TY - JOUR

T1 - Deterministic K-Identification for Future Communication Networks

T2 - The Binary Symmetric Channel Results †

AU - Salariseddigh, Mohammad Javad

AU - Dabbabi, Ons

AU - Deppe, Christian

AU - Boche, Holger

N1 - Publisher Copyright:
© 2024 by the authors.

PY - 2024/3

Y1 - 2024/3

N2 - 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., (Formula presented.), where (Formula presented.) is the identification goal rate, then the number of messages that can be accurately identified grows exponentially in n, i.e., (Formula presented.), 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.

AB - 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., (Formula presented.), where (Formula presented.) is the identification goal rate, then the number of messages that can be accurately identified grows exponentially in n, i.e., (Formula presented.), 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.

KW - Hamming distance

KW - binary symmetric channel

KW - capacity region

KW - deterministic K-identification

KW - internet of things

KW - post Shannon communications

UR - http://www.scopus.com/inward/record.url?scp=85188740486&partnerID=8YFLogxK

U2 - 10.3390/fi16030078

DO - 10.3390/fi16030078

M3 - Article

AN - SCOPUS:85188740486

SN - 1999-5903

VL - 16

JO - Future Internet

JF - Future Internet

IS - 3

M1 - 78

ER -