Joint Identification and Sensing for Discrete Memoryless Channels

In the identification (ID) scheme proposed by Ahlswede and Dueck, the receiver's goal is simply to verify whether a specific message of interest was sent. Unlike Shannon's transmission codes, which aim for message decoding, ID codes for a discrete memoryless channel (DMC) are far more efficient; their size grows doubly exponentially with the blocklength when randomized encoding is used. This indicates that when the receiver's objective does not require decoding, the ID paradigm is significantly more efficient than traditional Shannon transmission in terms of both energy consumption and hardware complexity. Further benefits of ID schemes can be realized by leveraging additional resources such as feedback. In this work, we address the problem of joint ID and channel state estimation over a DMC with independent and identically distributed (i.i.d.) state sequences. State estimation functions as the sensing mechanism of the model. Specifically, the sender transmits an ID message over the DMC while simultaneously estimating the channel state through strictly causal observations of the channel output. Importantly, the random channel state is unknown to both the sender and the receiver. For this system model, we present a complete characterization of the ID capacity-distortion function.