On the Rate-Distortion-Complexity Tradeoff for Semantic Communication

TL;DR

The paper introduces a rate-distortion-complexity (RDC) framework for semantic communication that augments classical rate-distortion theory with a model-complexity constraint inspired by minimum description length (MDL) and the information bottleneck (IB) principle. It derives closed-form RDC expressions for Gaussian and binary semantic sources, revealing a fundamental three-way tradeoff among rate, semantic fidelity, and encoder complexity, and extends this with a variational approach (VRDC) to handle unknown source distributions. Through extensive experiments on image classification, image generation, and video compression, the work demonstrates that the proposed complexity measure $I(X;U)$ correlates with practical computation (FLOPs) and enables more efficient encoder design under resource constraints, outperforming conventional baselines in task-driven scenarios. The results offer a principled, information-theoretic basis for balancing communication and computation in semantic systems and highlight the practical value of integrating MDL/IB-based complexity into semantic coding design.

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.

Figures (13)

• Figure 1: Illustration of the semantic communication model.
• Figure 2: Curve plots of the RDC functions for Gaussian semantic sources under (a) $\theta_p=0$ and various $\theta_c$; (b) various $\theta_p$ and $\theta_c$.
• Figure 3: 3D Surf plot of the RDC tradeoff of Gaussian semantic sources: (a) RDC functions under $\theta_p=0$; (b) RDC functions under $\theta_c=0.74$.
• Figure 4: Curve plots of the RDC functions for Gaussian semantic sources under $\theta_p=0$ and (a) $\theta_c=\infty$; (b) $\theta_c=1.12$.
• Figure 5: Curve plots of binary RDC tradeoffs: (a) Rate-complexity tradeoff; (b) Rate-distortion tradeoff.