| 1. |
- Buchberger, Andreas, 1990, et al.
(författare)
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Learned Decimation for Neural Belief Propagation Decoders
- 2021
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Ingår i: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. - 1520-6149. ; 2021-June, s. 8273-8277
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Konferensbidrag (refereegranskat)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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| 2. |
- Buchberger, Andreas, 1990
(författare)
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On Probabilistic Shaping and Learned Decoders with Application to Fiber-Optic Communications
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We live in an ubiquitously connected world whose backbone are optical fibers. Achieving high spectral efficiencies and hence high transmission rates requires a careful combination of forward error correction (FEC) and higher-order modulation. This is referred to as coded modulation. In this thesis, we focus on probabilistic shaping which aims to shape the distribution of the transmitted symbols to the capacity-achieving distribution. For symmetric distributions, probabilistic amplitude shaping (PAS) has been proposed by Böcherer et al.. Certain fiber-optic systems, however, have non-symmetric capacity-achieving distributions and hence, PAS can not be applied. In the first part of this thesis, we focus on probabilistic shaping for asymmetric distributions. For a nonlinear Fourier transform-based transmission scheme, we introduce probabilistic eigenvalue shaping, where the coded symbols are partially distributed according to the capacity-achieving distribution and partially uniformly distributed. Further, for an intensity modulation with direct-detection (IM/DD) system, we uncover a hidden symmetry of the capacity-achieving distribution. We propose to extend the PAS scheme with a compound construction of a low-density generator matrix code and a low-density parity-check code (LDGM/LDPC) to incorporate this hidden symmetry. For both shaping schemes, we demonstrate significant improvements over the state of the art. In the second part of this thesis, we address low-complexity, near-maximum-likelihood (ML) decoding of short linear block codes, which play an important role in FEC in fiber-optic communication systems as component codes in staircase codes or generalized LDPC codes. Our work extends neural belief propagation (NBP) introduced by Nachmani et al. where belief propagation decoding is unrolled and weights are placed on the edges. In particular, we 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. Unimportant CNs are successively pruned. This typically results in a different parity-check matrix in each iteration. We demonstrate that for codes with a dense parity-check matrix such as algebraic codes, our proposed decoder performs close to ML decoding. To further improve the decoding of short LDPC codes, we introduce a two-stage decimation process to NBP decoding. First, we create a list by iterating between a conventional NBP decoder and guessing the least reliable bit. This is followed by iterating between a conventional NBP decoder and learned decimation, where we use a neural network to decide the decimation value for each bit. For short LDPC codes, this results in a significant performance gain.
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| 3. |
- Buchberger, Andreas, 1990, et al.
(författare)
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Probabilistic Eigenvalue Shaping for Nonlinear Fourier Transform Transmission
- 2018
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Ingår i: Journal of Lightwave Technology. - 0733-8724 .- 1558-2213. ; 36:20, s. 4799-4807
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Tidskriftsartikel (refereegranskat)abstract
- We consider a nonlinear Fourier transform (NFT)-based transmission scheme, where data is embedded into the imaginary part of the nonlinear discrete spectrum. Inspired by probabilistic amplitude shaping, we propose a probabilistic eigenvalue shaping (PES) scheme as a means to increase the data rate of the system. We exploit the fact that for an NFT-based transmission scheme the pulses in the time domain are of unequal duration by transmitting them with a dynamic symbol interval and find a capacity-achieving distribution. The PES scheme shapes the information symbols according to the capacity-achieving distribution and transmits them together with the parity symbols at the output of a low-density parity-check encoder, suitably modulated, via time-sharing. We furthermore derive an achievable rate for the proposed PES scheme. We verify our results with simulations of the discrete-time model as well as with split-step Fourier simulations.
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| 4. |
- Buchberger, Andreas, 1990, et al.
(författare)
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Pruning and Quantizing Neural Belief Propagation Decoders
- 2021
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Ingår i: IEEE Journal on Selected Areas in Communications. - 0733-8716 .- 1558-0008. ; 39:7, s. 1957-1966
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Tidskriftsartikel (refereegranskat)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.
(författare)
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Pruning Neural Belief Propagation Decoders
- 2020
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Ingår i: IEEE International Symposium on Information Theory - Proceedings. - 2157-8095. ; 2020-June, s. 338-342
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Konferensbidrag (refereegranskat)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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