| 1. |
- Bravo, L, et al.
(author)
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- 2021
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swepub:Mat__t
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| 2. |
- Tabiri, S, et al.
(author)
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- 2021
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swepub:Mat__t
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| 3. |
- Buchberger, Andreas, 1990, et al.
(author)
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Learned Decimation for Neural Belief Propagation Decoders
- 2021
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In: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. - 1520-6149. ; 2021-June, s. 8273-8277
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Conference paper (peer-reviewed)abstract
- We introduce a two-stage decimation process to improve the performance of neural belief propagation (NBP), recently introduced by Nachmani et al., for short low-density parity-check (LDPC) codes. In the first stage, we build a list by iterating between a conventional NBP decoder and guessing the least reliable bit. The second stage iterates between a conventional NBP decoder and learned decimation, where we use a neural network to decide the decimation value for each bit. For a (128,64) LDPC code, the proposed NBP with decimation outperforms NBP decoding by 0.75dB and performs within 1dB from maximum-likelihood decoding at a block error rate of 10-4.
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| 4. |
- Buchberger, Andreas, 1990, et al.
(author)
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Pruning and Quantizing Neural Belief Propagation Decoders
- 2021
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In: IEEE Journal on Selected Areas in Communications. - 0733-8716 .- 1558-0008. ; 39:7, s. 1957-1966
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Journal article (peer-reviewed)abstract
- We consider near maximum-likelihood (ML) decoding of short linear block codes. In particular, we propose a novel decoding approach based on neural belief propagation (NBP) decoding recently introduced by Nachmani et al. in which we allow a different parity-check matrix in each iteration of the algorithm. The key idea is to consider NBP decoding over an overcomplete parity-check matrix and use the weights of NBP as a measure of the importance of the check nodes (CNs) to decoding. The unimportant CNs are then pruned. In contrast to NBP, which performs decoding on a given fixed parity-check matrix, the proposed pruning-based neural belief propagation (PB-NBP) typically results in a different parity-check matrix in each iteration. For a given complexity in terms of CN evaluations, we show that PB-NBP yields significant performance improvements with respect to NBP. We apply the proposed decoder to the decoding of a Reed-Muller code, a short low-density parity-check (LDPC) code, and a polar code. PB-NBP outperforms NBP decoding over an overcomplete parity-check matrix by 0.27–0.31 dB while reducing the number of required CN evaluations by up to 97%. For the LDPC code, PB-NBP outperforms conventional belief propagation with the same number of CN evaluations by 0.52 dB. We further extend the pruning concept to offset min-sum decoding and introduce a pruning-based neural offset min-sum (PB-NOMS) decoder, for which we jointly optimize the offsets and the quantization of the messages and offsets. We demonstrate performance 0.5 dB from ML decoding with 5-bit quantization for the Reed-Muller code.
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| 5. |
- Buchberger, Andreas, 1990, et al.
(author)
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Pruning Neural Belief Propagation Decoders
- 2020
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In: IEEE International Symposium on Information Theory - Proceedings. - 2157-8095. ; 2020-June, s. 338-342
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Conference paper (peer-reviewed)abstract
- We consider near maximum-likelihood (ML) decoding of short linear block codes based on neural belief propagation (BP) decoding recently introduced by Nachmani et al.. While this method significantly outperforms conventional BP decoding, the underlying parity-check matrix may still limit the overall performance. In this paper, we introduce a method to tailor an overcomplete parity-check matrix to (neural) BP decoding using machine learning. We consider the weights in the Tanner graph as an indication of the importance of the connected check nodes (CNs) to decoding and use them to prune unimportant CNs. As the pruning is not tied over iterations, the final decoder uses a different parity-check matrix in each iteration. For ReedMuller and short low-density parity-check codes, we achieve performance within 0.27dB and 1.5dB of the ML performance while reducing the complexity of the decoder.
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| 6. |
- Butler, Rick M., et al.
(author)
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Model-Based Machine Learning for Joint Digital Backpropagation and PMD Compensation
- 2021
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In: Journal of Lightwave Technology. - 0733-8724 .- 1558-2213. ; 39:4, s. 949-959
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Journal article (peer-reviewed)abstract
- In this article, we propose a model-based machine-learning approach for dual-polarization systems by parameterizing the split-step Fourier method for the Manakov-PMD equation. The resulting method combines hardware-friendly time-domain nonlinearity mitigation via the recently proposed learned digital backpropagation (LDBP) with distributed compensation of polarization-mode dispersion (PMD). We refer to the resulting approach as LDBP-PMD. We train LDBP-PMD on multiple PMD realizations and show that it converges within 1% of its peak dB performance after 428 training iterations on average, yielding a peak effective signal-to-noise ratio of only 0.30 dB below the PMD-free case. Similar to state-of-the-art lumped PMD compensation algorithms in practical systems, our approach does not assume any knowledge about the particular PMD realization along the link, nor any knowledge about the total accumulated PMD. This is a significant improvement compared to prior work on distributed PMD compensation, where knowledge about the accumulated PMD is typically assumed. We also compare different parameterization choices in terms of performance, complexity, and convergence behavior. Lastly, we demonstrate that the learned models can be successfully retrained after an abrupt change of the PMD realization along the fiber.
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| 7. |
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| 8. |
- Coskun, Mustafa C., et al.
(author)
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Successive Cancellation Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding
- 2023
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In: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 69:2, s. 823-841
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Journal article (peer-reviewed)abstract
- A product code with single parity-check component codes can be described via the tools of a multi-kernel polar code, where the rows of the generator matrix are chosen according to the constraints imposed by the product code construction. Following this observation, successive cancellation decoding of such codes is introduced. In particular, the error probability of single parity-check product codes over binary memoryless symmetric channels under successive cancellation decoding is characterized. A bridge with the analysis of product codes introduced by Elias is also established for the binary erasure channel. Successive cancellation list decoding of single parity-check product codes is then described. For the provided example, simulations over the binary input additive white Gaussian channel show that successive cancellation list decoding outperforms belief propagation decoding applied to the code graph. Finally, the performance of the concatenation of a product code with a high-rate outer code is investigated via distance spectrum analysis. Examples of concatenations performing within 0.7 dB from the random coding union bound are provided.
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| 9. |
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| 10. |
- Häger, Christian, 1986, et al.
(author)
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A Deterministic Construction and Density Evolution Analysis for Generalized Product Codes
- 2016
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Conference paper (other academic/artistic)abstract
- Generalized product codes (GPCs) are extensions of product codes (PCs) where code symbols are protected by two component codes but not necessarily arranged in a rectangular array. In this tutorial paper, we review a deterministic construction for GPCs that has been previously proposed by the authors together with an accompanying density evolution (DE) analysis. The DE analysis characterizes the asymptotic performance of the resulting GPCs under iterative bounded-distance decoding of the component codes over the binary erasure channel. As an application, we discuss the analysis and design of three different classes of GPCs: spatially-coupled PCs, symmetric GPCs, and GPCs based on component code mixtures.
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