Deterministic K-Identification for Binary Symmetric Channel

Deterministic K-Identification (DKI) for the binary symmetric channel (BSC) is developed. A full characterization of the DKI capacity for such a channel, with and without the Hamming weight constraint, is established. As a key finding, we find that for deterministic encoding the number of identifiable messages
$K$
may grow exponentially with the codeword length
$n$
, i.e.,
$K\ =\ 2^{\kappa n}$
, where
$\kappa$
is the target identification rate. Furthermore, the eligible region for
$\kappa$
as a function of the channel statistics, i.e., the crossover probability, is determined.