Deterministic Identification Codes for Fading Channels

Abstract: Many communication applications incorporate event-triggered behavior, where the conventional Shannon capacity may not effectively gauge performance. Consequently, we advocate for the concept of identification capacity as a more suitable metric for assessing these systems. We consider deterministic identification codes for the Gaussian AWGN, the slow fading, and the fast fading channels with power constraints. We prove lower bounds on capacities for the slow and the fast fading channels with side information for a wide range of fading distributions. Additionally, we present the code construction with efficient encoding which achieves the lower bound on capacity both for the slow and the fast fading channels. At last, we prove the same lower bound on the capacity of the fast fading channel without side information, i.e., the same lower bound holds even when the receiver does not know the fading coefficients. As a result we show that compared with Shannon's message transmission paradigm we achieved completely different capacity scaling for deterministic identification codes for all relevant fading channels.