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Distribution-Preserving Integrated Sensing and Communication with Secure Reconstruction

Yiqi Chen, Tobias Oechtering, Holger Boche, Mikael Skoglund, Yuan Luo

TL;DR

The paper studies distribution-preserving ISAC, where the reconstructed environmental state sequence must preserve its original distribution while achieving a distortion-limited sensing performance. It develops CR-assisted and non-CR inner bounds on the distribution-preserving capacity-distortion region using likelihood-encoder-based coding and soft-covering, and extends the results to deterministic encoders and Gaussian channels. A Gaussian example specializes the bounds to a linear-Gaussian model, illustrating the rate–distortion–distribution tradeoffs, and the secure ISAC extension introduces a henchman/eavesdropper framework with inner bounds on secrecy-constrained distortion. The findings highlight how preserving environment statistics interacts with communication-rate, sensing accuracy, and security requirements, informing robust ISAC design for 6G and beyond.

Abstract

Distribution-preserving integrated sensing and communication with secure reconstruction is investigated in this paper. In addition to the distortion constraint, we impose another constraint on the distance between the reconstructed sequence distribution and the original state distribution to force the system to preserve the statistical property of the channel states. An inner bound of the distribution-preserving capacity-distortion region is provided with some capacity region results under special cases. A numerical example demonstrates the tradeoff between the communication rate, reconstruction distortion and distribution preservation. Furthermore, we consider the case that the reconstructed sequence should be kept secret from an eavesdropper who also observes the channel output. An inner bound of the tradeoff region and a capacity-achieving special case are presented.

Distribution-Preserving Integrated Sensing and Communication with Secure Reconstruction

TL;DR

The paper studies distribution-preserving ISAC, where the reconstructed environmental state sequence must preserve its original distribution while achieving a distortion-limited sensing performance. It develops CR-assisted and non-CR inner bounds on the distribution-preserving capacity-distortion region using likelihood-encoder-based coding and soft-covering, and extends the results to deterministic encoders and Gaussian channels. A Gaussian example specializes the bounds to a linear-Gaussian model, illustrating the rate–distortion–distribution tradeoffs, and the secure ISAC extension introduces a henchman/eavesdropper framework with inner bounds on secrecy-constrained distortion. The findings highlight how preserving environment statistics interacts with communication-rate, sensing accuracy, and security requirements, informing robust ISAC design for 6G and beyond.

Abstract

Distribution-preserving integrated sensing and communication with secure reconstruction is investigated in this paper. In addition to the distortion constraint, we impose another constraint on the distance between the reconstructed sequence distribution and the original state distribution to force the system to preserve the statistical property of the channel states. An inner bound of the distribution-preserving capacity-distortion region is provided with some capacity region results under special cases. A numerical example demonstrates the tradeoff between the communication rate, reconstruction distortion and distribution preservation. Furthermore, we consider the case that the reconstructed sequence should be kept secret from an eavesdropper who also observes the channel output. An inner bound of the tradeoff region and a capacity-achieving special case are presented.
Paper Structure (12 sections, 10 theorems, 64 equations, 2 figures)

This paper contains 12 sections, 10 theorems, 64 equations, 2 figures.

Table of Contents

  1. introduction
  2. model and results
  3. No Common Randomness
  4. Deterministic Encoder
  5. Boundary Points: $C(0,\Delta)$ and $C(D_{min},\Delta)$, $\Delta \geq 0$
  6. Gaussian Example
  7. Secure ISAC
  8. coding scheme for theorem \ref{['the: capacity perception distortion with cr and noisy CSI']}
  9. proof of theorem \ref{['the: cpd with cr and causal csi and strict constraint']}
  10. optimal transport argument
  11. proof of theorem \ref{['the: cpddr with cr and noisy CSI and CSI']}
  12. Converse part of corollary \ref{['coro: deterministic cpddr with cr and noisy CSI and CSI']}

Key Result

Theorem 1

(Inner bound) An inner bound of the CR-assisted distribution-preserving capacity-distortion region is

Figures (2)

  • Figure 1: The state estimator has all the information at the encoder side with an additional feedback sequence $z^n$. It tries to reconstruct the state sequence preserving the distribution. The henchman shares all the information at the state estimator and communicates to the eavesdropper with a limited rate.
  • Figure 2: Rate-Common randomness region with different correlation values under distortion constraint $D=3$

Theorems & Definitions (18)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Remark 1
  • Corollary 1
  • Corollary 2
  • proof
  • Corollary 3
  • Theorem 2
  • Remark 2
  • ...and 8 more