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Integrated Sensing and Communication with Distributed Rate-Limited Helpers

Yiqi Chen, Holger Boche, Tobias J. Oechtering, Mikael Skoglund

TL;DR

This work investigates integrated sensing and communication (ISAC) over a state-dependent channel with two rate-limited helpers: one observing the channel state sequence $S^n$ noncausally and the other observing the feedback sequence $Z^n$, and it derives a capacity–compression–distortion tradeoff region $C(D)$. A novel coding scheme blends a noncausal description of part of the state at block start with a joint compression of the remainder alongside the feedback, yielding a computable inner bound that is tight in several special cases. The main contributions include a general inner bound $\mathcal{R}^{in}(D)$ with a joint distribution over auxiliary variables, multiple specialized bounds for rate-limited vs. rate-unlimited feedback, and a decomposable-channel analysis that reveals a common-component structure and two corner-point regimes. Special cases—such as rate-unlimited feedback with a message-cognizant state encoder and decomposable channels with receiver-side helpers—give exact capacity-distortion regions $C(D)$ or tight outer bounds, providing benchmarks for ISAC system design. Numerical examples illustrate the tradeoffs between state-description quality, communication rate, and distortion, demonstrating how rate-limited helpers can enhance both sensing and communication performance.

Abstract

This paper studies integrated sensing and communication (ISAC) systems with two rate-limited helpers who observe the channel state sequence and the feedback sequence, respectively. Depending on the timing of compressing and using the state information, our proposed coding scheme gives an inner bound of the capacity-compression-distortion tradeoff region. The tradeoff is realized by sending part of the state information at the beginning of the transmission to facilitate the communication and compressing the remaining part together with the feedback signal. The inner bound becomes tight bounds in several special cases.

Integrated Sensing and Communication with Distributed Rate-Limited Helpers

TL;DR

This work investigates integrated sensing and communication (ISAC) over a state-dependent channel with two rate-limited helpers: one observing the channel state sequence $S^n$ noncausally and the other observing the feedback sequence $Z^n$, and it derives a capacity–compression–distortion tradeoff region $C(D)$. A novel coding scheme blends a noncausal description of part of the state at block start with a joint compression of the remainder alongside the feedback, yielding a computable inner bound that is tight in several special cases. The main contributions include a general inner bound $\mathcal{R}^{in}(D)$ with a joint distribution over auxiliary variables, multiple specialized bounds for rate-limited vs. rate-unlimited feedback, and a decomposable-channel analysis that reveals a common-component structure and two corner-point regimes. Special cases—such as rate-unlimited feedback with a message-cognizant state encoder and decomposable channels with receiver-side helpers—give exact capacity-distortion regions $C(D)$ or tight outer bounds, providing benchmarks for ISAC system design. Numerical examples illustrate the tradeoffs between state-description quality, communication rate, and distortion, demonstrating how rate-limited helpers can enhance both sensing and communication performance.

Abstract

This paper studies integrated sensing and communication (ISAC) systems with two rate-limited helpers who observe the channel state sequence and the feedback sequence, respectively. Depending on the timing of compressing and using the state information, our proposed coding scheme gives an inner bound of the capacity-compression-distortion tradeoff region. The tradeoff is realized by sending part of the state information at the beginning of the transmission to facilitate the communication and compressing the remaining part together with the feedback signal. The inner bound becomes tight bounds in several special cases.

Paper Structure

This paper contains 21 sections, 11 theorems, 137 equations, 5 figures.

Table of Contents

  1. introduction
  2. Models and Results
  3. Models
  4. Main Results
  5. Rate-limited ISAC with Perfect Feedback
  6. Decomposable Channel with Perfect Feedback
  7. Capacity-achieving Case: Message-cognizant State Encoder
  8. examples and applications
  9. Z-channel with Random Parameters
  10. Successive Refinement of the State
  11. Binary Channel with Fading
  12. Causal Helper
  13. proof of theorem \ref{['the: inner bound']}
  14. Coding Scheme
  15. Cardinality bounds
  16. ...and 6 more sections

Key Result

Theorem 1

The capacity-distortion-compression region of the ISAC with rate-limited helpers satisfies

Figures (5)

  • Figure 1: The rate-limited ISAC System: The state encoder observes the channel state noncausally and sends the sender a message $M_{f_1}$. The feedback encoder observes a feedback signal $Z^n$ and sends the sender a message $M_{f_2}$.
  • Figure 2: Z-channel with random parameters $S$
  • Figure 3: The impact of $D'$ on the communication rate $R$ and the compression rate $R_{f_1}$. The dotted line is the capacity of the channel when no side information is available at the encoder side, and there is no distortion constraint.
  • Figure 4: The tradeoff between $I(V_{11};S)$ and $I(V_{12};S|X,Y,V_{11})$ depending on different values of $D'$.
  • Figure 5: Relation between $H(q),H(D)$ and $1$.

Theorems & Definitions (17)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Remark 1
  • Corollary 1
  • Theorem 2
  • Corollary 2
  • Corollary 3
  • Corollary 4
  • Corollary 5
  • ...and 7 more