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

TL;DR

This paper explores the fundamental limits of joint identification and sensing in 6G systems using noisy feedback, proposing bounds on capacity and distortion for integrated communication and sensing tasks.

Contribution

It introduces a theoretical framework for joint identification and sensing over channels with noisy feedback, deriving bounds that unify noiseless and noisy feedback scenarios.

Findings

Derived lower and upper bounds on capacity-distortion functions.

Quantified the impact of noisy feedback on joint identification and sensing.

Unified noiseless and noisy feedback cases within the same theoretical framework.

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.