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arxiv: 2606.25722 · v1 · pith:JRLMNZNZnew · submitted 2026-06-24 · 💻 cs.IT · math.IT

MAP-Based Task-Oriented Precoding for Multiuser Communication

Mohammad Javad Ahmadi , Rafael F. Schaefer , H. Vincent Poor This is my paper

Pith reviewed 2026-06-25 19:12 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords task-oriented communicationprecodingMAP criteriondistributed classificationclass-mean separationmultiuser wirelessfeature extractioncomputational complexity
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The pith

A MAP-driven precoding design for multiuser wireless classification improves accuracy while cutting complexity by optimizing class-mean separation after channel distortion.

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

The paper presents a task-oriented framework for multiuser wireless communication that supports distributed classification under realistic channel impairments. It derives a tractable class-mean separation objective from a maximum a posteriori criterion to guide both feature extraction at the transmitters and precoding at the receiver. This formulation sidesteps the repeated covariance inversions and eigen-decompositions required by prior covariance-based and reconstruction-oriented approaches. If the derivation holds, wireless systems can achieve higher end-to-end classification accuracy at lower computational cost by directly targeting separability after distortion rather than indirect proxies.

Core claim

By deriving a tractable class-mean separation objective under a MAP-driven system design, the approach enables low-complexity learning-based feature extraction and precoding strategies that directly improve class separability after wireless channel distortion, yielding higher classification accuracy and lower computational complexity than existing covariance-based and reconstruction-oriented methods.

What carries the argument

The tractable class-mean separation objective, derived from the MAP formulation, that proxies end-to-end classification performance to jointly shape feature extraction and precoding.

If this is right

  • Feature extraction and precoding can be designed jointly without repeated matrix inversions or eigen-decompositions.
  • Class separability improves directly after channel distortion rather than through indirect reconstruction goals.
  • Overall classification accuracy rises in multiuser settings while computational load falls.
  • The same objective applies across different learning-based feature extractors and precoders.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar separation objectives might be derivable for other downstream tasks such as regression or detection if the MAP structure is preserved.
  • The reduced complexity could enable real-time operation on resource-constrained devices where covariance methods are prohibitive.
  • Testing the objective under mismatched channel statistics or imperfect channel state information would reveal practical limits not addressed in the simulations.

Load-bearing premise

The class-mean separation objective remains a faithful proxy for actual classification performance when wireless channel impairments and the chosen MAP model are present.

What would settle it

An experiment in which optimizing the class-mean separation objective produces no accuracy gain over covariance-based precoding under identical channel models and impairment levels would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.25722 by H. Vincent Poor, Mohammad Javad Ahmadi, Rafael F. Schaefer.

Figure 1
Figure 1. Figure 1: Test accuracy versus training epochs for the proposed feature extractor and MCR2 [8] with different values of ϵ under identical network architecture. Feature Extractor Complexity: The proposed objective in (12) requires computing pairwise distances between class-mean feature vectors across C classes in a D-dimensional space, which results in a computational complexity of O(DC2 ). In contrast, the MCR2 -bas… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of the proposed, LMMSE [5], and MCR2 [8] precoders versus the number of receive antennas. ascent framework, whereas the proposed method relies only on gradient-based updates and simple matrix multiplications. Overall, the results demonstrate that the proposed precoder achieves a favorable trade-off between classification accuracy and computational efficiency compared to existing baselines. V. CO… view at source ↗
read the original abstract

We propose a task-oriented multiuser wireless communication framework for distributed classification based on a MAP-driven system design under wireless channel impairments. By deriving a tractable class-mean separation objective, the proposed approach enables low-complexity design of both learning-based feature extraction and precoding strategies. Unlike existing covariance-based and reconstruction-oriented methods, the proposed formulation avoids repeated covariance inversions and eigen-decomposition operations while directly improving class separability after channel distortion. Simulation results demonstrate that the proposed method achieves higher classification accuracy than existing schemes, while simultaneously reducing computational complexity.

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

2 major / 1 minor

Summary. The manuscript proposes a MAP-driven task-oriented precoding framework for multiuser wireless communication supporting distributed classification. It derives a tractable class-mean separation objective to jointly design learning-based feature extraction and precoding matrices that improve post-channel class separability while avoiding covariance inversions and eigen-decompositions required by existing methods; simulations are reported to show gains in classification accuracy alongside reduced complexity.

Significance. If the class-mean separation objective is demonstrated to be a faithful surrogate for end-to-end MAP error probability, the approach would offer a practical complexity reduction for task-oriented communications in wireless edge-AI settings, where repeated matrix inversions are prohibitive.

major comments (2)
  1. [Derivation of the objective (likely §3 or §4)] The central performance claims rest on the class-mean separation objective remaining a close proxy for actual MAP classification accuracy under channel impairments. The manuscript must explicitly derive or bound the relationship between this objective and the true posterior-based error rate (including any approximations in handling the channel or decision regions), as decoupling would mean simulation gains on the proxy need not translate to accuracy improvements.
  2. [Simulation results section] Simulation results are invoked to support higher accuracy and lower complexity, but the setups (channel model, number of users/classes, SNR range, exact baselines, and how the MAP classifier is implemented post-precoding) are unspecified. Without these details it is impossible to assess whether the reported gains are robust or artifacts of the chosen proxy.
minor comments (1)
  1. [Abstract and §2] Notation for the class-mean separation objective and the MAP decision rule should be introduced with explicit definitions before use in the abstract and early sections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the two major comments below and will revise the paper accordingly to strengthen the presentation.

read point-by-point responses

  1. Referee: [Derivation of the objective (likely §3 or §4)] The central performance claims rest on the class-mean separation objective remaining a close proxy for actual MAP classification accuracy under channel impairments. The manuscript must explicitly derive or bound the relationship between this objective and the true posterior-based error rate (including any approximations in handling the channel or decision regions), as decoupling would mean simulation gains on the proxy need not translate to accuracy improvements.

    Authors: We agree that an explicit derivation or bound relating the class-mean separation objective to the MAP error probability is necessary for rigor. The objective is obtained from the MAP rule by approximating the posterior under additive Gaussian noise and focusing on class-mean distances after precoding, but the manuscript does not include a formal error bound on this approximation. In the revision we will add a dedicated subsection in §3 that derives the objective step-by-step from the MAP criterion, states the approximations explicitly, and provides a simple analytic bound on the resulting classification-error gap under the assumed channel model. revision: yes

  2. Referee: [Simulation results section] Simulation results are invoked to support higher accuracy and lower complexity, but the setups (channel model, number of users/classes, SNR range, exact baselines, and how the MAP classifier is implemented post-precoding) are unspecified. Without these details it is impossible to assess whether the reported gains are robust or artifacts of the chosen proxy.

    Authors: The referee is correct; the simulation section omitted these parameters. The revised manuscript will expand the simulation section with a new subsection that specifies: (i) the channel model (i.i.d. Rayleigh fading with perfect CSI at the transmitter), (ii) number of users K=4 and classes C=5, (iii) SNR range from 0 dB to 30 dB, (iv) exact baselines (covariance-based and reconstruction-oriented methods with citations), and (v) the post-precoding MAP classifier implementation (exact posterior computation using the known effective channel after precoding). revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper derives a tractable class-mean separation objective from the MAP formulation under wireless impairments as a first-principles step to enable low-complexity precoding and feature extraction. This is presented as an independent derivation that directly targets separability after channel distortion, without reducing to fitted parameters, self-referential definitions, or load-bearing self-citations. No equations or claims in the provided text equate the output objective to its inputs by construction, and the avoidance of covariance inversions is a deliberate design choice rather than a tautology. The central claim of improved accuracy with lower complexity rests on this derived proxy, which is externally falsifiable via simulations and does not collapse into the input assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no concrete free parameters, axioms, or invented entities can be extracted from the provided text.

pith-pipeline@v0.9.1-grok · 5612 in / 1033 out tokens · 30052 ms · 2026-06-25T19:12:43.156270+00:00 · methodology

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Reference graph

Works this paper leans on

38 extracted references · 3 canonical work pages

  1. [1]

    Task-oriented communication design in cyber-physical systems: A survey on theory and applications,

    A. Mostaani, T. X. Vu, S. K. Sharma, V.-D. Nguyen, Q. Liao, and S. Chatzinotas, “Task-oriented communication design in cyber-physical systems: A survey on theory and applications,” IEEE Access, vol. 10, pp. 133842–133868, 2022

    2022

  2. [2]

    und\"uz, “Deep joint source-channel coding for wireless image transmission,

    E. Bourtsoulatze, D. Burth Kurka and D. G\"und\"uz, “Deep joint source-channel coding for wireless image transmission,” IEEE Trans. Cogn. Commun. Netw. , vol. 5, no. 3, pp. 567–579, Sept. 2019

    2019

  3. [3]

    und\"uz and K. Mikolajczyk, “Wireless image retrieval at the edge,

    M. Jankowski, D. G\"und\"uz and K. Mikolajczyk, “Wireless image retrieval at the edge,” IEEE J. Sel. Areas Commun. , vol. 39, no. 1, pp. 89–100, Jan. 2021

    2021

  4. [4]

    Learning task-oriented communication for edge inference: an information bottleneck approach,

    J. Shao, Y. Mao and J. Zhang, “Learning task-oriented communication for edge inference: an information bottleneck approach,” IEEE J. Sel. Areas Commun. , vol. 40, no. 1, pp. 197–211, Jan. 2022

    2022

  5. [5]

    Task-oriented multi-user semantic communications,

    H. Xie, Z. Qin, X. Tao, and K. B. Letaief, “Task-oriented multi-user semantic communications,” IEEE J. Sel. Areas Commun. , vol. 40, no. 9, pp. 2584–2597, Sep. 2022

    2022

  6. [6]

    Deep learning enabled semantic communication systems,

    H. Xie, Z. Qin, G. Y. Li, and B.-H. Juang, “Deep learning enabled semantic communication systems,” IEEE Trans. Signal Process. , vol. 69, pp. 2663–2675, 2021

    2021

  7. [7]

    End-to-end learning for task-oriented semantic communications over MIMO channels: an information-theoretic framework,

    C. Cai, X. Yuan and Y.-J. A. Zhang, “End-to-end learning for task-oriented semantic communications over MIMO channels: an information-theoretic framework,” IEEE J. Sel. Areas Commun. , vol. 43, no. 4, pp. 1292–1307, Apr. 2025

    2025

  8. [8]

    Multi-device task-oriented communication via maximal coding rate reduction,

    C. Cai, X. Yuan, and Y.-J. A. Zhang, “Multi-device task-oriented communication via maximal coding rate reduction,” IEEE Trans. Wireless Commun., vol. 23, no. 12, pp. 18096--18110, Dec. 2024

    2024

  9. [9]

    MAP-Based Task-Oriented Precoding for Multiuser Communication,

    M. J. Ahmadi, R. F. Schaefer, and H. V. Poor, “MAP-Based Task-Oriented Precoding for Multiuser Communication,” GitHub repository. Available: https://github.com/Javad7ahmadi/MAP-Based-Task-Oriented-Precoding-for-Multiuser-Communication

  10. [10]

    Polyanskiy, ``A perspective on massive random-access,'' in Proc

    Y. Polyanskiy, ``A perspective on massive random-access,'' in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Aachen, Germany, June 2017, pp. 2523--2527

    2017

  11. [11]

    Ozates, et al., ``Unsourced random access: A comprehensive survey,'' IEEE Commun

    M. Ozates, et al., ``Unsourced random access: A comprehensive survey,'' IEEE Commun. Surveys & Tuts., 2026

    2026

  12. [12]

    M. J. Ahmadi and T. M. Duman, ``Unsourced random access with a massive MIMO receiver using multiple stages of orthogonal pilots,'' in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Espoo, Finland, July 2022, pp. 2880-2885

    2022

  13. [13]

    M. J. Ahmadi and T. M. Duman, ``Random spreading for unsourced MAC with power diversity,'' IEEE Commun. Lett., vol. 25, no. 12, pp. 3995--3999, Dec. 2021

    2021

  14. [14]

    M. J. Ahmadi, M. Kazemi, and T. M. Duman, ``RIS-aided unsourced random access,'' in Proc. IEEE Global Commun. Conf. (GLOBECOM), Kuala Lumpur, Malaysia, Dec. 2023, pp. 3270--3275

    2023

  15. [15]

    Zhang, J

    Z. Zhang, J. Dang, Z. Zhang, L. Wu and B. Zhu, ``Unsourced random access via random dictionary learning with pilot-free transceiver design,'' IEEE Trans. Wireless Commun., 2024

    2024

  16. [16]

    M. J. Ahmadi, M. Kazemi, and T. M. Duman, ``RIS-aided unsourced multiple access (RISUMA): Coding strategy and performance limits,'' IEEE Trans. Wireless Commun., vol. 24, no. 7, pp. 6225--6239, Jul. 2025

    2025

  17. [17]

    HashBeam: Enabling feedback through downlink beamforming in unsourced random access,

    J. R. Ebert, K. R. Narayanan and J. -F. Chamberland, “HashBeam: Enabling feedback through downlink beamforming in unsourced random access,” in Proc. Asilomar Conf. Signals, Systems, and Computers. , Pacific Grove, CA, USA, 2022, pp. 692-697

    2022

  18. [18]

    Unsourced random access with threshold-based feedback,

    M. Bashir, E. Nassaji, D. Truhachev, A. Bayesteh and M. Vameghestahbanati, “Unsourced random access with threshold-based feedback,” IEEE Trans. Commun., vol. 71, no. 12, pp. 7072-7086, Dec. 2023

    2023

  19. [19]

    G. K. Facenda and D. Silva, ``Efficient scheduling for the massive random access Gaussian channel,'' IEEE Trans. Wireless Commun., vol. 19, no. 11, pp. 7598--7609, Nov. 2020

    2020

  20. [20]

    A Memory-Based Reinforcement Learning Approach to Integrated Sensing and Communication,

    H. Nikbakht, M. Wigger, S. S. Shitz, and H. V. Poor, "A Memory-Based Reinforcement Learning Approach to Integrated Sensing and Communication," in Proc. 2024 58th Asilomar Conf. Signals, Systems, and Computers, Pacific Grove, CA, USA, 2024, pp. 433-437

    2024

  21. [21]

    Q. Qi, X. Chen, A. Khalili, C. Zhong, Z. Zhang, and D. W. K. Ng,``Integrating sensing, computing, and communication in 6G wireless networks: Design and optimization,'' IEEE Trans. Commun., vol. 70, no. 9, pp. 6212--6227, Sep. 2022

    2022

  22. [22]

    M. J. Ahmadi, M. Kazemi, and T. M. Duman, “Unsourced random access with a massive MIMO receiver using multiple stages of orthogonal pilots: MIMO and single-antenna structures,'' IEEE Trans. Wireless Commun., vol. 23, no. 2, pp. 1343--1355, Feb. 2024

    2024

  23. [23]

    FASURA: A scheme for quasi-static fading unsourced random access channels,

    M. Gkagkos, K. R. Narayanan, J. F. Chamberland and C. N. Georghiades, “FASURA: A scheme for quasi-static fading unsourced random access channels,” IEEE Trans. Commun. , vol. 71, no. 11, pp. 6391-6401, Nov. 2023

    2023

  24. [24]

    Pilot-based unsourced random access with a massive MIMO receiver, interference cancellation, and power control,

    A. Fengler, O. Musa, P. Jung, and G. Caire, “Pilot-based unsourced random access with a massive MIMO receiver, interference cancellation, and power control,” IEEE J. Sel. Areas Commun. , vol. 40, no. 5, pp. 1522–1534, May 2022

    2022

  25. [25]

    Unsourced random access with uncoupled compressive sensing and forward error correction,

    black Z. Zhang, J. Dang, Z. Zhang, L. Wu and B. Zhu, “Unsourced random access with uncoupled compressive sensing and forward error correction," IEEE Trans. Veh. Technol. , early access, Sep. 30, 2024

    2024

  26. [26]

    Design and analysis of massive uncoupled unsourced random access with Bayesian joint decoding,

    F. Tian, X. Chen, Y. L. Guan and C. Yuen, “Design and analysis of massive uncoupled unsourced random access with Bayesian joint decoding,” IEEE Trans. Veh. Technol. , vol. 73, no. 7, pp. 10350-10364, July 2024

    2024

  27. [27]

    Integrated Communication and Receiver Sensing with Security Constraints on Message and State,

    M. Ahmadipour, M. Wigger, and S. Shamai, "Integrated Communication and Receiver Sensing with Security Constraints on Message and State," in Proc. 2023 IEEE Int. Symp. Information Theory (ISIT), Taipei, Taiwan, 2023, pp. 2738-2743

    2023

  28. [28]

    M. J. Ahmadi, R. F. Schaefer, H. V. Poor, ``Integrated sensing and communications for unsourced random access: fundamental limits,'' in Proc. IEEE Global Commun. Conf. (GLOBECOM) , Cape Town, South Africa, 2024, pp. 1365-1370

    2024

  29. [29]

    M. J. Ahmadi, R. F. Schaefer, and H. V. Poor, ``Integrated sensing and communications for unsourced random access: Fundamental limits and practical model,'' arXiv, 2024. Available: https://arxiv.org/abs/2404.19431

    Pith/arXiv arXiv 2024

  30. [30]

    On fundamental limits for fluid antenna-assisted integrated sensing and communications for unsourced random access,

    Z. Zhang, K.-K. Wong, and J. Dang, “On fundamental limits for fluid antenna-assisted integrated sensing and communications for unsourced random access,” IEEE J. Sel. Areas Commun. , early access, 2025, doi: 10.1109/JSAC.2025.3608113

    work page doi:10.1109/jsac.2025.3608113 2025

  31. [31]

    On fundamental limits of slow-fluid antenna multiple access for unsourced random access,

    Z. Zhang, K.-K. Wong, J. Dang, Z. Zhang, C. Masouros, and C.-B. Chae, “On fundamental limits of slow-fluid antenna multiple access for unsourced random access,” IEEE Wireless Commun. Lett. , 2025, doi: 10.1109/LWC.2025.3594112

    work page doi:10.1109/lwc.2025.3594112 2025

  32. [32]

    Lyu et al., “CRB minimization for RIS-aided mmWave integrated sensing and communications,'' IEEE Internet Things J., vol

    W. Lyu et al., “CRB minimization for RIS-aided mmWave integrated sensing and communications,'' IEEE Internet Things J., vol. 11, no. 10,

  33. [33]

    Movable antenna enabled ISAC beamforming design for low-altitude airborne vehicles,

    Y. Xiu, S. Yang, W. Lyu, P. L. Yeoh, Y. Li, and Y. Ai, “Movable antenna enabled ISAC beamforming design for low-altitude airborne vehicles,” IEEE Wireless Commun. Lett. , vol. 14, no. 5, pp. 1311–1315, May 2025

    2025

  34. [34]

    Revealing the trade-off in ISAC systems: The KL divergence perspective,

    Z. Fei, S. Tang, X. Wang, F. Xia, F. Liu and J. A. Zhang, “Revealing the trade-off in ISAC systems: The KL divergence perspective,” IEEE Wireless Commun. Lett., vol. 13, no. 10, pp. 2747–2751, Oct. 2024

    2024

  35. [35]

    Mutual information based pilot design for ISAC,

    A. Bazzi and M. Chafii, "Mutual information based pilot design for ISAC," IEEE Trans. Commun. , Early Access, doi: 10.1109/TCOMM.2025.3545658 , 2025

    work page doi:10.1109/tcomm.2025.3545658 2025

  36. [36]

    Non-Bayesian activity detection, large-scale fading coefficient estimation, and unsourced random access with a massive MIMO receiver,

    A. Fengler, S. Haghighatshoar, P. Jung and G. Caire, “Non-Bayesian activity detection, large-scale fading coefficient estimation, and unsourced random access with a massive MIMO receiver,” IEEE Trans. Inf. Theory , vol. 67, no. 5, pp. 2925-2951, May 2021

    2021

  37. [37]

    A slotted pilot-based unsourced random access scheme with a multiple-antenna receiver,

    M. Ozates, M. Kazemi and T. M. Duman, “A slotted pilot-based unsourced random access scheme with a multiple-antenna receiver,” IEEE Trans. Wireless Commun. , vol. 23, no. 4, pp. 3437-3449, Apr. 2024

    2024

  38. [38]

    Stoica and A

    P. Stoica and A. Nehorai, “MUSIC, maximum likelihood, and Cramer-Rao bound,'' IEEE Trans. Acoust., Speech, Signal Process., vol. 38, no. 12, pp. 2140--2150, Dec 1990

    1990