We determine the identification capacity of compound channels with and without wiretapper. It turned out, that the secure capacity formula fulfill a dichotomy theorem. It is positive if its secure capacity is positive and equals the transmission capacity of the channel. Otherwise the capacity is zero. We analyze the (dis-)continuity and (super-)additivity of the capacities, which we determined. Alon gave in [6] a conjecture about maximal violation for the additivity for capacity functions. We show that this maximal violation holds for the secure identification capacity. This is the first example of a capacity function, which has this behavior.
We determine the identification capacity of compound channels with and without wiretapper. It turned out, that the secure capacity formula fulfill a dichotomy theorem. It is positive if its secure capacity is positive and equals the transmission capacity of the channel. Otherwise the capacity is zero. We analyze the (dis-)continuity and (super-)additivity of the capacities, which we determined. Alon gave in [6] a conjecture about maximal violation for the additivity for capacity functions. We show that this maximal violation holds for the secure identification capacity. This is the first example of a capacity function, which has this behavior.
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.
We study the identification capacity of classical-quantum channels (“cq-channels”), under channel uncertainty and privacy constraints. To be precise, we consider first compound memoryless cq-channels and determine their identification capacity; then we add an eavesdropper, considering compound memoryless wiretap cqq-channels, and determine their secret identification capacity. In the first case (without privacy), we find the identification capacity always equal to the transmission capacity. In the second case, we find a dichotomy: either the secrecy capacity (also known as private capacity) of the channel is zero, and then also the secrecy identification capacity is zero, or the secrecy capacity is positive and then the secrecy identification capacity equals the transmission capacity of the main channel without the wiretapper. We perform the same analysis for the case of arbitrarily varying wiretap cqq-channels (cqq-AVWC), with analogous findings, and make several observations regarding the continuity and super-additivity of the identification capacity in the latter case.
We study the identification capacity of classical-quantum channels (“cq-channels”) under channel uncertainty and privacy constraints. To be precise, we first consider compound memoryless cq-channels and determine their identification capacity; then we add an eavesdropper by considering compound memoryless wiretap cqq-channels, and determine their secret identification capacity. In the first case (without privacy), we find the identification capacity always equal to the transmission capacity. In the second case, we find a dichotomy: either the secrecy capacity (also known as private capacity) of the channel is zero, and then the secrecy identification capacity is also zero, or the secrecy capacity is positive and then the secrecy identification capacity equals the transmission capacity of the main channel without the wiretapper. We perform the same analysis for the case of arbitrarily varying wiretap cqq-channels (cqq-AVWC) with analogous findings, and make several observations regarding the continuity and super-additivity of the identification capacity in the latter case.
Studies two problems in the theory of identification via channels. The first problem concerns the identification via channels with noisy feedback. Whereas for Shannon's transmission problem the capacity of a discrete memoryless channel does not change with feedback, it is known that the identification capacity is affected by feedback. The authors study its dependence on the feedback channel. They 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 known result for channels without feedback and the known result for channels with complete feedback, are both special cases of these two new theorems, because in these cases the bounds coincide. The second problem is the identification via wiretap channels. A secrecy identification capacity is defined for the wiretap channel. A "dichotomy theorem" is proved which says that the second-order secrecy identification 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, one can say that the identification capacity is not lowered by the presence of a wiretapper as long as 1 bit can be transmitted (or identified) correctly with arbitrarily small error probability. This is in strong contrast to the case of transmission.>
In the theory of identification via noisy channels randomization in the encoding has a dramatic effect on the optimal code size, namely, it grows double-exponentially in the blocklength, whereas in the theory of transmission it has the familiar exponential growth. We consider now instead of the discrete memoryless channel (DMC) more robust channels such as the familiar compound (CC) and arbitrarily varying channels (AVC). They can be viewed as models for jamming situations. We make the pessimistic assumption that the jammer knows the input sequence before he acts. This forces communicators to use the maximal error concept and also makes randomization in the encoding superfluous. Now, for a DMC W by a simple observation, made by Ahlswede and Dueck (1989), in the absence of randomization the identification capacity, say C/sub NRI/(W), equals the logarithm of the number of different row-vectors in W. We generalize this to compound channels. A formidable problem arises if the DMC W is replaced by the AVC W. In fact, for 0-1-matrices only in W we are-exactly as for transmission-led to the equivalent zero-error-capacity of Shannon. But for general W the identification capacity C/sub NRI/(W) is quite different from the transmission capacity C(W). An observation is that the separation codes of Ahlswede (1989) are also relevant here. We present a lower bound on C/sub NRI/(W). It implies for instance for W={(/sub 0 1//sup 1 0/), (/sub /spl delta/ (1-/spl delta/)(1 0)/)}, /spl delta//spl isin/(0, 1/2 ) that C/sub NRI/(W)=1, which is obviously tight. It exceeds C(W), which is known to exceed 1-h(/spl delta/), where h is the binary entropy function. We observe that a separation code, with worst case average list size L~ (which we call an NRA code) can be partitioned into L~2/sup ne/ transmission codes. This gives a nonsingle-letter characterization of the capacity of AVC with maximal probability of error in terms of the capacity of codes with list decoding. We also prove that randomization in the decoding does not increase C/sub I/(W) and C/sub NRI/(W). Finally, we draw attention to related work on source coding.
In this survey we contrast the classical transmission theory of Shannon and the identification theory of Ahlswede and Dueck. We show that it may be useful to take a closer look at the recipient's goals. In identification theory, the recipient's goal is changed, thereby significantly increasing the channel capacity. Furthermore, there are further gains in the secure transmission of data. In this work we review the results for robust and secure discrete memoryless channels and jamming attacks. We analyze the capacity functions for various channels. It turns out that there may be discontiuity points of these functions. It is very important to use this result in practical implementations.