Deterministic K-Identification for Future Communication Networks: The Binary Symmetric Channel Results

Mohammad Javad Salariseddigh (), Ons Dabbabi, Christian Deppe and Holger Boche
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Mohammad Javad Salariseddigh: Institute for Communications Engineering, Technical University of Munich (TUM), 80333 Munich, Germany
Ons Dabbabi: Institute for Communications Engineering, Technical University of Munich (TUM), 80333 Munich, Germany
Christian Deppe: Federal Ministry of Education and Research, Hub 6G-Life, Technical University of Munich (TUM), 80333 Munich, Germany
Holger Boche: Federal Ministry of Education and Research, Hub 6G-Life, Technical University of Munich (TUM), 80333 Munich, Germany

Future Internet, 2024, vol. 16, issue 3, 1-45

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 n κ , where κ is the identification goal rate, then the number of messages that can be accurately identified grows exponentially in n , i.e., 2 n 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.

Keywords: deterministic K-identification; capacity region; binary symmetric channel; Hamming distance; post Shannon communications; internet of things (search for similar items in EconPapers)
JEL-codes: O3 (search for similar items in EconPapers)
Date: 2024
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