty in the CSI estimate and how it affects the bit error rate (BER) output by the LDPC decoder. To improve these APP estimates, we propose a Bayesian equalizer that takes into consideration not only the uncertainty due to the noise in the channel, but also the uncertainty in the CSI estimate, reducing the BER after the LDPC decoder.}, keywords = {a posteriori probability, Bayesian equalizer, Bayesian methods, BER, Bit error rate, Channel Coding, channel decoding, channel estate information, Communication channels, Decoding, equalisers, Equalizers, error statistics, low-density parity-check decoders, LPDC decoders, Maximum likelihood decoding, maximum likelihood detection, maximum likelihood estimation, Noise reduction, parity check codes, Probability, Uncertainty}, pubstate = {published}, tppubtype = {inproceedings} } Low-density parity-check (LPDC) decoders assume the channel estate information (CSI) is known and they have the true a posteriori probability (APP) for each transmitted bit. But in most cases of interest, the CSI needs to be estimated with the help of a short training sequence and the LDPC decoder has to decode the received word using faulty APP estimates. In this paper, we study the uncertainty in the CSI estimate and how it affects the bit error rate (BER) output by the LDPC decoder. To improve these APP estimates, we propose a Bayesian equalizer that takes into consideration not only the uncertainty due to the noise in the channel, but also the uncertainty in the CSI estimate, reducing the BER after the LDPC decoder. |