###### Abstract  
Numerous applications of the Internet of Things (IoT) feature an event recognition behavior where the established Shannon capacity is not authorized to be the central performance measure. Instead, the identification capacity for such systems is considered to be an alternative metric, and has been developed in the literature. In this paper, we develop deterministic K-identification (DKI) for the binary symmetric channel (BSC) with and without a Hamming weight constraint imposed on the codewords. This channel may be of use for IoT in the context of smart system technologies, where sophisticated communication models can be reduced to a BSC for the aim of studying basic information theoretical properties. We derive inner and outer bounds on the DKI capacity of the BSC when the size of the goal message set \(K\) may grow in the codeword length \(n\). As a major observation, we find that, for deterministic encoding, assuming that \(K\) grows exponentially in \(n\), i.e., \(K=2^{\text{nr}}\), where \(\kappa\) is the identification goal rate, then the number of messages that can be accurately identified grows exponentially in \(n\), i.e., \(2^{\pi R}\), where \(R\) is the DKI coding rate. Furthermore, the established inner and outer bound regions reflects impact of the input constraint (Hamming weight) and the channel statistics, i.e., the cross-over probability. deterministic K-identification; capacity region; binary symmetric channel; Hamming distance; post Shannon communications; internet of things +
Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)]([https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/))). Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/by/4.0/0](https://creativecommons.org/licenses/by/4.0/0)]([https://creativecommons.org/licenses/by/4.0/0](https://creativecommons.org/licenses/by/4.0/0))). Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/)]([https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/))). Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons. data collection and analysis. The smart cities exploit state-of-the-art technologies such as cloud computing [6] and machine learning [7] to provide a better quality of government service, enhancing infrastructure, public utilities, and citizen services. In particular, in the context of smart mobility and transportation systems [8], IoT may provide opportunities for integrating control, communications, and date processing across a heterogeneous network of transportation systems. IoT applications can be extended to different aspects of such systems, including the infrastructure, vehicle, and user/driver. The interactions between such components give rise to inter- and intra-vehicular communication, smart traffic control, safety, logistics, user/vehicle control, electronic toll collection systems, etc. [9]. Specifically, a potential IoT application scenario for these contexts is exploiting sensors for the sake of environmental monitoring [10]. That is, in a wireless sensor network, a group of sensors which monitor the environment are expected to send the minimum amount of information to the decision center for the sake of performing an appropriate and reliable timely act. **Smart medical and health-care systems:** Applications of IoT for medical and healthcare purposes are referred to as the Internet of Medical Things (IoMT) [11; 12].