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arxiv: 2506.17530 · v2 · submitted 2025-06-21 · 💻 cs.IT · math.IT

Deep-OFDM: Neural Modulation for High Mobility

S. Ashwin Hebbar , Sravan Kumar Ankireddy , Harshithanjani Athi , Brandon Nguyen , Pramod Viswanath , Hyeji Kim This is my paper

Pith reviewed 2026-05-19 07:44 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords neural modulationOFDMhigh mobilityDopplerpilotless communicationjoint transmitter-receiver designconstellation learning
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The pith

A neural modulator for OFDM spreads symbols across time-frequency neighborhoods to break QAM rotational symmetry, letting the receiver infer phase directly from data symbols.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a joint transmitter-receiver design for OFDM where a small CNN at the transmitter spreads each symbol's information across nearby time and frequency resources instead of placing it on a single resource element. This learned spreading is trained end-to-end with a neural receiver on simulated high-Doppler channels. Because the resulting constellation points lose the usual rotational symmetry of QAM, the receiver gains the ability to estimate residual phase offsets directly from the data-carrying symbols. As a result the system maintains good performance even when pilots are very sparse or absent altogether, which is valuable in fast-moving scenarios where channel estimates quickly become outdated.

Core claim

DeepOFDM augments conventional OFDM with a lightweight convolutional neural network modulator that spreads information across local time-frequency neighborhoods rather than mapping symbols independently. Jointly optimized with a neural receiver, the learned modulation breaks the rotational symmetry of conventional QAM constellations. This enables the receiver to infer residual phase directly from data symbols, allowing reliable operation with sparse pilots and even in fully pilotless settings under high Doppler conditions while remaining compatible with FFT-based processing.

What carries the argument

The lightweight convolutional neural network modulator that spreads information across local time-frequency neighborhoods in the OFDM resource grid.

Load-bearing premise

End-to-end training on simulated high-Doppler channels yields a modulator-receiver pair that generalizes to real-world propagation and hardware without retraining or extra side information.

What would settle it

A high-mobility over-the-air test in which the learned pair shows no block-error-rate improvement over conventional OFDM unless the model is retrained on measured channel data.

Figures

Figures reproduced from arXiv: 2506.17530 by Brandon Nguyen, Harshithanjani Athi, Hyeji Kim, Pramod Viswanath, S. Ashwin Hebbar, Sravan Kumar Ankireddy.

Figure 1
Figure 1. Figure 1: End-to-end optimization of transmitter and receiver. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Neural Modulation architecture Neural Modulator. To enable time-frequency diversity at the transmitter, we design the neural modulator as a convolu￾tional neural network (CNN). CNNs are a natural fit for this purpose, as their spatial structure enables the model to effec￾tively couple nearby time-frequency components, potentially enhancing robustness against mobility-induced impairments, such as inter-carr… view at source ↗
Figure 3
Figure 3. Figure 3: Neural receiver to predict LLRs. Layer Channels (Modulator) Channels (Receiver) Kernel size Dilation rate Input Conv2D 36 48 (3,3) (1,1) ResNet block 1 72 96 (7,7) (7,2) ResNet block 2 72 96 (7,5) (7,1) ResNet block 3 72 96 (5,3) (1,2) ResNet block 4 72 96 (3,3) (1,1) ResNet block 5 72 96 (3,3) (1,1) Output Conv2D 2 2m (1,1) (1,1) TABLE I: Architecture details for neural modulator and receiver. Training. W… view at source ↗
Figure 4
Figure 4. Figure 4: Deep-OFDM exhibits gains in BLER compared to NRx with trainable constellations (GS). The gains are more pronounced in the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Pilotless Deep-OFDM (0P) outperforms NRx and explicit SIP in BLER; It matcehes BLER of NRx with 2 pilots, while there is a [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: BLER performance comparison in MIMO systems. Deep [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: SVD of the neural modulator’s output mean reveals a strong [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Implicitly learned pilot pattern [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The combined Deep-OFDM + SIP system outperforms both components individually, demonstrating that explicit pilot structure (SIP) [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: A simple modulator consisting of a 5 × 5 convolution and a batch normalization achieves non-trivial performance under pilotless communication. This outperforms Deep-OFDM when restricted to 1 × 1 convolutions, highlighting the importance of time-frequency mixing for robustness in high-mobility channels. are zeroed out or blocked in each training iteration, forcing the model to learn representations that ar… view at source ↗
Figure 14
Figure 14. Figure 14: BLER performance of Deep-OFDM with varying numbers [PITH_FULL_IMAGE:figures/full_fig_p010_14.png] view at source ↗
Figure 13
Figure 13. Figure 13: BLER performance of Deep-OFDM when the time-frequency [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: BLER performance of Deep-OFDM with and without non [PITH_FULL_IMAGE:figures/full_fig_p011_15.png] view at source ↗
read the original abstract

Orthogonal Frequency Division Multiplexing (OFDM) is the dominant waveform in modern wireless systems, but suffers performance degradation in high-mobility environments due to Doppler-induced inter-carrier interference and unreliable pilot-based channel estimation. Neural receivers have recently shown strong performance in OFDM systems by learning equalization and detection directly from the received time-frequency grid. However, when channel estimation becomes unreliable, receiver-side learning alone is insufficient to fully recover performance. In this work we introduce DeepOFDM, a learnable modulation framework that augments conventional OFDM with a lightweight convolutional neural network (CNN) modulator jointly optimized with a neural receiver. Instead of mapping symbols independently to resource elements, DeepOFDM spreads information across local time-frequency neighborhoods while remaining fully compatible with FFT-based OFDM processing. The learned modulation breaks the rotational symmetry of conventional QAM constellations, enabling the receiver to infer residual phase directly from data symbols. This structure allows reliable operation with sparse pilots and even in fully pilotless settings. Extensive simulations demonstrate improvements in block error rate and goodput under high Doppler, while over-the-air experiments confirm practical feasibility. These results highlight the potential of transmitter-receiver co-design for robust and spectrally efficient AI-native physical layer design.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The manuscript introduces DeepOFDM, a learnable modulation framework for OFDM in high-mobility scenarios. A lightweight CNN modulator spreads information across local time-frequency neighborhoods and is jointly optimized with a neural receiver. The design breaks the rotational symmetry of conventional QAM constellations, enabling the receiver to infer residual phase directly from data symbols. This facilitates reliable operation with sparse pilots or in fully pilotless settings. Simulations demonstrate BLER and goodput improvements under high Doppler, and over-the-air experiments confirm practical feasibility.

Significance. If the central claims hold, this work has significant implications for AI-native physical layer design in wireless systems facing high mobility challenges. By co-designing the modulator and receiver to reduce reliance on pilots, it could improve spectral efficiency in challenging environments. The provision of over-the-air validation adds practical value, distinguishing it from purely simulation-based studies. Strengths include the compatibility with standard FFT-based OFDM processing and the focus on a concrete problem in existing standards.

major comments (3)
  1. [§3.1 (Modulator Architecture)] The claim that the CNN modulator breaks rotational symmetry is central to the pilotless phase-inference argument, yet the section provides no visualization of the learned constellation or quantitative measure of deviation from QAM symmetry (e.g., via rotational invariance metric). Without this, it is difficult to verify that the phase inference is indeed enabled by the learned structure rather than other aspects of the joint training.
  2. [§4 (Performance Evaluation)] No ablation results are presented on the spreading neighborhood size, which directly impacts the information spreading and the resulting symmetry properties. This parameter choice is load-bearing for the reported gains in high-Doppler BLER and goodput, and its sensitivity should be analyzed to support the robustness of the approach.
  3. [§5 (Over-the-Air Validation)] The OTA experiments use the trained weights without reported adaptation or mismatch analysis. Given that the weakest assumption is generalization to real propagation and hardware, the section should include quantitative comparison of simulation vs. OTA performance under the pilotless setting to substantiate the feasibility claim.
minor comments (3)
  1. [Abstract] While the abstract summarizes the contributions well, it would benefit from including specific quantitative improvements (e.g., dB gains in BLER) to give readers an immediate sense of the effect size.
  2. [§2 (Related Work)] The discussion of prior neural receiver works could be expanded with more recent references on end-to-end learning in OFDM to better position the novelty of the transmitter-side learning.
  3. [Notation] The notation for the time-frequency grid and neighborhood spreading could be clarified with a figure or explicit equations to aid readers unfamiliar with the setup.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thoughtful and constructive comments on our manuscript. We address each of the major comments in detail below, proposing specific revisions to improve the clarity and support for our claims.

read point-by-point responses

  1. Referee: [§3.1 (Modulator Architecture)] The claim that the CNN modulator breaks rotational symmetry is central to the pilotless phase-inference argument, yet the section provides no visualization of the learned constellation or quantitative measure of deviation from QAM symmetry (e.g., via rotational invariance metric). Without this, it is difficult to verify that the phase inference is indeed enabled by the learned structure rather than other aspects of the joint training.

    Authors: We agree that explicit evidence for the breaking of rotational symmetry would strengthen the central argument. In the revised manuscript, we will add a new figure in Section 3.1 visualizing the learned constellation points after training, overlaid with standard QAM for comparison. Furthermore, we will introduce a quantitative metric, such as the average phase variance across rotated versions of the constellation, to measure deviation from rotational invariance. This addition will help confirm that the symmetry breaking is a key enabler for phase inference from data symbols. revision: yes

  2. Referee: [§4 (Performance Evaluation)] No ablation results are presented on the spreading neighborhood size, which directly impacts the information spreading and the resulting symmetry properties. This parameter choice is load-bearing for the reported gains in high-Doppler BLER and goodput, and its sensitivity should be analyzed to support the robustness of the approach.

    Authors: We recognize the value of an ablation study on the spreading neighborhood size to demonstrate robustness. The neighborhood size was chosen to match the coherence time and frequency in high-mobility channels. In the revision, we will include an ablation analysis in Section 4, presenting BLER and goodput results for neighborhood sizes ranging from 3x3 to 9x9 under various Doppler conditions. This will illustrate the sensitivity and justify our selection while showing that the gains persist across reasonable choices. revision: yes

  3. Referee: [§5 (Over-the-Air Validation)] The OTA experiments use the trained weights without reported adaptation or mismatch analysis. Given that the weakest assumption is generalization to real propagation and hardware, the section should include quantitative comparison of simulation vs. OTA performance under the pilotless setting to substantiate the feasibility claim.

    Authors: We concur that a quantitative simulation-to-OTA comparison is important for validating generalization. In the updated Section 5, we will add a direct comparison of performance metrics (BLER and goodput) between simulation and OTA experiments in the pilotless setting. We will also discuss potential mismatches due to hardware and channel differences. Note that the experiments intentionally used fixed trained weights to test transferability without online adaptation, which aligns with practical deployment scenarios; however, we will clarify this rationale. revision: partial

Circularity Check

0 steps flagged

No circularity: joint training yields independent empirical gains against external channel models

full rationale

The paper's core procedure is standard end-to-end supervised training of a CNN modulator and neural receiver on simulated high-Doppler OFDM channels (Jakes or equivalent), with performance measured by BLER and goodput against conventional QAM baselines. The claimed symmetry-breaking property emerges as an observed outcome of optimization rather than an input definition; no equation equates a fitted parameter to a subsequent prediction by construction. OTA results use the same weights on real hardware, providing an external check outside the training distribution. No self-citation chains, uniqueness theorems, or ansatz smuggling appear in the derivation. The claims remain falsifiable against independent channel realizations and hardware measurements.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The framework assumes standard OFDM FFT processing remains unchanged and that end-to-end gradient descent on simulated channels yields a modulator whose spreading pattern transfers to real hardware.

free parameters (1)
  • CNN modulator weights
    Learned parameters of the lightweight convolutional modulator that determine how symbols are spread across local time-frequency neighborhoods.
axioms (1)
  • domain assumption High-mobility channels can be adequately modeled by the Doppler spreads used during training.
    The paper relies on this to claim generalization from simulation to OTA experiments.
invented entities (1)
  • DeepOFDM modulator no independent evidence
    purpose: Learned spreading of information across time-frequency resource elements while preserving FFT compatibility.
    New transmitter-side neural component introduced to augment conventional QAM mapping.

pith-pipeline@v0.9.0 · 5764 in / 1248 out tokens · 36816 ms · 2026-05-19T07:44:40.327170+00:00 · methodology

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Reference graph

Works this paper leans on

32 extracted references · 32 canonical work pages · 2 internal anchors

  1. [1]

    Challenges toward wireless communications for high-speed railway,

    B. Ai, X. Cheng, T. Kürner, Z.-D. Zhong, K. Guan, R.-S. He, L. Xiong, D. W. Matolak, D. G. Michelson, and C. Briso-Rodriguez, “Challenges toward wireless communications for high-speed railway,”IEEE transac- tions on intelligent transportation systems, vol. 15, no. 5, pp. 2143–2158, 2014

    work page 2014

  2. [2]

    6g: The next horizon,

    W. Tong and P. Zhu, “6g: The next horizon,” inTITLES, 2022, p. 54

    work page 2022

  3. [3]

    Twelve scientific challenges for 6g: Rethinking the foundations of communications the- ory,

    M. Chafii, L. Bariah, S. Muhaidat, and M. Debbah, “Twelve scientific challenges for 6g: Rethinking the foundations of communications the- ory,”IEEE Communications Surveys & Tutorials, vol. 25, no. 2, pp. 868–904, 2023

    work page 2023

  4. [4]

    Orthogonal time frequency space modula- tion,

    R. Hadani, S. Rakib, M. Tsatsanis, A. Monk, A. J. Goldsmith, A. F. Molisch, and R. Calderbank, “Orthogonal time frequency space modula- tion,” in2017 IEEE wireless communications and networking conference (WCNC). IEEE, 2017, pp. 1–6

    work page 2017

  5. [5]

    Deepcode: Feedback codes via deep learning,

    H. Kim, Y . Jiang, S. Kannan, S. Oh, and P. Viswanath, “Deepcode: Feedback codes via deep learning,”Advances in neural information processing systems, vol. 31, 2018

    work page 2018

  6. [6]

    TinyTurbo: Efficient Turbo Decoders on Edge,

    S. A. Hebbar, R. K. Mishra, S. K. Ankireddy, A. V . Makkuva, H. Kim, and P. Viswanath, “TinyTurbo: Efficient Turbo Decoders on Edge,” in2022 IEEE International Symposium on Information Theory (ISIT). IEEE, 2022, pp. 2797–2802

    work page 2022

  7. [7]

    CRISP: Curriculum based Sequential neural decoders for Polar code family,

    S. A. Hebbar, V . V . Nadkarni, A. V . Makkuva, S. Bhat, S. Oh, and P. Viswanath, “CRISP: Curriculum based Sequential neural decoders for Polar code family,” inInternational Conference on Machine Learning. PMLR, 2023, pp. 12 823–12 845

    work page 2023

  8. [8]

    Interpreting Neural Min-Sum De- coders,

    S. K. Ankireddy and H. Kim, “Interpreting Neural Min-Sum De- coders,” inICC 2023-IEEE International Conference on Communica- tions. IEEE, 2023, pp. 6645–6651

    work page 2023

  9. [9]

    Neural video compression with diverse contexts,

    J. Li, B. Li, and Y . Lu, “Neural video compression with diverse contexts,” inProceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2023, pp. 22 616–22 626

    work page 2023

  10. [10]

    DeepPolar: Inventing non-linear large-kernel Polar Codes via Deep Learning,

    S. A. Hebbar, S. K. Ankireddy, H. Kim, S. Oh, and P. Viswanath, “DeepPolar: Inventing non-linear large-kernel Polar Codes via Deep Learning,” inProceedings of the 41st International Conference on Machine Learning, ser. ICML’24. JMLR.org, 2024

    work page 2024

  11. [11]

    Residual diffusion models for variable-rate joint source channel coding of mimo csi,

    S. K. Ankireddy, H. Kim, and H. Kim, “Residual diffusion models for variable-rate joint source channel coding of mimo csi,”arXiv preprint arXiv:2505.21681, 2025

    work page arXiv 2025

  12. [12]

    Power of deep learning for channel estimation and signal detection in ofdm systems,

    H. Ye, G. Y . Li, and B.-H. Juang, “Power of deep learning for channel estimation and signal detection in ofdm systems,”IEEE Wireless Communications Letters, vol. 7, no. 1, pp. 114–117, 2017

    work page 2017

  13. [13]

    Deeprx: Fully convolutional deep learning receiver,

    M. Honkala, D. Korpi, and J. M. Huttunen, “Deeprx: Fully convolutional deep learning receiver,”IEEE Transactions on Wireless Communica- tions, vol. 20, no. 6, pp. 3925–3940, 2021

    work page 2021

  14. [14]

    Design of a standard-compliant real-time neural receiver for 5g nr,

    R. Wiesmayr, S. Cammerer, F. A. Aoudia, J. Hoydis, J. Zakrzewski, and A. Keller, “Design of a standard-compliant real-time neural receiver for 5g nr,”arXiv preprint arXiv:2409.02912, 2024

    work page arXiv 2024

  15. [15]

    Joint learning of geometric and probabilistic constellation shaping,

    M. Stark, F. Ait Aoudia, and J. Hoydis, “Joint learning of geometric and probabilistic constellation shaping,” in2019 IEEE Globecom Workshops (GC Wkshps). IEEE, 2019, pp. 1–6

    work page 2019

  16. [16]

    End-to-end learning for ofdm: From neural receivers to pilotless communication,

    F. A. Aoudia and J. Hoydis, “End-to-end learning for ofdm: From neural receivers to pilotless communication,”IEEE Transactions on Wireless Communications, vol. 21, no. 2, pp. 1049–1063, 2021

    work page 2021

  17. [17]

    Ai/ml optimized high-order modulations,

    P. Madadi, J. Cho, C. J. Zhang, and D. Burghal, “Ai/ml optimized high-order modulations,” inICC 2023-IEEE International Conference on Communications. IEEE, 2023, pp. 6373–6378

    work page 2023

  18. [18]

    Turbo autoencoder: Deep learning based channel codes for point-to-point communication channels,

    Y . Jiang, H. Kim, H. Asnani, S. Kannan, S. Oh, and P. Viswanath, “Turbo autoencoder: Deep learning based channel codes for point-to-point communication channels,”Advances in neural information processing systems, vol. 32, 2019

    work page 2019

  19. [19]

    Ko codes: inventing nonlinear encoding and decoding for reliable wireless communication via deep-learning,

    A. V . Makkuva, X. Liu, M. V . Jamali, H. Mahdavifar, S. Oh, and P. Viswanath, “Ko codes: inventing nonlinear encoding and decoding for reliable wireless communication via deep-learning,” inInternational Conference on Machine Learning. PMLR, 2021, pp. 7368–7378

    work page 2021

  20. [20]

    Productae: Toward training larger channel codes based on neural product codes,

    M. V . Jamali, H. Saber, H. Hatami, and J. H. Bae, “Productae: Toward training larger channel codes based on neural product codes,” inICC 2022-IEEE International Conference on Communications. IEEE, 2022, pp. 3898–3903

    work page 2022

  21. [21]

    LightCode: Light ana- lytical and neural codes for channels with feedback,

    S. K. Ankireddy, K. Narayanan, and H. Kim, “LightCode: Light ana- lytical and neural codes for channels with feedback,”IEEE Journal on Selected Areas in Communications, 2025

    work page 2025

  22. [22]

    Study on Channel Model for Frequencies from 0.5 to 100 GHz,

    3GPP, “Study on Channel Model for Frequencies from 0.5 to 100 GHz,” 3rd Generation Partnership Project (3GPP), Technical Report TR 38.901, 2022, Technical Specification Group Radio Access Network. [Online]. Available: https://www.3gpp.org/DynaReport/38901.htm

    work page 2022

  23. [23]

    One-bit ofdm receivers via deep learning,

    E. Balevi and J. G. Andrews, “One-bit ofdm receivers via deep learning,” IEEE Transactions on Communications, vol. 67, no. 6, pp. 4326–4336, 2019

    work page 2019

  24. [24]

    Deep learning based ofdm physical-layer receiver for extreme mobility,

    J. Pihlajasalo, D. Korpi, M. Honkala, J. M. Huttunen, T. Riihonen, J. Talvitie, M. A. Uusitalo, and M. Valkama, “Deep learning based ofdm physical-layer receiver for extreme mobility,” in2021 55th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2021, pp. 395–399

    work page 2021

  25. [25]

    arXiv preprint arXiv:2203.11854 , year=

    J. Hoydis, S. Cammerer, F. A. Aoudia, A. Vem, N. Binder, G. Marcus, and A. Keller, “Sionna: An open-source library for next-generation physical layer research,”arXiv preprint arXiv:2203.11854, 2022

    work page arXiv 2022

  26. [26]

    Superimposed pilot symbols for channel estimation in ofdm systems,

    T. Cui and C. Tellambura, “Superimposed pilot symbols for channel estimation in ofdm systems,” inProc. IEEE Globecom, vol. 5, 2005, pp. 2229–2233

    work page 2005

  27. [27]

    Pruning Convolutional Neural Networks for Resource Efficient Inference

    P. Molchanov, S. Tyree, T. Karras, T. Aila, and J. Kautz, “Pruning convolutional neural networks for resource efficient inference,”arXiv preprint arXiv:1611.06440, 2016

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  28. [28]

    Exact solutions to the nonlinear dynamics of learning in deep linear neural networks

    A. M. Saxe, J. L. McClelland, and S. Ganguli, “Exact solutions to the nonlinear dynamics of learning in deep linear neural networks,”arXiv preprint arXiv:1312.6120, 2013

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  29. [29]

    A closer look at memorization in deep networks,

    D. Arpit, S. Jastrz˛ ebski, N. Ballas, D. Krueger, E. Bengio, M. S. Kanwal, T. Maharaj, A. Fischer, A. Courville, Y . Bengioet al., “A closer look at memorization in deep networks,” inInternational conference on machine learning. PMLR, 2017, pp. 233–242

    work page 2017

  30. [30]

    Interpreting deep-learned error- correcting codes,

    N. Devroye, N. Mohammadi, A. Mulgund, H. Naik, R. Shekhar, G. Turán, Y . Wei, and M. Žefran, “Interpreting deep-learned error- correcting codes,” in2022 IEEE International Symposium on Informa- tion Theory (ISIT). IEEE, 2022, pp. 2457–2462

    work page 2022

  31. [31]

    Higher-order interpreta- tions of deepcode, a learned feedback code,

    Y . Zhou, N. Devroye, G. Turan, and M. Zefran, “Higher-order interpreta- tions of deepcode, a learned feedback code,” in2024 60th Annual Aller- ton Conference on Communication, Control, and Computing. IEEE, 2024, pp. 1–8

    work page 2024

  32. [32]

    Advances in the neural network quantization: A comprehensive review,

    L. Wei, Z. Ma, C. Yang, and Q. Yao, “Advances in the neural network quantization: A comprehensive review,”Applied Sciences, vol. 14, no. 17, p. 7445, 2024

    work page 2024