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Integrated Sensing and Communication: Rate-Distortion Fundamental Limits of State Estimator

Lugaoze Feng, Guocheng Lv, Xunan Li, Ye Jin

TL;DR

This paper addresses ISAC in the SDMC framework by formulating a rate-distortion problem for sensing and a unified capacity-rate-distortion region that jointly characterizes communication and estimation performance. It introduces a modified Blahut-Arimoto–type algorithm to compute the sensing rate-distortion function $R(D)$ with proven convergence and provides a formal operational interpretation of the estimator design under distortions. The results show that waveform design based solely on maximizing $I(\mathsf{S};\mathsf{T}|\mathsf{X})$ is not always optimal, and coding can improve estimation rates in several channel models, including binary, general DMC, and real Gaussian ISAC channels. Overall, the work offers a rigorous information-theoretic foundation for balancing sensing and communication in ISAC through the rate-distortion lens and presents practical algorithms to compute the optimal estimators.

Abstract

The state-dependent memoryless channel (SDMC) is employed to model the integrated sensing and communication (ISAC) system, where the transmitter conveys messages to the receiver while simultaneously estimating the state parameter of interest via the received echo signals. However, the performance of sensing has often been neglected in existing works. To address this gap, we establish the rate-distortion function for sensing performance in the SDMC model, which is defined based on standard information-theoretic principles to ensure clear operational meaning. In addition, we propose a modified Blahut-Arimoto type algorithm for solving the rate-distortion function and provide convergence proofs for the algorithm. We further define the capacity-rate-distortion tradeoff region, which unifies information-theoretic results for communication and sensing within a single optimization framework. Finally, we numerically evaluate the capacity-rate-distortion region and demonstrate the benefit of coding in terms of estimation rate for certain channels.

Integrated Sensing and Communication: Rate-Distortion Fundamental Limits of State Estimator

TL;DR

This paper addresses ISAC in the SDMC framework by formulating a rate-distortion problem for sensing and a unified capacity-rate-distortion region that jointly characterizes communication and estimation performance. It introduces a modified Blahut-Arimoto–type algorithm to compute the sensing rate-distortion function with proven convergence and provides a formal operational interpretation of the estimator design under distortions. The results show that waveform design based solely on maximizing is not always optimal, and coding can improve estimation rates in several channel models, including binary, general DMC, and real Gaussian ISAC channels. Overall, the work offers a rigorous information-theoretic foundation for balancing sensing and communication in ISAC through the rate-distortion lens and presents practical algorithms to compute the optimal estimators.

Abstract

The state-dependent memoryless channel (SDMC) is employed to model the integrated sensing and communication (ISAC) system, where the transmitter conveys messages to the receiver while simultaneously estimating the state parameter of interest via the received echo signals. However, the performance of sensing has often been neglected in existing works. To address this gap, we establish the rate-distortion function for sensing performance in the SDMC model, which is defined based on standard information-theoretic principles to ensure clear operational meaning. In addition, we propose a modified Blahut-Arimoto type algorithm for solving the rate-distortion function and provide convergence proofs for the algorithm. We further define the capacity-rate-distortion tradeoff region, which unifies information-theoretic results for communication and sensing within a single optimization framework. Finally, we numerically evaluate the capacity-rate-distortion region and demonstrate the benefit of coding in terms of estimation rate for certain channels.

Paper Structure

This paper contains 17 sections, 6 theorems, 51 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Notation
  3. Preliminaries
  4. System Model
  5. Code
  6. Main Result
  7. Rate-Distortion Functions
  8. Computation of Rate-Distortion Functions
  9. Capacity-Rate-Distortion Region
  10. Numerical Results
  11. Binary Channels with Multiplicative Bernoulli States
  12. General DMCs with Multiplicative States
  13. Real Gaussian Channels with Sensing Echo Signals Reflected From the Target
  14. Conclusion and Discussion
  15. Blahut-Arimoto Iterative algorithm
  16. ...and 2 more sections

Key Result

Theorem 1

Fix a $P_{\mathsf{X}}$ and $P_{\mathsf{S}}$. For stationary memoryless channels $P_{\mathsf{T}|\mathsf{XS}}^{ n}$, we have

Figures (6)

  • Figure 1: State-dependent memoryless channel model.
  • Figure 2: Capacity-distortion tradeoff of the binary channel with multiplicative bernoulli state with $q=0.5$.
  • Figure 3: Capacity-distortion tradeoff of the binary channel with multiplicative bernoulli state with $q=0.3$.
  • Figure 4: Capacity-distortion tradeoff of the DMC with multiplicative state with $P_{\mathsf{S}}=[1/4,1/4,1/4,1/4]$.
  • Figure 5: Capacity-distortion tradeoff of the DMC with multiplicative state with $P_{\mathsf{S}}=[1/3,1/4,1/4,1/6]$.
  • ...and 1 more figures

Theorems & Definitions (17)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Theorem 1
  • Remark 1
  • proof
  • Lemma 1
  • proof
  • Theorem 2
  • ...and 7 more