Learned Digital Over-the-Air Computing for Federated Edge Learning

Antonio Tarizzo; Deniz G\"und\"uz; Mohammad Kazemi

REVIEW 3 major objections 4 minor 1 cited by

Learned Digital Over-the-Air Computing for Federated Edge Learning

T0 review · 3 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read Learned digital over-the-air computation keeps federated learning accurate at 0 dB SNR.

desk verdict Worth refereeing: a real architectural novelty in learned digital OTA aggregation, but the 7 dB claim needs more than one simulated pipeline and the BS-side popularity prior is doing more work than the paper verifies. read the letter →

arxiv 2509.16577 v2 pith:NJC453VS submitted 2025-09-20 cs.LG eess.SP

Antonio Tarizzo , Mohammad Kazemi , Deniz Gündüz This is my paper · ORCID

classification cs.LGeess.SP

keywords federatededgelearningover-the-aircomputationunsourcedrandomaccessapproximatemessagepassinglearneddecodercodebookcompressedsensinglow-SNRaggregation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper proposes replacing the fixed encoder–decoder pair in digital over-the-air (OTA) computation with a learned one: an unsourced random access (URA) codebook and an unrolled approximate message passing decoder (AMP-DA-Net) trained jointly end to end. The authors show that at the same uplink overhead as the state-of-the-art AMP-DA baseline, the learned system extends reliable aggregation by roughly 7 dB, achieving 0.690 test accuracy at 0 dB SNR where the baseline collapses to 0.139. The design keeps the digital robustness that makes OTA aggregation practical while pushing usable operation into the low-SNR regime typical of IoT devices. This matters because OTA aggregation is a leading approach to make federated edge learning communication-efficient; if the reported margin holds, learned digital OTA could make it viable in noise regimes where current digital schemes fail to converge.

What carries the argument

AMP-DA-Net, an unrolled generalized approximate message passing decoder with a learned Bayesian denoiser (spike at zero, Poisson slab, temperature sharpening), per-layer learnable damping and residual scaling, a CNN refinement, and alternating EM updates of K_a, π, and σ². The URA codebook is jointly trained via the factorized parameterization C = DW with row normalization and popularity ordering; ordering makes the codeword usage predictable and supplies the prior for the denoiser. The decoder alternates an output block (measurement-domain residual update with learnable Onsager correction) and an input block (pseudo-channel denoising in codeword domain), then post-processes via non-negativi

What would settle it

Deploy the same pipeline with a deliberate mismatch: give the base station a small IID dataset while devices draw from label-sharded non-IID shards, then measure final test accuracy at 0–3 dB SNR. If accuracy falls toward the AMP-DA baseline (about 0.14) rather than the reported 0.69–0.79, the representativeness of the local dataset is the load-bearing assumption.

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Extended reading notes

Core claim

The paper's central claim is that the OTA decoding bottleneck is not the compressed-sensing formulation itself but the fixed codebook and the hand-tuned denoiser: both can be replaced by learned components whose parameters are optimized offline and then frozen at deployment. The URA codebook is factorized as C = DW (a data-driven base matrix times a learned shear/rotation), row-normalized, and trained jointly with AMP-DA-Net, a ten-layer unrolled AMP decoder that adds per-layer damping, residual scaling, a temperature-controlled spike-and-slab (spike at zero, Poisson slab) Bayesian denoiser, a CNN refinement, and EM updates for the number of active devices, the codeword popularity distributi

Load-bearing premise

The decoder's Bayesian prior is built from the popularity of codewords in the base station's own local update, and the whole design assumes that this local distribution matches what the devices actually transmit; when it does not, the Poisson prior and the EM updates that depend on it become miscalibrated.

Editorial extensions

If this is right

The same uplink overhead as the state-of-the-art baseline supports reliable aggregation down to roughly 0 dB SNR, extending the usable range by about 7 dB.
At 0 dB SNR, global model test accuracy is 0.690 with the proposed method versus 0.139 with AMP-DA; at 3 dB, 0.788 versus 0.135, approaching the perfect-aggregation ceiling of 0.804.
Jointly learned codebooks outperform fixed constructions (0.949 vs 0.696 test accuracy at 5 dB SNR for the best fixed baseline), and data-driven initialization beats Gaussian or Bernoulli initializations.
The method generalizes across models (trained on ResNet updates, deployed with a simpler CNN at 5 dB without noticeable convergence loss), varying numbers of active devices, and highly non-IID data.
Active-device estimation remains within the ±0.5 tolerance needed to correctly normalize the aggregated update, avoiding instability from underestimation and slowdown from overestimation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the codebook is learned jointly with the decoder, the same end-to-end training recipe could benefit unsourced random access beyond federated learning, wherever representative activity patterns are available for offline training.
The popularity-ordering trick suggests a general principle for non-stationary compressed sensing: steering the input distribution toward a predictable prior can be as valuable as improving the decoder's representation.
The temperature-controlled Bayesian denoiser can be read as a learned annealing schedule; adapting temperature online per round could extend the operating SNR range further without retraining.
The paper validates generalization to different models and data splits but not to mismatched popularity distributions; a direct test would reveal whether the base station's local dataset is a sufficient statistical proxy for device updates.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a solid, honest systems paper that combines two known ideas — unrolled AMP decoding and a learned URA codebook — into a new pipeline for digital OTA federated learning. It is the first, to my reading, to jointly train the codebook and decoder end-to-end, and the public code plus the codebook ablations give me confidence the authors built what they claim. The 7 dB low-SNR extension over MD-AirComp/AMP-DA is real in the tested setup, but it is not yet shown to be robust.

What is good. The decoder is well-constructed: per-layer damping, residual scaling, temperature-controlled Bayesian denoiser, CNN refinement, and EM updates for K_a and pi are standard pieces assembled sensibly. The two-matrix codebook parameterization (SimVQ-style) with data-driven initialization is a reasonable way to avoid dead codewords. The ablations in Table 2 are useful and show popularity ordering and learning both matter. Table 1 is clear: at 0/3 dB the proposed method holds accuracy near the perfect-aggregation level while the baseline collapses.

Where it is soft. The headline depends on a single simulation scenario (ResNet, 80/20 non-IID, one SNR grid), with no error bars or repeated seeds. The AMP-DA baseline tuning is unspecified; a fair comparison needs the baseline's hyperparameters stated. Generalization is tested on one simpler CNN at 5 dB only. These are fixable with more experiments, but as it stands the 'generalises across models, activity levels, and heterogeneous data' claim is broader than the evidence.

The more interesting worry is the popularity prior. The Bayesian denoiser assumes lambda_j = K_a pi_j with pi estimated by k-means on the BS's own local update (Eqs. 8, 16). In the experiments, BS and devices come from the same data-generation pipeline, so the prior is calibrated by construction. The paper gives only a contribution bullet claiming BS local training on small non-IID subsets captures device dynamics; there is no experiment with a deliberately skewed BS distribution. If the BS's local data is label-skewed relative to devices, the spike-and-slab prior points at the wrong codewords and the low-SNR margin could shrink toward the baseline. This is not a fatal flaw — the architecture could still help via the learned codebook and CNN refinement — but it is a load-bearing assumption and it is unverified.

Bottom line: this is a genuine contribution to the wireless FL subfield, not a paradigm shift. It deserves peer review, but I would ask for seeds/error bars, baseline tuning, and a popularity-mismatch experiment before I would trust the 7 dB claim outside the exact setup tested. I would bring it to a reading group interested in learned physical-layer schemes.

Referee Report

3 major / 4 minor

Summary. The paper proposes a learned digital over-the-air (OTA) aggregation scheme for federated edge learning (FEEL). The method, AMP-DA-Net, is an unrolled approximate message passing (AMP) decoder with per-layer damping, residual scaling, temperature-controlled Bayesian denoising, CNN refinement, and EM-based updates of active-device count, popularity, and noise variance. It is trained jointly with a URA codebook parameterized as a product of two matrices (C = DW). The central claim is a roughly 7 dB extension of the reliable SNR range over the state-of-the-art AMP-DA baseline at the same uplink overhead, together with generalization across models, activity levels, and heterogeneous data. Experiments on a non-IID FEEL setup with a ResNet global model show large improvements at low SNR (Table 1), and one additional experiment transfers the trained system to a simpler CNN at 5 dB SNR.

Significance. If the reported gains hold, this is a useful contribution to digital OTA aggregation: it demonstrates that end-to-end learning of the URA codebook and the AMP decoder can extend reliable operation into low-SNR IoT regimes without increasing uplink overhead. Strengths include the well-structured decoder design, the two-matrix codebook parameterization, and the release of code, which supports reproducibility. The paper does not fit constants to a target result; test accuracies are measured on held-out rounds after training on separate data. However, the central 7 dB claim currently rests on a critical assumption about the representativeness of the BS-local popularity prior and on a single simulation scenario, so the demonstrated scope is narrower than the abstract and conclusions suggest.

major comments (3)

[Secs. 3.1 and 3.2, Eq. (16)] The low-SNR advantage in Table 1 (proposed 0.690/0.788 at 0/3 dB vs AMP-DA 0.139/0.135) depends on the Poisson prior lambda_j = K_a pi_j in Eq. (16), where pi is estimated from the BS's own local update (Eq. (8)). If the BS-local data is label-skewed relative to the device population, lambda_j is miscalibrated and the EM updates for K_a and pi inherit that bias. The paper claims generalization to heterogeneous data, but the only evidence is a contribution bullet in Sec. 1 without a quantitative experiment. Please either add a controlled mismatch study (e.g., varying label skew between BS-local and device data and re-running Table 1) or qualify the claims. As written, the 7 dB claim is not shown to survive the heterogeneity the paper advertises.
[Section 4, Table 1] The central 'more than 7 dB' claim is supported by a single simulation scenario: one global model (ResNet), one non-IID split, one activity range (K_a uniform in [7,13]), and one SNR grid. No standard deviations or seed counts are reported, and the AMP-DA baseline's hyperparameters (damping, number of iterations, prior settings) are not specified. The reader cannot assess whether the improvement is statistically robust or an artifact of baseline de-tuning. Please report multiple independent runs with error bars, specify the baseline tuning, and ideally include ablations over activity levels and data heterogeneity.
[Section 4, generalization paragraph] The abstract claims the method 'generalises across models, activity levels, and heterogeneous data', and the conclusions repeat this. The only direct test is one simpler CNN at 5 dB SNR; K_a is varied only in the sense that training and evaluation draw from the same [7,13] range, and no systematic variation of IID/non-IID composition is presented. This is a mismatch between claim and evidence. Either add a systematic generalization study (different architectures, heterogeneity levels, and activity-count distributions) or restrict the generalization statements to the tested regime.

minor comments (4)

[Notation, Sec. 1] The notation paragraph says '⊙ and circ denote element-wise multiplication and exponentiation, respectively,' but the exponentiation symbol is garbled. Please fix the rendering.
[Eq. (15)] The definitions of var1 and var2 are ambiguous. Specify dimensions and transposes explicitly (e.g., 'C⊙2' should likely be the squared matrix or its transpose).
[Table 2] The caption says 'Codebook setup evaluation accuracy' but reports 0.949 for the proposed setup at 5 dB, while Table 1 reports 0.794 at the same SNR for the same system. If Table 2 reports codeword-recovery accuracy rather than final test accuracy, say so explicitly; otherwise reconcile the two numbers.
[References] Reference [16] appears to have an incomplete author list ('... and Safi'). Please complete it.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the decoder and codebook are trained on separate rounds and evaluated on held-out rounds; reported accuracies are measured, not fitted.

full rationale

The paper's central derivation is the AMP-DA-Net architecture and joint codebook training. The reported 7 dB extension is an empirical result from Table 1, obtained by evaluating a fixed trained system on held-out rounds. The decoder's Bayesian prior (Eq. 16) uses λ_j = K_a π_j with π estimated from the BS's local data, but this is an architectural assumption about deployment, not a parameter fitted to the target test accuracies. The EM updates infer K_a and π online from the received signal, and the training loss (Section 3.2) includes reconstruction MSE, sparsity, and active-device MSE, none of which encode the test accuracy values. Self-citations (e.g., [14] for MD-AirComp) are used as background/baseline, not as an unexamined uniqueness theorem or ansatz. The main limitation is that the BS-local popularity prior is assumed to match device codeword usage; this is an external-validity risk, not a circularity, because the low-SNR results would still be valid under that stated assumption. The paper's claim that BS local training on small non-IID subsets captures device dynamics is asserted without a dedicated experiment, but that is missing support, not a circular reduction. No step in the derivation reduces by construction to its own inputs.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The performance gain rests on a large learned parameter set (decoder weights, codebook matrices, per-layer scalars) and several domain priors (Poisson activity, popularity transfer, representativeness of training data). These are not derived from first principles; the paper provides empirical validation only.

free parameters (8)

Per-layer damping factors η(t)
Learned scalars constrained to (0,1) that stabilize AMP updates in Eq. (13). Value not reported in the paper.
Per-layer residual scaling γ(t)
Learned scalars constrained to [0.3,2] via tanh mapping that scale the Onsager correction in Eq. (12). Value not reported.
Per-layer temperature τ(t)
Learned scalars controlling the sharpness of the Bayesian posterior mean and variance in Eq. (17). Value not reported.
Per-layer mixing weight ρ(t)
Learned blending weight between Bayesian mean and CNN refinement in Eq. (20), initialized at 0.85.
CNN denoiser weights f_CNN(t)
Learned 1D CNN parameters per layer: 10 layers, 32 filters, kernel size 3. Fit during offline training.
URA codebook matrices D and W
Learned end-to-end via factorized parameterization C_syn = DW; D initialized with data-driven pseudo-inverse, W with identity. Rows renormalized to unit norm.
EM smoothing step sizes
Learned convex combination coefficients for updating K_a and π in the EM block; detailed values not specified.
Loss weights λ1, λW, λK = 0.01, 0.001, 0.01
Hand-chosen hyperparameters balancing reconstruction, codebook conditioning, and active-device estimation in the training loss.

assumptions (6)

standard math AMP/GAMP theory: residual behaves like Gaussian noise after Onsager correction
Used in Section 3.2 to justify the pseudo-channel model and residual updates (Eqs. 11-14).
domain assumption Channel noise is Gaussian with known variance σ2
Invoked in Eq. (6) and used for the Gaussian pseudo-likelihood in the Bayesian denoiser.
domain assumption Perfect synchronization of device transmissions
Stated in Section 2: 'Synchronisation is assumed so that simultaneous transmissions align in time and frequency.'
domain assumption Activity vector x is sparse, non-negative, and integer-valued with a spike-and-slab Poisson prior
Introduced in Eq. (16) as the prior p(xj) = (1-αj)δ0 + αj Pois(λj), where λj = K_a πj.
domain assumption BS's local popularity distribution approximates devices' codeword usage
Section 3.1: 'the BS's popularity distribution provides a reliable estimate of other devices' codeword usage.' This underpins Eq. (8) and the decoder's prior.
domain assumption Training data from perfect-aggregation FEEL pipeline is representative of deployment
Section 3.2, Dataset Collection: data generated with a ResNet model and non-IID splits; the decoder is fixed for deployment under the assumption these statistics transfer.

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Cite this review

Pith. "Pith review of Learned Digital Over-the-Air Computing for Federated Edge Learning." pith.science (2026). https://pith.science/paper/NJC453VS

@misc{pith2026250916577,
  author       = {Pith},
  title        = {Pith review of: Learned Digital Over-the-Air Computing for Federated Edge Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NJC453VS}},
  note         = {Machine review of arXiv:2509.16577}
}

read the original abstract

Over-the-air (OTA) aggregation enables federated edge learning (FEEL) by exploiting the superposition property of the wireless channel to merge communication with computation, eliminating the need to schedule and decode devices individually. Analog OTA schemes transmit uncoded updates but are sensitive to noise, fading, and power misalignment, motivating more robust digital alternatives. However, state-of-the-art (SoTA) digital OTA designs that combine unsourced random access (URA) with compressed sensing struggle in the low signal-to-noise ratio (SNR) regimes common in Internet of Things (IoT) deployments, where symbol recovery and active-device estimation become unreliable. We propose a learned digital OTA framework that jointly trains a URA codebook with an unrolled approximate message passing (AMP)-based decoder. The learned decoder incorporates per-layer damping, residual scaling, temperature-controlled Bayesian denoising, and a lightweight convolutional neural network (CNN) refinement, while the codebook is optimised end-to-end through a factorised parameterisation. At near-perfect-aggregation accuracy, the proposed design extends the viable SNR range by approximately 7\,dB over the SoTA baseline at the same uplink overhead, and generalises across models, activity levels, and heterogeneous data.

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Forward citations

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Works this paper leans on

34 extracted references · 2 linked inside Pith · cited by 1 Pith paper

[1]

INTRODUCTION Federated learning (FL) has become a well-established approach in machine learning (ML), where by keeping data local, it addresses privacy concerns and reduces reliance on centralised storage [1][2]. Naturally, this interest has extended to wireless edge devices such as phones, Internet of things (IoT) sensors, autonomous vehicles, and other ...

arXiv 2025
[2]

Each devicekhas a single antenna and local datasetD k

SYSTEM MODEL We consider FEEL amongK t edge devices, of which a random sub- set ofK a devices are active per round. Each devicekhas a single antenna and local datasetD k. For simplicity, datasets are assumed equal size|D k|=Band devices have equal compute capability. In practice, heterogeneity in data and hardware affects participation dynamics, but this ...
[3]

The re- sulting URA codebook and decoder can be reused across tasks and communication rounds without retraining, much like a conventional un-learnt design

PROPOSED SOLUTION To integrate a learnt scheme into FEEL, in the proposed solution, the encoder and decoder are jointly trained offline on a representa- tive dataset, then fixed for deployment (see Section 3.2). The re- sulting URA codebook and decoder can be reused across tasks and communication rounds without retraining, much like a conventional un-lear...
[4]

Non-negative clipping
[5]

Greedy Rounding Error Feedback Error Feedback Error Feedback Local non-IID Datasets Fig. 2. AMP-DA-Net decoder structure. 3.2. AMP-DA-Net (Learnt Decoder) The core component of the proposed solution is a learnt unrolled decoder, AMP-DA-Net, which builds upon approximate message passing (AMP), generalised AMP (GAMP), AMP-Net, and the AMP-based digital aggr...
[6]

RESULTS & ANALYSIS The proposed method was compared with the AMP-DA baseline 2. The datasets were split20%IID and80%non-IID, with10,000 samples randomly assigned across devices and the remaining40,000 label-sorted into contiguous shards, distributed sequentially to each device. The number of active devicesKa was drawn uniformly from [7,13]. The global mod...
[7]

The method retains the same uplink cost as the state-of-the-art, while extending reliable operation by more than 7 dB

CONCLUSIONS This paper presented a digital OTA FEEL solution, combining a learnt decoder (AMP-DA-Net) with a jointly trained URA codebook. The method retains the same uplink cost as the state-of-the-art, while extending reliable operation by more than 7 dB. Results show strong improvements in recovery and stability, particularly under challeng- ing low-SN...
[8]

Communication-efficient learning of deep networks from decentralized data,

Brendan McMahan, Eider Moore, Daniel Ramage, Seth Hamp- son, and Blaise Aguera y Arcas, “Communication-efficient learning of deep networks from decentralized data,” inInt’l Conf. on Artificial Intelligence and Statistics (AISTATS). Apr 2017, vol. 54, pp. 1273–1282, PMLR

2017

Show all 34 references

[9]

Fed- erated learning: Strategies for improving communication effi- ciency,

Jakub Kone ˇcn´y, H. Brendan McMahan, Felix X. Yu, Peter Richt´arik, Ananda Theertha Suresh, and Dave Bacon, “Fed- erated learning: Strategies for improving communication effi- ciency,” Oct 2016

2016
[10]

A comprehensive survey on communication-efficient federated learning in mobile edge en- vironments,

Ninghui Jia, Zhihao Qu, Baoliu Ye, Yanyan Wang, Shi- hong Hu, and Song Guo, “A comprehensive survey on communication-efficient federated learning in mobile edge en- vironments,”IEEE Comm. Surveys & Tutorials, 2025

2025
[11]

Distributed learning in wireless networks: Recent progress and future challenges,

Mingzhe Chen, Deniz G ¨und¨uz, Kaibin Huang, Walid Saad, Mehdi Bennis, Aneta Vulgarakis Feljan, and H. Vincent Poor, “Distributed learning in wireless networks: Recent progress and future challenges,”IEEE Journal on Selected Areas in Communications, vol. 39, no. 12, pp. 3579–3...

2021
[12]

Sparse communica- tion for distributed gradient descent,

Alham Fikri Aji and Kenneth Heafield, “Sparse communica- tion for distributed gradient descent,” inConf. on Empirical Methods in Natural Language Proc. (EMNLP), Copenhagen, Denmark, Sep 2017

2017
[13]

Time- correlated sparsification for communication-efficient federated learning,

Emre Ozfatura, Kerem Ozfatura, and Deniz G ¨und¨uz, “Time- correlated sparsification for communication-efficient federated learning,” in2021 IEEE International Symposium on Informa- tion Theory (ISIT), 2021, pp. 461–466

2021
[14]

QSGD: Communication-efficient SGD via gradient quantization and encoding,

Dan Alistarh, Demjan Grubic, Jerry Li, Ryota Tomioka, and Milan V ojnovic, “QSGD: Communication-efficient SGD via gradient quantization and encoding,” 2017

2017
[15]

signSGD: Compressed optimisation for non-convex problems,

Jeremy Bernstein, Yu-Xiang Wang, Kamyar Azizzadenesheli, and Anima Anandkumar, “signSGD: Compressed optimisation for non-convex problems,” inInt’l Conference on Machine Learning (ICML). Jul 2018, vol. 80, pp. 560–569, PMLR

2018
[16]

1-bit stochastic gradient descent and its application to data- parallel distributed training of speech DNNs,

Frank Seide, Hao Fu, Jasha Droppo, Gang Li, and Dong Yu, “1-bit stochastic gradient descent and its application to data- parallel distributed training of speech DNNs,” inInterSpeech 2014, Sep 2014, pp. 1058–1062

2014
[17]

Machine learning at the wireless edge: Distributed stochastic gradient descent over-the-air,

Mohammad Mohammadi Amiri and Deniz G ¨und¨uz, “Machine learning at the wireless edge: Distributed stochastic gradient descent over-the-air,”IEEE Trans. on Signal Proc., vol. 68, pp. 2155–2169, 2020

2020
[18]

Feder- ated learning over wireless fading channels,

Mohammad Mohammadi Amiri and Deniz G ¨und¨uz, “Feder- ated learning over wireless fading channels,”IEEE Trans.s on Wireless Comms., vol. 19, no. 5, pp. 3546–3557, 2020

2020
[19]

Dynamic scheduling for over-the-air federated edge learning with energy constraints,

Yuxuan Sun, Sheng Zhou, Zhisheng Niu, and Deniz G ¨und¨uz, “Dynamic scheduling for over-the-air federated edge learning with energy constraints,”IEEE Journal on Selected Areas in Communications, vol. 40, no. 1, pp. 227–242, Jan 2022

2022
[20]

One-bit over-the-air aggregation for communication-efficient federated edge learning: Design and convergence analysis,

Guangxu Zhu, Yuqing Du, Deniz G ¨und¨uz, and Kaibin Huang, “One-bit over-the-air aggregation for communication-efficient federated edge learning: Design and convergence analysis,” IEEE Trans. on Wireless Comms., vol. 20, no. 3, Mar 2021

2021
[21]

Massive digital over-the-air computation for communication-efficient federated edge learning,

Li Qiao, Zhen Gao, Mahdi Boloursaz Mashhadi, and Deniz G¨und¨uz, “Massive digital over-the-air computation for communication-efficient federated edge learning,”IEEE Jour- nal on Selected Areas in Communications, vol. 42, no. 11, pp. 3078–3094, Nov 2024

2024
[22]

Ofdma-f 2l: Federated learning with flexible aggregation over an ofdma air interface,

Shuyan Hu, Xin Yuan, Wei Ni, Xin Wang, Ekram Hossain, and H. Vincent Poor, “Ofdma-f 2l: Federated learning with flexible aggregation over an ofdma air interface,”IEEE Trans. on Wireless Comms., vol. 23, no. 7, Jul 2024

2024
[23]

Distributed learning over a wireless network with fsk-based majority vote,

Alphan S ¸ahin, Bryson Everette, and Safi, “Distributed learning over a wireless network with fsk-based majority vote,”arXiv preprint arXiv:2111.01850, Nov 2021

2021 arXiv
[24]

A perspective on massive random-access,

Yury Polyanskiy, “A perspective on massive random-access,” in2017 IEEE International Symposium on Information Theory (ISIT), Jun 2017, pp. 2523–2527

2017
[25]

Digital over-the-air federated learn- ing in multi-antenna systems,

Sihua Wang, Mingzhe Chen, Cong Shen, Changchuan Yin, and Christopher G. Brinton, “Digital over-the-air federated learn- ing in multi-antenna systems,”IEEE Transactions on Wireless Communications, vol. 23, no. 6, pp. 4184–4198, Jun 2024

2024
[26]

Federated optimiza- tion in heterogeneous networks,

Tian Li, Anit Kumar Sahu, Manzil Zaheer, Maziar Sanjabi, Ameet Talwalkar, and Virginia Smith, “Federated optimiza- tion in heterogeneous networks,” inConf. on Machine Learn- ing and Sys. (MLSys), Apr 2020, vol. 2

2020
[27]

On the feasibility of distributed phase synchro- nization for coherent signal superposition,

Alphan Sahin, “On the feasibility of distributed phase synchro- nization for coherent signal superposition,” inIEEE PIMRC Workshops - Integrated, Intelligent and Ubiquitous Connectiv- ity for 6G and Beyond, Sep 2025

2025
[28]

k-means++: The ad- vantages of careful seeding,

David Arthur and Sergei Vassilvitskii, “k-means++: The ad- vantages of careful seeding,” inAnnual ACM-SIAM Symp. on Discrete Algs. (SODA’07), New Orleans, LA, Jan 2007

2007
[29]

Generalized approximate message passing for estimation with random linear mixing,

Sundeep Rangan, “Generalized approximate message passing for estimation with random linear mixing,” inIEEE Int’l Symp. on Inform. Theory (ISIT), Jul 2011

2011
[30]

Amp-net: Denoising-based deep unfolding for compressive image sensing,

Zhonghao Zhang, Yipeng Liu, Jiani Liu, Fei Wen, and Ce Zhu, “Amp-net: Denoising-based deep unfolding for compressive image sensing,”IEEE Transactions on Image Processing, vol. 30, pp. 1487–1500, Mar 2021

2021
[31]

Some intriguing observations on the learnt matrices in deep unfolded networks,

Kartheek K. R. Nareddy, Inbasekaran Perumal, and Chandra Seelamantula, “Some intriguing observations on the learnt matrices in deep unfolded networks,” inIEEE Intl Conf. on Acoustics, Speech and Signal Proc. (ICASSP), Apr 2025

2025
[32]

Deep residual learning for image recognition,

Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun, “Deep residual learning for image recognition,”2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), p. 770–778, Jun 2016

2016
[33]

Address- ing representation collapse in vector quantized models with one linear layer,

Yongxin Zhu, Bocheng Li, Yifei Xin, and Linli Xu, “Address- ing representation collapse in vector quantized models with one linear layer,” 2024

2024
[34]

Ista-net: Interpretable optimization-inspired deep network for image compressive sensing,

Jian Zhang and Bernard Ghanem, “Ista-net: Interpretable optimization-inspired deep network for image compressive sensing,” inIEEE/CVF Conf. on Comp. Vision and Pattern Recog. (CVPR), 2018

2018

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.

[1] [1]

INTRODUCTION Federated learning (FL) has become a well-established approach in machine learning (ML), where by keeping data local, it addresses privacy concerns and reduces reliance on centralised storage [1][2]. Naturally, this interest has extended to wireless edge devices such as phones, Internet of things (IoT) sensors, autonomous vehicles, and other ...

arXiv 2025

[2] [2]

Each devicekhas a single antenna and local datasetD k

SYSTEM MODEL We consider FEEL amongK t edge devices, of which a random sub- set ofK a devices are active per round. Each devicekhas a single antenna and local datasetD k. For simplicity, datasets are assumed equal size|D k|=Band devices have equal compute capability. In practice, heterogeneity in data and hardware affects participation dynamics, but this ...

[3] [3]

The re- sulting URA codebook and decoder can be reused across tasks and communication rounds without retraining, much like a conventional un-learnt design

PROPOSED SOLUTION To integrate a learnt scheme into FEEL, in the proposed solution, the encoder and decoder are jointly trained offline on a representa- tive dataset, then fixed for deployment (see Section 3.2). The re- sulting URA codebook and decoder can be reused across tasks and communication rounds without retraining, much like a conventional un-lear...

[4] [4]

Non-negative clipping

[5] [5]

Greedy Rounding Error Feedback Error Feedback Error Feedback Local non-IID Datasets Fig. 2. AMP-DA-Net decoder structure. 3.2. AMP-DA-Net (Learnt Decoder) The core component of the proposed solution is a learnt unrolled decoder, AMP-DA-Net, which builds upon approximate message passing (AMP), generalised AMP (GAMP), AMP-Net, and the AMP-based digital aggr...

[6] [6]

RESULTS & ANALYSIS The proposed method was compared with the AMP-DA baseline 2. The datasets were split20%IID and80%non-IID, with10,000 samples randomly assigned across devices and the remaining40,000 label-sorted into contiguous shards, distributed sequentially to each device. The number of active devicesKa was drawn uniformly from [7,13]. The global mod...

[7] [7]

The method retains the same uplink cost as the state-of-the-art, while extending reliable operation by more than 7 dB

CONCLUSIONS This paper presented a digital OTA FEEL solution, combining a learnt decoder (AMP-DA-Net) with a jointly trained URA codebook. The method retains the same uplink cost as the state-of-the-art, while extending reliable operation by more than 7 dB. Results show strong improvements in recovery and stability, particularly under challeng- ing low-SN...

[8] [8]

Communication-efficient learning of deep networks from decentralized data,

Brendan McMahan, Eider Moore, Daniel Ramage, Seth Hamp- son, and Blaise Aguera y Arcas, “Communication-efficient learning of deep networks from decentralized data,” inInt’l Conf. on Artificial Intelligence and Statistics (AISTATS). Apr 2017, vol. 54, pp. 1273–1282, PMLR

2017