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.

翻译：面向任务通信是新兴6G系统的关键使能技术，其目标在于支持决策与行动，而非完整的消息重建。从信息论角度而言，识别（ID）码通过使接收端能够检测是否发送了与任务相关的消息（而无需解码全部消息），为该范式提供了天然抽象。鉴于反馈对识别性能的显著影响，以及集成通信与感知领域日益增长的研究兴趣，本文研究了在具有噪声严格因果反馈的状态依赖离散无记忆信道上的联合识别与感知（JIDAS）。发射端在同时从反馈信号中估计信道状态的同时传输识别消息。针对确定性与随机编码方案，我们推导了容量-失真函数的下界与上界。研究结果量化了噪声反馈条件下JIDAS的基本极限，并作为特例还原了现有无噪声反馈的特性刻画。