NEW DIRECTIONS IN THE THEORY OF IDENTIFICATION VIA CHANNELS

We study two problems in the theory of identification via channels. Th e first problem concerns the identification via channels with noisy fe edback. Whereas for Shannon's transmission problem the capacity of a d iscrete memoryless channel does not change with feedback, we know that the identification capacity is affected by feedback. We study its dep endence on the feedback channel. We prove both, a direct and a convers e coding theorem. Although a gap exists between the upper and lower bo unds provided by these two theorems, the known result for channels wit hout feedback and the known result for channels with complete feedback , are both special cases of these two new theorems, because in these c ases the bounds coincide. The second problem is the identification via wiretap channels. A secrecy identification capacity is defined for th e wiretap channel. A ''Dichotomy Theorem'' is proved which says here t hat the second-order secrecy identification capacity is the same as Sh annon's capacity for the main channel as long as the secrecy transmiss ion capacity of the wiretap channel is not zero, and zero otherwise. E quivalently, we can say that the identification capacity is not lowere d by the presence of a wiretapper as long as 1 bit can be transmitted (or identified) correctly with arbitrarily small error probability. Th is is in strong contrast to the case of transmission.