New directions in the theory of identification via channels

We study two problems in the theory of identi cation via channels. The rst problem concerns the identi cation via channels with noisy feedback. Whereas for Shannon's transmission problem the capacity of a discrete memoryless channel does not change with feedback, we know from [3] and [4] that the identi cation capacity is a ected by feedback. We study its dependence on the feedback channel. We prove both, a direct and a converse, coding theorem. Although a gap exists between the upper and lower bounds provided by these two theorems, the results of [3] and [4], namely the result for channels without feedback and the result for channels with complete feedback, are all special cases of these two new theorems, because in these cases the bounds coincide. The second problem is the identi cation via wiretap channels. A secrecy identi cation capacity is de ned for the wiretap channel in analogy to the de nition of [1]. A \Dichotomy Theorem" is proved which says here that the second order secrecy identi cation capacity is the same as Shannon's capacity for the main channel as long as the secrecy transmission capacity of the wiretap channel is not zero, and zero otherwise. Equivalently we can say that the identi cation capacity is not lowered by the presence of a wiretapper as long as one bit can be transmitted (or identi ed) correctly with arbitrarily small error probability. This is in strong contrast to the case of transmission.