We determine the identification capacity of compound channels in the presence of a wiretapper. It turns out that the secure identification capacity formula fulfills a dichotomy theorem: It is positive and equals the identification capacity of the channel if its message transmission secrecy capacity is positive. Otherwise, the secure identification capacity is zero. Thus, we show in the case that the secure identification capacity is greater than zero we do not pay a price for secure identification, i.e., the secure identification capacity is equal to the identification capacity. This is in strong contrast to the transmission capacity of the compound wiretap channel. We then use this characterization to investigate the analytic behavior of the secure identification capacity. In particular, it is practically relevant to investigate its continuity behavior as a function of the channels. We completely characterize this continuity behavior. We analyze the (dis-) continuity and (super-) additivity of the capacities. In 1998, N. Alon gave a conjecture about maximal violation for the additivity of capacity functions in graphs. We show that this maximal violation as well holds for the secure identification capacity of compound wiretap channels. This is the first example of a capacity function exhibiting this behavior.

The deterministic identification (DI) capacity is developed in multiple settings of channels with power constraints. A full characterization is established for the DI capacity of the discrete memoryless channel (DMC) with and without input constraints. Originally, Ahlswede and Dueck established the identification capacity with local randomness at the encoder, resulting in a double exponential number of messages in the block length $n$ . In the deterministic setup, the number of messages scales exponentially, as in Shannon’s transmission paradigm, but the achievable identification rates are higher. An explicit proof was not provided for the deterministic setting. In this paper, a detailed proof is presented for the DMC. Furthermore, Gaussian channels with fast and slow fading are considered, when channel side information is available at the decoder. A new phenomenon is observed as we establish that the number of messages scales as $2^{n\log (n)R}$ by deriving lower and upper bounds on the DI capacity on this scale. Consequently, the DI capacity of the Gaussian channel is infinite in the exponential scale and zero in the double exponential scale, regardless of the channel noise.

In next generation connectivity systems, which rely on robust and low-latency information exchange, there exists communication tasks in which the Ahlswede/Dueck identification scheme is much more efficient than Shannon’s transmission scheme. We concentrate on the arbitrarily varying wiretap channel (AVWC) which models jamming attacks. We provide a coding scheme for secure identification and determine the secrecy capacity of the AVWC. Furthermore, we analyze important properties of this capacity function, e.g. continuity and super-additivity. These properties are important for the design of robust secure communication design and for the optimization of the Medium Access Control (MAC).

We determine the secrecy capacity of the compound channel with quantum wiretapper and channel state information at the transmitter. Moreover, we derive a lower bound on the secrecy capacity of this channel without channel state information and determine the secrecy capacity of the compound classical-quantum wiretap channel with channel state information at the transmitter. We use this result to derive a proof for a lower bound on the entanglement generating capacity of the compound quantum channel. We also derive a proof for the formula for entanglement generating capacity of the compound quantum channel with channel state information at the encoder which was given in additional information [Bjelaković, Boche, and Nötzel, in Proceedings of International Symposium on Information Theory ISIT, Korea, 2009 (IEEE, New York, 2009), pp. 1889–1893].

Various applications of molecular communications (MC) are event-triggered, and, as a consequence, the prevalent Shannon capacity may not be the right measure for performance assessment. Thus, in this paper, we motivate and establish the identification capacity as an alternative metric. In particular, we study deterministic identification (DI) for the discrete-time Poisson channel (DTPC), subject to an average and a peak molecule release rate constraint, which serves as a model for MC systems employing molecule counting receivers. It is established that the number of different messages that can be reliably identified for this channel scales as 2(nlogn)R, where n and R are the codeword length and coding rate, respectively. Lower and upper bounds on the DI capacity of the DTPC are developed. The obtained large capacity of the DI channel sheds light on the performance of natural DI systems such as natural olfaction, which are known for their extremely large chemical discriminatory power in biology. Furthermore, numerical results for the empirical miss-identification and false identification error rates are provided for finite length codes. This allows us to characterize the behaviour of the error rate for increasing codeword lengths, which complements our theoretically-derived scale for asymptotically large codeword lengths.

Communication over a quantum channel that depends on a quantum state is considered when the encoder has channel side information (CSI) and is required to mask information on the quantum channel state from the decoder. A full characterization is established for the entanglement-assisted masking equivocation region with a maximally correlated channel state, and a regularized formula is given for the quantum capacity-leakage function without assistance. For Hadamard channels without assistance, we derive single-letter inner and outer bounds, which coincide in the standard case of a channel that does not depend on a state.