Symbol Distributions in Semantic Communications: A Source-Channel Equilibrium Perspective

Chan-Byoung Chae; Dongha Choi; Hanju Yoo; Robert W. Heath Jr; Songkuk Kim

REVIEW 4 major objections 5 minor 30 references

Symbol Distributions in Semantic Communications: A Source-Channel Equilibrium Perspective

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Semantic encoder symbols follow a Student's t-distribution, the paper contends, because end-to-end training forces a balance between source coding and channel throughput.

desk verdict First parametric model of pre-noise semantic symbol distributions as Student's t; the math is clean for the heuristic surrogate, but the link to MSE training is asserted and the empirical fit lacks error bars. read the letter →

arxiv 2512.14022 v2 pith:ULZB2DM6 submitted 2025-12-16 cs.IT eess.SPmath.IT

Hanju Yoo , Dongha Choi , Songkuk Kim , Chan-Byoung Chae , Robert W. Heath Jr This is my paper · ORCID

classification cs.ITeess.SPmath.IT

keywords semanticcommunicationsjointsource-channelcodingsymboldistributionStudent'st-distributionprobabilisticconstellationshapingkerneldensityestimationDeepJSCCvariable-length

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

The paper tries to explain why the continuous symbols produced by end-to-end trained semantic communication encoders have heavy-tailed, non-Gaussian distributions. It argues that the encoder implicitly trades off two pressures: a source-coding pressure that minimizes average description length via power allocation, and a channel-coding pressure that maximizes mutual information over an AWGN channel. Solving a heuristic Lagrangian that couples these pressures yields a Student's t-distribution as the predicted symbol distribution, with a single shape parameter nu interpolating between Cauchy (source-dominant) and Gaussian (channel-dominant) limits. Experiments on image-based systems show that fitted nu varies with coding scheme, dataset entropy variance, and SNR in the predicted directions, and that a mild Gaussian regularizer accelerates training convergence, supporting the model.

What carries the argument

The key object is a Lagrangian objective L_source + λ L_channel, where L_channel = −h(Y) is the negative differential entropy (a surrogate for maximizing mutual information) and L_source = E[log2(1 + αY^2/σ^2)] is the expected per-symbol payload (a surrogate for minimizing source coding overhead). Maximizing entropy subject to a fixed average payload yields the Student's t-distribution; the Lagrange multiplier λ maps to the tail exponent ν. A second mechanism is the unit-variance normalization of the Student's t, which eliminates the scale parameter and makes ν the only free parameter. The paper also uses kernel density estimation to estimate the empirical symbol distribution for both fittin

What would settle it

Train a semantic encoder with a different source-side loss (e.g., perceptual or cross-entropy rather than MSE) or without the batch power normalization layer, then measure the empirical symbol distribution. If it does not fit a variance-normalized Student's t with ν in (2, ∞), or if the fitted ν does not move toward Gaussian when switching from fixed-length to variable-length coding, the claimed universality of the Student's t model is falsified.

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Extended reading notes

Core claim

The central claim is that the pre-noise symbol distribution of a neural semantic encoder is a variance-normalized Student's t-distribution, p(y) ∝ (1 + y^2/(ν−2))^(−(ν+1)/2), where ν is a single parameter controlling tail heaviness. This arises from maximizing differential entropy subject to a fixed average payload constraint E[log2(1 + αY^2/σ^2)] = C, where the payload function is derived from an APSK packing analogy. The model unifies the Gaussian and Cauchy extremes: ν→∞ recovers the channel-capacity-achieving Gaussian, while ν→1 recovers the source-coding-dominant Cauchy. The paper validates this by fitting ν to empirical symbols from DeepJSCC and NTSCC systems and by showing that the KL

Load-bearing premise

The whole derivation rests on assuming that end-to-end MSE training makes the encoder implicitly minimize the heuristic Lagrangian L_source + λ L_channel, with L_source given by the log(1+αy²/σ²) payload surrogate—an assumption the paper calls heuristic, not derived from the actual training loss.

Editorial extensions

If this is right

If the model is correct, the symbol distribution of a semantic encoder is predictable from the architecture and data: systems that rely on power-based rate allocation will have small ν (heavy tails), while those with explicit variable-length control or low-entropy-variance datasets will have large ν (near-Gaussian).
A mild regularizer that pushes the empirical symbol distribution toward a Gaussian prior can speed up training convergence, especially at high compression ratios and high SNR, without sacrificing final performance.
The derived Student's t model provides a parametric family that can be used for downstream tasks such as quantization, compression, and peak-power-limited clipping analysis, since real transmitters truncate heavy tails.
The framework suggests that the empirical symbol distribution is a signature of the implicit rate-distortion trade-off, offering a way to monitor and steer an encoder's behavior without changing the end-to-end loss.

Reading between the lines

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

A testable extension: if the heuristic Lagrangian is right, then explicitly varying λ in an alternative training objective (e.g., adding a term proportional to the payload expectation) should produce a monotone shift in fitted ν; the paper does not run this control experiment.
The model implies that for a fading or non-Gaussian channel, the channel-pressure surrogate (maximize entropy) would no longer favor a Gaussian, so the predicted distribution would deviate from Student's t; this is an untested boundary of the theory.
The convergence improvement from a Gaussian prior might be explained more simply as variance stabilization (avoiding the infinite moments of low-ν t-distributions) rather than as confirmation of the source-channel equilibrium; the paper's interpretation is plausible but not uniquely forced.
The APSK-derived payload function has the same functional form as the Gaussian channel capacity, so the Student's t result may be a consequence of choosing a log(1+SNR) cost; a different payload model would yield a different distribution, which could be explored to test the universality of the claim.

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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

First, the useful thing: this is the first paper to look at the actual distribution of pre-noise DeepJSCC symbols and propose a single-parameter model (Student's t) that fits them. The max-entropy derivation is textbook, but the framing as a source-channel equilibrium is new, and the empirical link between the tail index ν and coding scheme/dataset entropy is a real observation the field can build on. The paper also ships a practical regularizer that speeds convergence, which is a nice bonus.

The theory, however, is a model, not a derivation. The paper itself repeatedly calls the objective 'heuristic' and 'surrogate' (Sec. IV-A, IV-B), which is honest. But the load-bearing step is the claim that an MSE-trained encoder implicitly minimizes L_source + λ L_channel. The argument for that is conceptual, not mathematical: nothing in the paper shows that SGD on distortion drives the encoder toward the optimum of that marginal-only surrogate. If the surrogate is wrong, the t-distribution conclusion doesn't follow.

The empirical section is decent for the field but not airtight. The shape parameter ν is estimated by MLE from the same symbols used to validate the model; there are no error bars on ν, and no comparison to other heavy-tailed families (Laplace, alpha-stable). The two headline orderings (NTSCC > DeepJSCC, CIFAR-10 > ImageNet) match the hypotheses, but they are observed after fitting, not predicted from the theory. The SNR sweep shows a small, consistent trend, which is good.

There's also a mathematical wrinkle: under the unit-variance normalization used throughout, the ν→1 Cauchy limit is not realized. As ν→2+, the normalized distribution becomes a spike at zero with heavy tails, not a Cauchy. The paper acknowledges this in a parenthetical ('ignoring the unit-variance normalization'), but the interpolation story in Fig. 1 and the surrounding text is misleading for the model actually fitted.

For a first cut, the paper is worth engaging. The core idea is plausible, the authors are transparent about the heuristic nature, and the empirical regularities are real even if not decisive. The weak points are addressable: derive (or test) the surrogate link more directly, add confidence intervals, and fix the limit discussion.

Send it to peer review. It deserves serious refereeing, with the expectation of moderate revision.

Referee Report

4 major / 5 minor

Summary. The paper proposes an information-theoretic explanation for the heavy-tailed distributions observed in the continuous symbols produced by end-to-end trained semantic communication encoders. It models training as minimizing a heuristic Lagrangian L_source + lambda*L_channel, where L_source is the expected payload E[log2(1+alpha Y^2/sigma^2)] (motivated by an APSK packing analogy) and L_channel is -h(Y). Solving the resulting max-entropy problem yields a scaled Student's t-distribution; imposing unit-variance normalization gives a one-parameter t-family. Experiments on DeepJSCC and NTSCC, across ImageNet/CIFAR-10 and different SNRs, fit this model via MLE and report that fitted nu values are lower for fixed-rate DeepJSCC than for variable-rate NTSCC, and lower for ImageNet than for CIFAR-10, consistent with the paper's qualitative predictions. A KDE-based KL regularizer that nudges the symbol distribution toward a Gaussian is shown to improve training convergence.

Significance. If the central claim were established, the paper would provide a principled, parametric account of empirically observed heavy-tailed semantic symbols, unifying Gaussian and Cauchy extremes in a single family and offering practical guidance (e.g., distribution regularization). The authors are refreshingly explicit that their objective is heuristic rather than derived, and the reported experiments span multiple architectures, datasets, and SNRs. However, the theoretical derivation does not connect to the actual MSE training loss, the empirical validation lacks error bars and alternative-distribution comparisons, and the variance-normalized model does not actually realize the claimed Cauchy limit. The paper is an interesting phenomenological contribution, but the stated 'theoretical consequence' claim is currently disproportionate to the evidence.

major comments (4)

[§IV-B–C] Claim 1 is mathematically correct for the stated max-entropy problem, but it does not establish the paper's central claim about end-to-end MSE-trained encoders. The surrogate L_source (Eq. 15) is constructed from an APSK packing analogy with free parameters alpha and kappa; it is never shown that minimizing the actual MSE loss (Eq. 5) is equivalent to minimizing L_source + lambda*L_channel (Eq. 10), nor that SGD drives the encoder's marginal p(y) to the optimum of this marginal-only surrogate. The derivation ignores X, the decoder, and the distortion metric. Please provide a direct derivation or a controlled experiment (e.g., training with the surrogate objective and showing identical symbol statistics) to bridge this gap; otherwise the t-distribution is a heuristic model, not a theoretical consequence.
[§V] The empirical validation fits nu by MLE (Eq. 28) on the same samples used to assess the fit, and reports no error bars, confidence intervals, or comparisons against other heavy-tailed families (e.g., generalized Gaussian, Pareto, or an unnormalized Cauchy). The reported NLL values (1.27 for DeepJSCC vs 1.41 for NTSCC; 1.27 for ImageNet vs 1.38 for CIFAR-10) are not sufficient to discriminate the t-family from alternatives, and cross-modal comparisons of NLL are not meaningful. The predictions 'DeepJSCC < NTSCC' and 'ImageNet < CIFAR-10' are qualitative orderings of fitted parameters, not computed outputs from system parameters. Please add split-sample or cross-validated fits, error bars on nu, and likelihood-ratio or AIC/BIC comparisons against baseline distributions.
[§IV-C] The variance-normalized t-distribution in Eq. (23) is only defined for nu>2, yet the paper describes the source-coding-dominant limit as the Cauchy distribution (nu→1, 'ignoring the unit-variance normalization'). In the model actually fit to the data, the limit nu→2+ corresponds to a degenerate point mass at zero (the scale sqrt(nu-2) goes to zero), not to a heavy-tailed Cauchy-like law. Thus the interpolation narrative between Cauchy and Gaussian is not realized by the fitted model, and interpreting nu≈2.84 as 'Cauchy-like' is misleading. Please reconcile the limits or revise the interpretation of nu in terms of tail behavior under the enforced power normalization.
[§VI–VII] The KL-regularizer experiment (Eq. 29) is presented as supporting the theory, but the observed convergence improvement may be a generic regularization effect; it does not test the specific claim that the optimal symbol distribution is t-distributed. The paper does not compare against a t-distributed target with the fitted nu, nor against other priors. A falsifiable prediction of the framework would be, e.g., that a t-regularizer with the measured nu outperforms a Gaussian regularizer in settings where nu is small. Without such a test, the regularizer result is only weak evidence for the proposed equilibrium model.

minor comments (5)

[Abstract / I] The abstract states that empirical symbols 'closely follow' the Student's t-distribution, but Section V-C acknowledges deviations in sparsely sampled regions. Consider softening the wording to match the evidence.
[Fig. 8] The compressed-rate distributions for ImageNet (8,000 images) and CIFAR-10 (50,000 images) use different sample sizes; the comparison of variability should be confirmed with equal-size subsamples or normalized histograms.
[Eq. (2)] The batch-normalization layer in Eq. (2) scales the entire symbol vector, but the scalar normalization is computed over the batch. The effect of this batch-dependent scaling on the marginal distribution (e.g., across batches with different empirical second moments) is not discussed; this may introduce additional stochasticity beyond the model.
[Eq. (23)] The relationship nu = 2*nu_t - 1 is stated without derivation; adding one line showing the exponent match would improve clarity.
[Section VI-A] The KL term D_KL(q(y) || p(y)) uses KDE with Silverman's rule, but the bandwidth choice affects the gradient of the KL loss. A brief comment on the sensitivity to the KDE bandwidth would be useful.

Circularity Check

1 steps flagged · score 6.0 of 10

The empirical 'predictions' of the shape parameter are MLE fits from the same data used for validation; the Student-t derivation is conditional on a deliberately chosen surrogate constraint.

fitted input called prediction [Abstract; Section V-B (Eq. 28); Section V-C/D; Section VI-A]
"Experiments on image-based semantic systems show that the model closely predicts how the shape parameter varies... For quantitative analysis, we fit the empirical symbols to our proposed Student's t-based symbol probability model and examine the fittedν... ν=arg max Σ log p(y_i^(b);ν)... While our analysis suggests that a Student's t-distribution may be a reasonable choice, its ideal degrees of freedom parameter, ν, is unknown a priori."

The quantitative content of the claimed prediction is the tail index ν, and Eq. (28) defines ν as the MLE fit to the very empirical symbols later used as validation. The theory provides no mapping from coding scheme, dataset entropy, or SNR to ν; the paper concedes ν is 'unknown a priori.' Therefore the reported ordering (DeepJSCC ν=2.84 vs NTSCC ν=7.92; ImageNet ν=2.84 vs CIFAR ν=4.75) is a post-hoc reading of fitted constants, not a model output. A one-parameter heavy-tailed family with MLE-fitted ν will naturally attain lower NLL than Gaussian/Cauchy, so the fit does not independently confirm the mechanism; the 'prediction' reduces to the fitting step.

full rationale

The core max-entropy calculation (Claim 1, Eqs. 18-22) is mathematically valid: maximizing h(Y) subject to E[log_2(1+αY^2/σ^2)] = C forces p(y) ∝ (1+αy^2/σ^2)^{-Λ}, a Student-t. However, this is a conditional derivation from a surrogate objective the paper itself labels 'heuristic' (Sections I and IV), not a consequence of the actual MSE loss (Eq. 5); that is a validity/correctness gap rather than a circularity. The significant circularity is in the empirical validation: ν is obtained by maximum likelihood from the same empirical symbols that are then compared with the t-model, and the abstract's wording 'predicts how the shape parameter varies' is not supported by any derivation of ν from system parameters (the paper states ν is 'unknown a priori'). The dataset/coding-scheme comparisons are post-hoc orderings of fitted values. I found no load-bearing self-citation or imported uniqueness argument: references to the authors' prior work are architectural/experimental, and the t-distribution's max-entropy characterization is standard. The ν→1 Cauchy-limit statement also conflicts with the unit-variance normalization (which requires ν>2), but this is a mathematical consistency issue, not circularity. Overall, the derivation is self-contained but its predictive claims partially reduce to the fitting step, so a score of 6 reflects partial circularity in the empirical 'prediction,' not a fully circular derivation.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The conclusion rests on a heuristic Lagrangian objective (Eq. 10) whose source term is an APSK-inspired payload surrogate (Eq. 15), and on a shape parameter nu fitted from data (Eq. 28). No new physical entities are introduced; 'pressures' are explanatory constructs.

free parameters (5)

nu (degrees of freedom / tail exponent) = 2.84 (DeepJSCC/ImageNet), 7.92 (NTSCC/ImageNet), 4.75 (DeepJSCC/CIFAR-10), 2.66-2.96 across SNR
Estimated by MLE (Eq. 28) per model/dataset/SNR; the central parameter of the model, not predicted a priori from system parameters.
alpha (payload scaling constant in Eq. 15) = Not estimated directly; absorbed into scale s^2 = sigma^2/alpha and eliminated by unit-variance normalization
Absorbs APSK geometry, packing efficiency, and implementation losses; its value affects the derived distribution but is never measured.
lambda (Lagrange multiplier in joint objective Eq. 10) = Not directly estimated; maps monotonically to nu
Controls the balance between source and channel pressure; the theory only says larger lambda gives larger nu, with no quantitative mapping.
kappa (packing efficiency factor in Eq. 13) = Absorbed into alpha
Packing efficiency of the multi-ring APSK constellation; part of the surrogate payload model.
lambda_reg (regularization weight in Eq. 29) = 1e-4
Hand-chosen small value; the paper notes higher values degraded performance (not shown) and smaller values had negligible impact.

assumptions (6)

ad hoc to paper End-to-end encoder behavior can be modeled as minimizing L_source + lambda*L_channel with L_source = E[log2(1+alpha*Y^2/sigma^2)] (Eq. 10).
The paper calls this a heuristic objective; it is not derived from the MSE training loss. If false, the t-distribution derivation does not apply.
domain assumption Maximizing differential entropy h(Y) is an appropriate surrogate for maximizing I(Y;Y_hat) over the AWGN channel.
Under a power constraint, Gaussian maximizes both h(Y) and I(Y;Y_hat), but for arbitrary non-Gaussian distributions the two are not equivalent; Section IV-A.
ad hoc to paper The number of distinguishable constellation points within radius r is M(r)=1+kappa*pi*r^2/A0, so payload b=log2(1+kappa*pi*r^2/A0).
APSK packing model with constant SER; identifies r^2 with symbol energy; Section IV-B, Eqs. (12)-(15).
domain assumption Symbol dimensions are i.i.d. and can be factorized for KDE and fitting.
Assumed for tractability; Fig. 4 shows similar but not identical marginals; Section V-A.
domain assumption X' is transmitted without error, h(Y)=H(X')+delta_codeword, and delta_tr is a fixed overhead.
Conceptual decomposition to separate source and channel coding; not directly testable; Section III-B.
domain assumption Dataset entropy variability can be approximated by PNG compressed size distribution.
Used to predict ImageNet vs CIFAR-10 nu differences; Section V-D.

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Cite this review

Pith. "Pith review of Symbol Distributions in Semantic Communications: A Source-Channel Equilibrium Perspective." pith.science (2026). https://pith.science/paper/ULZB2DM6

@misc{pith2026251214022,
  author       = {Pith},
  title        = {Pith review of: Symbol Distributions in Semantic Communications: A Source-Channel Equilibrium Perspective},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ULZB2DM6}},
  note         = {Machine review of arXiv:2512.14022}
}

read the original abstract

Semantic communication systems often use end-to-end neural networks to map input data into continuous symbols. These symbols, which are essentially neural network features, have fixed dimensions and often exhibit heavy-tailed distributions. However, the mechanism behind this distributional shape remains underexplored due to the end-to-end nature of encoder training, hindering systematic analysis and design. In this paper, we propose a parametric model for semantic symbol distributions. We model end-to-end training as inducing two coupled pressures on the symbol distribution: a source pressure that favors power allocation minimizing the average description cost, and a channel pressure that favors distributions with higher channel utilization. Under surrogate objectives that capture these effects, we obtain a Student's t-distribution as a model for the semantic symbols. Experiments on image-based semantic systems show that the model closely predicts how the shape parameter varies with (i) explicit symbol rate control and (ii) dataset entropy variability. Furthermore, enforcing a target symbol distribution via regularization (e.g., a Gaussian prior) improves training convergence, which is consistent with our hypothesis.

Figures

Figures reproduced from arXiv: 2512.14022 by the authors.

**Figure 1.** Conceptual block diagram of a typical semantic communication system. The symbols produced by semantic encoders may exhibit a distribution that [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Conceptual entropy analysis of the transmitted information for (a) maximizing the transmitted information (Gaussian), (b) the end-to-end learned [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Multi-ring APSK constellation illustrating a symbol within radius [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: Empirical symbol distributions qi(y) for each symbol dimension, represented with distinct colors. The results are from a fixed-length model trained on the ImageNet dataset. The visualization illustrates that the empirical distributions across various dimensions exhibit…

**Figure 5.** Figure 5: System architecture of DeepJSCC and NTSCC. The key difference in NTSCC compared to DeepJSCC is its feature-wise entropy calculation block, [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: Symbol distributions with respect to coding schemes. (a, d) Linear-scale probability density function plots comparing the empirical symbol distributions [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: Symbol distributions with respect to training datasets. (a, d) Linear-scale probability density function plots comparing the empirical symbol distributions [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: Compressed rate distribution of the randomly cropped input images [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 9.** Figure 9: Symbol distributions with respect to channel SNRs. (a, b, c) Log-scale probability density function plots comparing the empirical symbol distributions [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

**Figure 10.** Figure 10: Training curves of the semantic system with (orange) and without the proposed loss (blue) on the CIFAR-10 dataset, evaluated with respect to [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

**Figure 11.** Figure 11: (a), (b) Training curves showing reconstructed image quality of the semantic system with and without the proposed loss for DeepJSCC and NTSCC, [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]

Discussion (0). Continue with ORCID to comment.

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J. Deng, W. Dong, R. Socher, L.-J. Li, K. Li, and L. Fei-Fei, “Imagenet: A large-scale hierarchical image database,” inProc. IEEE/CVF Conf. Comput. Vis. and Pattern Recognit. (CVPR), pp. 248–255, June 2009

2009
[29]

Elic: Efficient learned image compression with unevenly grouped space- channel contextual adaptive coding,

D. He, Z. Yang, W. Peng, R. Ma, H. Qin, and Y . Wang, “Elic: Efficient learned image compression with unevenly grouped space- channel contextual adaptive coding,” inProc. IEEE/CVF Conf. Comput. Vis. and Pattern Recognit. (CVPR), pp. 5718–5727, June 2022

2022
[30]

Kodak lossless true color image suite,

R. Franzen, “Kodak lossless true color image suite,”available at http://r0k.us/graphics/kodak/, 1999

1999

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [1]

Beyond transmitting bits: Context, seman- tics, and task-oriented communications,

D. G ¨und¨uz, Z. Qin, I. E. Aguerri, H. S. Dhillon, Z. Yang, A. Yener, K. K. Wong, and C.-B. Chae, “Beyond transmitting bits: Context, seman- tics, and task-oriented communications,”IEEE J. Sel. Areas Commun., vol. 41, pp. 5–41, Nov. 2023

2023

[2] [2]

Demo: Real-time semantic communications with a vision transformer,

H. Yoo, T. Jung, L. Dai, S. Kim, and C.-B. Chae, “Demo: Real-time semantic communications with a vision transformer,” inProc. IEEE Int. Conf. on Commun. Workshops (ICC WKSHPS), pp. 1–2, May 2022

2022

[3] [3]

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. and Netw., vol. 5, pp. 567–579, May 2019

2019

[4] [4]

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, Apr. 2021

2021

[5] [5]

Semantic communication systems for speech transmission,

Z. Weng and Z. Qin, “Semantic communication systems for speech transmission,”IEEE J. Sel. Areas Commun., vol. 39, pp. 2434–2444, Aug. 2021

2021

[6] [6]

DeepWiVe: Deep-learning-aided wireless video transmission,

T.-Y . Tung and D. G ¨und¨uz, “DeepWiVe: Deep-learning-aided wireless video transmission,”IEEE J. Sel. Areas Commun., vol. 40, pp. 2570– 2583, July 2022

2022

[7] [7]

Wireless image transmission using deep source channel coding with attention modules,

J. Xu, B. Ai, W. Chen, A. Yang, P. Sun, and M. Rodrigues, “Wireless image transmission using deep source channel coding with attention modules,”IEEE Trans. Circuits and Syst. Video Technol., vol. 32, pp. 2315–2328, May 2022

2022

[8] [8]

On the role of ViT and CNN in semantic communications: Analysis and prototype validation,

H. Yoo, L. Dai, S. Kim, and C.-B. Chae, “On the role of ViT and CNN in semantic communications: Analysis and prototype validation,”IEEE Access, vol. 11, pp. 71528–71541, July 2023

2023