Converse Techniques for Identification via Channels

There is a growing interest in models that extend beyond Shannon's classical transmission scheme, renowned for its channel capacity formula $C$. One such promising direction is message identification via channels, introduced by Ahlswede and Dueck. Unlike in Shannon's classical model, where the receiver aims to determine which message was sent from a set of $M$ messages, message identification focuses solely on discerning whether a specific message $m$ was transmitted. The encoder can operate deterministically or through randomization, with substantial advantages observed particularly in the latter approach. While Shannon's model allows transmission of $M = 2^{nC}$ messages, Ahlswede and Dueck's model facilitates the identification of $M = 2^{2^{nC}}$ messages, exhibiting a double exponential growth in block length. In their seminal paper, Ahlswede and Dueck established the achievability and introduced a "soft" converse bound. Subsequent works have further refined this, culminating in a strong converse bound, applicable under specific conditions. Watanabe's contributions have notably enhanced the applicability of the converse bound. The aim of this survey is multifaceted: to grasp the formalism and proof techniques outlined in the aforementioned works, analyze Watanabe's converse, trace the evolution from earlier converses to Watanabe's, emphasizing key similarities and differences that underpin the enhancements. Furthermore, we explore the converse proof for message identification with feedback, also pioneered by Ahlswede and Dueck. By elucidating how their approaches were inspired by preceding proofs, we provide a comprehensive overview. This overview paper seeks to offer readers insights into diverse converse techniques for message identification, with a focal point on the seminal works of Hayashi, Watanabe, and, in the context of feedback, Ahlswede and Dueck.