Funded by the Spanish Ministry of Economy, Grant No. TEC2016-78434-C3-{1,2,3}-R

Involved Members

Overview

Shannons channel capacity establishes the largest information rate at which data can be reliably transmitted over a noisy channel; in this context, reliability is attained by using codes that add redundancy to the information message. Recently, a number of code families have been recently shown to perform close to the channel capacity. Among them, low-density parity-check (LDPC) codes have been adopted in many modern standards. The decoders of such codes are based on the belief propagation (BP) principle, an efficient algorithm to solve inference problems by iteratively passing local messages. The current analysis of BP iterative decoding algorithms focuses on their infinite-length performance. However, due to delay and complexity constraints, practical communication schemes transmit information in finite-length packets. Even if a coding scheme can be shown to asymptotically achieve capacity, it may perform far from the theoretical limit at finite blocklength. This can be attributed either to the code itself or to the poor performance of BP when loops in the associated graph shorten as the parity-check matrix becomes denser. Nowadays, there are no theoretical tools characterizing these two effects in a unified manner. In this project, we will provide an information-theoretic analysis of iterative decoding. Then, we will define design criteria for finite-length Generalized LDPC (GLDPC) codes that approach the corresponding fundamental limits. We shall also propose novel beyond-BP decoders based on recent advances in expectation propagation (EP) approximate inference for discrete distributions. Implementation constraints will be taken into account. In particular, we shall consider quantization methods for iterative decoders based on the theories of rate-distortion and mismatched decoding.

The iterative decoding principle extends to modern receivers, where general soft-input soft-output algorithms for receiver blocks such as multiple-input multiple-output detectors or turbo equalizers play a central role. In this context, optimal solutions are computationally unaffordable and BP fails as approximate inference approach. We shall extend the novel EP approach developed for channel coding into a soft-input soft-output algorithm receiver coupled to the decoder.

This project aims at building an ambitious theoretical framework for iterative approximate inference with focus on the finite-length regime. Specific project contributions are the following. First, the theoretical characterization, in terms of tradeoffs between rate, block length, and error probability, of short-length transmission under iterative decoding. Second, original GLDPC coding schemes under state-of-the-art decoding to approach these limits. Third, novel techniques to improve approximate inference in iterative decoders and detectors. And fourth, comprehensive experimental scenarios and toolboxes to evaluate code performance as a trade-off between computational complexity and gap to capacity limits, including realistic implementation constraints.

Outline of Our Results

On of the main results of the project is the development of new designs for SISO equalization and MIMO detection. We reviewed the classic designs of

  • equalizer based on the one-shot LMMSE,
  • the Wiener-type filter and
  • the Kalman-smoother equalizers

to greatly improve their performance by just iterating the LMMSE a few times. Furthermore, we include the channel decoder in the detection to propose novel turbo-equalizers, testing the solutions with LDPCs codes. Results were outstanding. Same ideas were exploited in the design of a MIMO channel detector, with remarkable gains in BER and robutness.

We also focused on the inference for complex valued processes. We found some flaws in the state-of-the-art. We have rewritten the reproducing kernel Hilbert spaces for complex-valued and apply it to kernel least mean square (KLMS), Gaussian processes for regression (GPR) and then for adaptive versions.

In Gaussian processes we researched in more powerful tools by means of deep learning architectures. Then in applications to crowdsourcing in localization.

We also exploited our knowledge on frequency analysis for communications to other applications.

Involved Members at US

Research Team: Juan J. Murillo Fuentes, Rafael Boloix Tortosa, Eva Arias de Reyna, Francisco J. Simois Tirado.

Working Team: Petar Djuric (Stony Brook Univ.), Irene Santos Velázquez, José Carlos Aradillas Jaramillo, Marta Ternero Gutiérrez, Rafael Vaquero Acevedo.

Publications

Journals

  1. I. Santos, J. J. Murillo-Fuentes, José C. Aradillas and E. Arias-de-Reyna (2020), “Channel Equalization with Expectation Propagation at Smoothing Level,” in IEEE Transactions on Communications, see paper. Accepted.
  2. I. Santos, J. J. Murillo-Fuentes and E. Arias-de-Reyna (2020), “A Double EP-Based Proposal for Turbo Equalization,” in IEEE Signal Processing Letters, vol. 27, pp. 121-125, 2020. See DOI: 10.1109/LSP.2019.2959900, see also the paper.
  3. Boloix-Tortosa, J.J. Murillo-Fuentes S.A. Tsaftaris. (2019). “The Generalized Complex Kernel Least-Mean-Square Algorithm” IEEE Transactions on Signal Processing, Vol. 67, no. 20, pp. 5213 – 5222. Oct.15, 2019. DOI 10.1109/TSP.2019.2937289, https://arxiv.org/abs/1902.08692
  4. Santos, J.J. Murillo-Fuentes. (2019). “Self and Turbo Iterations for MIMO Receivers and Large-Scale Systems” IEEE Wireless Communications Letters. 8-4, pp.1095-1098 2019. DOI 10.1109/LWC.2019.2907941, https://arxiv.org/abs/1805.05065
  5. Santos, J.J. Murillo-Fuentes, P. M. Djuric. (2019). Recursive Estimation of Dynamic RSS Fields Based on Crowdsourcing and Gaussian Processes. IEEE Transactions on Signal Processing. 2019. EEE (2017) Q1, 32/260. DOI 10.1109/TSP.2018.2889987, https://arxiv.org/abs/1806.02530.
  6. Santos, J. J. Murillo-Fuentes, E. Arias-de-Reyna and P. M. Olmos (2018), “Turbo EP-Based Equalization: A Filter-Type Implementation,” in IEEE Transactions on Communications, vol. 66, no. 9, pp. 4259-4270, Sept. 2018.  DOI: 10.1109/TCOMM.2018.2832202, https://arxiv.org/abs/1711.08188
  7. Eva Arias-de-Reyna, Pau Closas, Davide Dardari, Petar M. Djuric (2018). “Crowd-based Learning of Spatial Fields for the IoT: from Harvesting of Data to Inference.” IEEE Signal Processing Magazine. Special Issue on Signal Processing and the Internet-of-Things, vol. 35, num.5. pp 130-139. September 2018, DOI 10.1109/Msp.2018.2840156
  8. R. Boloix-Tortosa, J. J. Murillo-Fuentes, F. J. Payán-Somet and F. Pérez-Cruz, “Complex Gaussian Processes for Regression,” in IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 11, pp. 5499-5511, Nov. 2018. DOI: 10.1109/TNNLS.2018.2805019 https://arxiv.org/abs/1511.05710
  9. Francisco J. Simois, Juan José Murillo-Fuentes, (2017) “On the power spectral density applied to the analysis of old canvases”, Signal Processing, 2017, ISSN 0165-1684. Paper in Signal Processing or arxiv.org.
  10. R. Boloix-Tortosa, J. J. Murillo-Fuentes, I. Santos and F. Pérez-Cruz, (2017) “Widely Linear Complex-Valued Kernel Methods for Regression,” in IEEE Transactions on Signal Processing, vol. 65, no. 19, pp. 5240-5248, Oct.1, 1 2017. Paper, also in IEEE TSP, arxiv.org
  11. I. Santos, J. J. Murillo-Fuentes, E. Arias-de-Reyna and P. M. Olmos (2017), “Probabilistic Equalization With a Smoothing Expectation Propagation Approach,” in IEEE Transactions on Wireless Communications, vol. 16, no. 5, pp. 2950-2962, May 2017. Paper, also in IEEE TWCOM. Code
  12. I. Santos, J.J. Murillo-Fuentes, R. Boloix-Tortosa, Eva Arias de Reyna and Pablo M. Olmos, (2017). “Expectation Propagation as Turbo Equalizer in ISI Channels“. IEEE Transactions on Communications, vol. 65, no.1, pp.360-370, January 2017. code

Conferences and Workshops

  1. Havasi, J.M. Hernández-Lobato, J.J. Murillo-Fuentes (2018). “Inference in Deep Gaussian Processes using Stochastic Gradient Hamiltonian Monte Carlo“ Neural Information and Processing Systems (NeurIPS), 2018.
  2. E. Arias-de-Reyna , D. Dardari, P. Closas, P. M. Djurić, (2018). “Estimation of Spatial Fields of NLOS/LOS Conditions for Improved Localization in Indoor Environments”, IEEE Statistical Signal Processing Workshop (SSP). Freiburg (Germany), 2018.
  3. C. Aradillas, J.J. Murillo-Fuentes, P.M. Olmos (2018). “Boosting Handwriting Text Recognition in Small Databases with Transfer Learning”. Int. Conf. on Frontiers in Handwriting Recognition (ICFHR) 2018. Niagara Falls, NY, USA. 2018.
  4. I. Santos, J.J. Murillo-Fuentes, (2018). “Improved probabilistic EP-based receiver for MIMO systems and high-order modulations”. Comunicación en congreso. XXXIII Simposium Nacional de la Unión Científica Internacional de Radio URSI 2018. Granada, España. 2018.
  5. I. Santos, P. Djuric, (2017). “Crowdsource-based signal strength field estimation by Gaussian Processes”. Proc of 25th European Signal Processing Conference (EUSIPCO). Kos (Greece). 2017
  6. I. Santos Velázquez, J.J. Murillo-Fuentes, P.M. Djuric, (2017). “Recursive Estimation of Time-Varying RSS Fields Based on Crowdsourcing and Gaussian Processes”. IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) 2017.

Invited Talks

  • J. Murillo-Fuentes, I. Santos, P. M. Olmos, E. Arias de Reyna Domínguez, (2018). “Expectation Propagation applied to Digital Communications Systems with Large Dimensions”. Sesión plenaria en Congreso. 3rd Workshop on Communication Networks and Power Systems. Brasilia, Brasil. 2018.

Collaborations

This work was also possible thanks to the fruitful collaboration with

  • prof Djuric (Stony Brook University, USA),
  • prof. Hernández-Lobato (University of Cambridge, UK),
  • prof. Pérez-Cruz, from Swiss Data Science Center (EPFL/ETZH, Swiss)
  • prof. Dardari de la Universidad de Bolonia
  • prof. Closas, de la Northeastern University, USA

Acknowledgements

These results were possible thanks to public fundings. The Universidad de Sevilla trusted us to carry out this research. The Spanish Government and the European Union (FEDER) also founded this research through the Grant TEC2006-13514-C02-2/TCM.

USfeder

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