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Joint Identification and Sensing with Noisy Feedback: A Task-Oriented Communication Framework for 6G

Yaning Zhao, Holger Boche, Christian Deppe

Abstract

Task-oriented communication is a key enabler of emerging 6G systems, where the objective is to support decisions and actions rather than full message reconstruction. From an information-theoretic perspective, identification (ID) codes provide a natural abstraction for this paradigm by enabling receivers to test whether a task-relevant message was sent, without decoding the entire message. Motivated by the strong impact of feedback on ID and by the growing interest in integrated communication and sensing, this paper studies joint identification and sensing (JIDAS) over state-dependent discrete memoryless channels with noisy strictly causal feedback. The transmitter conveys identification messages while simultaneously estimating the channel state from the feedback signal. For both deterministic and randomized coding schemes, we derive lower and upper bounds on the capacity--distortion function. The results quantify the fundamental limits of JIDAS under noisy feedback and recover existing noiseless-feedback characterizations as special cases.

Joint Identification and Sensing with Noisy Feedback: A Task-Oriented Communication Framework for 6G

Abstract

Task-oriented communication is a key enabler of emerging 6G systems, where the objective is to support decisions and actions rather than full message reconstruction. From an information-theoretic perspective, identification (ID) codes provide a natural abstraction for this paradigm by enabling receivers to test whether a task-relevant message was sent, without decoding the entire message. Motivated by the strong impact of feedback on ID and by the growing interest in integrated communication and sensing, this paper studies joint identification and sensing (JIDAS) over state-dependent discrete memoryless channels with noisy strictly causal feedback. The transmitter conveys identification messages while simultaneously estimating the channel state from the feedback signal. For both deterministic and randomized coding schemes, we derive lower and upper bounds on the capacity--distortion function. The results quantify the fundamental limits of JIDAS under noisy feedback and recover existing noiseless-feedback characterizations as special cases.

Paper Structure

This paper contains 8 sections, 7 theorems, 34 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model and Main Results
  3. Coding Scheme for the Achievability
  4. Achievability proof of Theorem \ref{['thm:JDIFAS']}
  5. Achievability proof of Theorem \ref{['thm:JRIDAS']}
  6. Converse Proof
  7. Example
  8. Conclusion

Key Result

Theorem 1

If the transmission capacity of the marginal channel $\tilde{W}_{Y|X}$ is positive, then for all $\lambda_1,\lambda_2 \ge 0$ with $\lambda_1+\lambda_2<1$, and where $\mathcal{X}_D \triangleq \{x\in\mathcal{X}: d^{\star}(x)\le D\}$. If the transmission capacity of $\tilde{W}_{Y|X}$ is zero, then $C_{DIF}(D)=0$.

Figures (3)

  • Figure 1: System model
  • Figure 2: Superposition coding structure
  • Figure 3: Lower and upper bound of $C(D)$ ($p_N=0.1$)

Theorems & Definitions (14)

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