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Fundamental Limitation of Semantic Communications: Neural Estimation for Rate-Distortion

Dongxu Li, Jianhao Huang, Chuan Huang, Xiaoqi Qin, Han Zhang, Ping Zhang

TL;DR

This work analyzes the fundamental limits of semantic communications via the semantic rate-distortion function (SRDF) for a source pair $(X,S)$ over a discrete memoryless channel. It introduces NESRD, a neural estimator that learns a generative model to approximate the SRDF when the semantic source distribution is unknown, and also presents a cascade network variant for deterministic $S=h(X)$ and a Blahut-Arimoto algorithm for the perfectly known distribution case. The results demonstrate the neural estimator's strong consistency and provide practical SRDF computation methods, validated on joint Gaussian sources and datasets such as MNIST and SVHN. Overall, the paper advances theoretical understanding and practical estimation tools for rate-distortion tradeoffs in semantic communications, enabling more efficient joint source-channel design under distribution uncertainty.

Abstract

This paper studies the fundamental limit of semantic communications over the discrete memoryless channel. We consider the scenario to send a semantic source consisting of an observation state and its corresponding semantic state, both of which are recovered at the receiver. To derive the performance limitation, we adopt the semantic rate-distortion function (SRDF) to study the relationship among the minimum compression rate, observation distortion, semantic distortion, and channel capacity. For the case with unknown semantic source distribution, while only a set of the source samples is available, we propose a neural-network-based method by leveraging the generative networks to learn the semantic source distribution. Furthermore, for a special case where the semantic state is a deterministic function of the observation, we design a cascade neural network to estimate the SRDF. For the case with perfectly known semantic source distribution, we propose a general Blahut-Arimoto algorithm to effectively compute the SRDF. Finally, experimental results validate our proposed algorithms for the scenarios with ideal Gaussian semantic source and some practical datasets.

Fundamental Limitation of Semantic Communications: Neural Estimation for Rate-Distortion

TL;DR

This work analyzes the fundamental limits of semantic communications via the semantic rate-distortion function (SRDF) for a source pair over a discrete memoryless channel. It introduces NESRD, a neural estimator that learns a generative model to approximate the SRDF when the semantic source distribution is unknown, and also presents a cascade network variant for deterministic and a Blahut-Arimoto algorithm for the perfectly known distribution case. The results demonstrate the neural estimator's strong consistency and provide practical SRDF computation methods, validated on joint Gaussian sources and datasets such as MNIST and SVHN. Overall, the paper advances theoretical understanding and practical estimation tools for rate-distortion tradeoffs in semantic communications, enabling more efficient joint source-channel design under distribution uncertainty.

Abstract

This paper studies the fundamental limit of semantic communications over the discrete memoryless channel. We consider the scenario to send a semantic source consisting of an observation state and its corresponding semantic state, both of which are recovered at the receiver. To derive the performance limitation, we adopt the semantic rate-distortion function (SRDF) to study the relationship among the minimum compression rate, observation distortion, semantic distortion, and channel capacity. For the case with unknown semantic source distribution, while only a set of the source samples is available, we propose a neural-network-based method by leveraging the generative networks to learn the semantic source distribution. Furthermore, for a special case where the semantic state is a deterministic function of the observation, we design a cascade neural network to estimate the SRDF. For the case with perfectly known semantic source distribution, we propose a general Blahut-Arimoto algorithm to effectively compute the SRDF. Finally, experimental results validate our proposed algorithms for the scenarios with ideal Gaussian semantic source and some practical datasets.
Paper Structure (23 sections, 55 equations, 9 figures, 3 algorithms)

This paper contains 23 sections, 55 equations, 9 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Unknown Semantic Source Distributions
  4. Reformulation of $R(D_{\text{o}},D_{\text{s}})$
  5. Neural-network-based Approach
  6. A Special Case for NESRD
  7. Perfectly Known Semantic Source Distributions
  8. General BA Algorithm
  9. Computational Complexity
  10. Numercial and Simulation Results
  11. Joint Gaussian Source
  12. Datasets
  13. Training settings
  14. Experiments
  15. Image Datasets
  16. ...and 8 more sections

Figures (9)

  • Figure 1: Framework of SSCC scheme for semantic communications.
  • Figure 2: Training diagram for NESRD with $S = h(X)$.
  • Figure 3: NESRD $\hat{R}_\Theta(D_{\text{o}}, D_{\text{s}})$ for joint Gaussian source by Algorithm \ref{['alg_NESRD']}.
  • Figure 4: Performance comparisons among NESRD, SDP method9844779, and proposed general BA method for joint Gaussian semantic source.
  • Figure 5: NESRD $\hat{R}_\Theta(D_{\text{o}}, D_{\text{s}})$ for MNIST dataset.
  • ...and 4 more figures