Deterministic $K$-identification For Slow Fading Channel

Deterministic $K$-identification (DKI) is addressed for Gaussian channels with slow fading (GSF), where the transmitter is restricted to an average power constraint and channel side information is available at the decoder. We derive lower and upper bounds on the DKI capacity when the number identifiable messages $K$ may grow with the codeword length $n$. As a key finding, we establish that for deterministic encoding, the codebook size scales as $2^{(n\log n)R}$ assuming that the number of identifiable messages scales as $K = 2^{\kappa \log n}$, where $R$ is the coding rate and $\kappa \in [0,1)$ is the identification target rate.