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arxiv: 2602.14481 · v2 · submitted 2026-02-16 · 💻 cs.IT · cs.AI· math.IT

On the Rate-Distortion-Complexity Tradeoff for Semantic Communication

Jingxuan Chai , Yong Xiao , Guangming Shi This is my paper

Pith reviewed 2026-05-15 22:05 UTC · model grok-4.3

classification 💻 cs.IT cs.AImath.IT
keywords semantic communicationrate-distortion-complexity tradeoffinformation bottleneckminimum description lengthGaussian sourcesbinary sourcessemantic distancemodel complexity
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The pith

Semantic communication exhibits a three-way tradeoff among rate, semantic distance, and model complexity.

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

The paper extends classical rate-distortion theory into a rate-distortion-complexity framework that adds constraints on semantic distance and on model complexity. Closed-form expressions are derived for the minimum rate needed to meet given semantic-distance and complexity targets, first for Gaussian sources and then for binary sources. These expressions show that the three quantities cannot be improved independently: lower complexity forces either a higher rate or greater semantic distance. The tradeoff is validated through experiments on image and video data, where the information-theoretic complexity measure tracks actual training and inference costs.

Core claim

Incorporating semantic distance (via both bit-wise distortion and statistical divergence) and complexity (via minimum description length and information bottleneck) into rate-distortion analysis produces closed-form minimum-rate expressions for Gaussian and binary semantic sources under joint constraints on distance and complexity.

What carries the argument

The rate-distortion-complexity framework, which augments rate-distortion analysis with semantic-distance metrics and an MDL/IB complexity measure.

Load-bearing premise

The complexity measure drawn from minimum description length and information bottleneck theory accurately reflects the practical computational cost of training and running the deep-learning semantic encoders and decoders.

What would settle it

An experiment that trains semantic encoders and decoders of measured complexity, records the rates and semantic distances they actually achieve, and checks whether any point falls below the derived rate bound for its semantic distance and complexity.

Figures

Figures reproduced from arXiv: 2602.14481 by Guangming Shi, Jingxuan Chai, Yong Xiao.

Figure 1
Figure 1. Figure 1: Illustration of the semantic communication model. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Curve plots of the RDC functions for Gaussian semantic sources [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Curve plots of the RDC functions for Gaussian semantic sources [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Curve plots of binary RDC tradeoffs: (a) Rate-complexity tradeoff; [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: RDC curves of the image classification task: (a) Rate-complexity [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The RDC tradeoff curves. objective function for video compression: Lvc := I(U; Sˆ) + λdE[d(S, Sˆ)] + λcI(X;U), (27) where λd and λc denote the tuning parameters that control the RDC tradeoff. Based on (20), the expected loss function Lvc is then lower-bounded by L˜ vcE:=pUSˆ log p(ˆs|u) r(ˆs) + λdE[d(S, Sˆ)] + λcEpXU log p(u|x) t(u) (28) where tU is a given probability distribution. VI. EXPERIMENTAL RESULT… view at source ↗
Figure 9
Figure 9. Figure 9: (a) The classification accuracy of the proposed VRDC method under [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Visual results of the reconstructed image samples across different [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Curve plots of the reconstruction performance across different [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Curve plots of the relationship between computation cost (FLOPs) [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
read the original abstract

Semantic communication is a novel communication paradigm that focuses on conveying the user's intended meaning rather than the bit-wise transmission of source signals. One of the key challenges is to effectively represent and extract the semantic meaning of any given source signals. While deep learning (DL)-based solutions have shown promising results in extracting implicit semantic information from a wide range of sources, existing work often overlooks the high computational complexity inherent in both model training and inference for the DL-based encoder and decoder. To bridge this gap, this paper proposes a rate-distortion-complexity (RDC) framework which extends the classical rate-distortion theory by incorporating the constraints on semantic distance, including both the traditional bit-wise distortion metric and statistical difference-based divergence metric, and complexity measure, adopted from the theory of minimum description length and information bottleneck. We derive the closed-form theoretical results of the minimum achievable rate under given constraints on semantic distance and complexity for both Gaussian and binary semantic sources. Our theoretical results show a fundamental three-way tradeoff among achievable rate, semantic distance, and model complexity. Extensive experiments on real-world image and video datasets validate this tradeoff and further demonstrate that our information-theoretic complexity measure effectively correlates with practical computational costs, guiding efficient system design in resource-constrained scenarios.

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 / 2 minor

Summary. The paper proposes a rate-distortion-complexity (RDC) framework extending classical rate-distortion theory to semantic communication by incorporating semantic distance constraints (bit-wise distortion and statistical divergence metrics) and a complexity measure drawn from minimum description length and information bottleneck principles. It derives closed-form minimum achievable rates for Gaussian and binary semantic sources under joint constraints on semantic distance and complexity, establishing a fundamental three-way tradeoff among rate, semantic distance, and model complexity. Experiments on real-world image and video datasets are reported to validate the tradeoff and to show that the information-theoretic complexity measure correlates with practical computational costs.

Significance. If the derivations are rigorous and the complexity measure is shown to be practically relevant, the work would be significant for providing an information-theoretic foundation to guide resource-efficient design of deep-learning-based semantic encoders and decoders in constrained environments, moving beyond pure rate-distortion analysis.

major comments (2)
  1. [Theoretical Results] Theoretical Results section: the closed-form minimum-rate expressions for Gaussian and binary sources are presented without derivation steps, explicit definitions of the semantic distance function, or the precise optimization problem being solved; this prevents verification that the expressions are independent rather than reparameterizations of the input MDL/IB definitions.
  2. [Experiments] Complexity measure and experimental validation: the claim that the adopted MDL/IB complexity correlates with practical DL costs (FLOPs, memory, training time) is load-bearing for the practical relevance of the RDC tradeoff, yet the manuscript provides no quantitative correlation coefficients, sensitivity analysis to alternative complexity definitions, or error bars on the dataset results.
minor comments (2)
  1. [Abstract] Abstract and introduction: clarify whether the semantic distance combines bit-wise and divergence metrics additively or via a weighted sum, and state the weighting parameters explicitly.
  2. [Notation] Notation: ensure the complexity scaling constants and semantic distance weighting parameters are defined once and used consistently in all equations and figures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback on our manuscript. We address each major comment below and outline the revisions we plan to make.

read point-by-point responses

  1. Referee: [Theoretical Results] Theoretical Results section: the closed-form minimum-rate expressions for Gaussian and binary sources are presented without derivation steps, explicit definitions of the semantic distance function, or the precise optimization problem being solved; this prevents verification that the expressions are independent rather than reparameterizations of the input MDL/IB definitions.

    Authors: We appreciate this observation. In the original manuscript, we presented the closed-form expressions directly to focus on the key results, assuming familiarity with rate-distortion theory extensions. However, to allow full verification, we will include the detailed derivation steps, explicit definitions of the semantic distance function (including bit-wise distortion and divergence metrics), and the precise formulation of the optimization problem in the revised Theoretical Results section. This will clarify that the expressions are derived from the joint constraints rather than being mere reparameterizations of the MDL/IB definitions. revision: yes

  2. Referee: [Experiments] Complexity measure and experimental validation: the claim that the adopted MDL/IB complexity correlates with practical DL costs (FLOPs, memory, training time) is load-bearing for the practical relevance of the RDC tradeoff, yet the manuscript provides no quantitative correlation coefficients, sensitivity analysis to alternative complexity definitions, or error bars on the dataset results.

    Authors: We agree that quantitative validation of the correlation is important for practical relevance. In the revision, we will add correlation coefficients between the information-theoretic complexity measure and practical metrics such as FLOPs, memory usage, and training time. We will also include error bars on the experimental results and a sensitivity analysis to alternative complexity definitions where feasible. This will strengthen the claim regarding the correlation with DL costs. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in the RDC derivation chain

full rationale

The paper extends classical rate-distortion theory by adding explicit constraints on semantic distance (bit-wise and divergence-based) and an externally adopted complexity measure from minimum description length and information bottleneck principles. Closed-form minimum-rate expressions are then derived for Gaussian and binary sources under these joint constraints, yielding the claimed three-way tradeoff. This constitutes a standard constrained optimization extension rather than a reduction of the output to the inputs by definition or by self-citation. The complexity measure is imported from established external theory, not fitted or redefined within the paper to force the result. Experiments on image/video datasets supply independent empirical checks. No load-bearing self-citation, ansatz smuggling, or renaming of known results appears in the derivation steps described.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The framework rests on importing complexity definitions from MDL and IB without new independent justification, plus domain assumptions about how semantic distance combines bit-wise and statistical metrics.

free parameters (2)
  • semantic distance weighting parameters
    Weights balancing bit-wise distortion against statistical divergence are introduced to define the composite semantic distance metric.
  • complexity scaling constants
    Scaling factors taken from MDL/IB theory that convert description length into a complexity cost term.
axioms (2)
  • domain assumption Semantic distance is adequately captured by a linear combination of bit-wise distortion and statistical divergence
    Invoked when extending rate-distortion to semantic sources in the abstract.
  • domain assumption MDL/IB complexity measure is a faithful proxy for deep-learning encoder/decoder computational cost
    Adopted without further derivation to incorporate complexity constraints.

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