The impact of diversity on reliable communication over arbitrarily varying channels (AVC) is investigated as follows. First, the concept of an identical state-constrained jammer is motivated. Second, it is proved that symmetrizability of binary symmetric AVCs (AVBSC) caused by identical state-constrained jamming is circumvented when communication takes place over at least three orthogonal channels. Third, it is proved that the deterministic capacity of the identical state-constrained AVBSC is continuous and shows super-activation. This effect was hitherto demonstrated only for quantum communication and for classical communication under secrecy constraints.
The impact of diversity on reliable communication over arbitrarily varying channels (AVC) is investigated as follows. First, the concept of an identical state-constrained jammer is motivated. Second, it is proved that symmetrizability of binary symmetric AVCs (AVBSC) caused by identical state-constrained jamming is circumvented when communication takes place over at least three orthogonal channels. Third, it is proved that the deterministic capacity of the identical state-constrained AVBSC is continuous and shows super-activation. This effect was hitherto demonstrated only for quantum communication and for classical communication under secrecy constraints.
Availability of channel state information, especially to non-legitimate users, is one major challenge for secure communication in wireless systems. For arbitrarily varying channels (AVC), coordination resources such as common randomness have been shown to be important for reliable communication; especially for symmetrizable AVCs. In this paper, the arbitrarily varying wiretap channel (AVWC) with active wiretapper is studied. Such an wiretapper may or may not exploit his knowledge about the coordination resources to control the channel conditions. Secrecy capacity results are derived for different forms of coordination resources including common randomness and correlated sources. Finally, it is demonstrated how two orthogonal AVWCs, each with zero secrecy capacity, i.e., useless for secure transmission, can be super-activated to a useful channel allowing for secure communication at non-zero secrecy rates.
We study the problem of data transmission under the influence of a jammer, which is typical for wireless systems and commonly modeled as an arbitrarily varying channel (AVC) in information theory. AVC fulfilling a certain set of linear equations are called symmetrizable and are known to be prone to denial of service attacks. Recent work has shown that deciding if a given AVC is symmetrizable or not is a non-Turing computable problem. By relaxing the formulation of symmetrizability, we show the existence of a polynomial-time algorithm that determines whether a given AVC is non-symmetrizable, but displays a critical dependence on the number of jammer input states. We then show how imposing an energy constraint on the jammer allows the same algorithm to efficiently identify large classes of AVCs which are non-symmetrizable.
The classical wiretap channel models secure communication in the presence of a nonlegitimate wiretapper who has to be kept ignorant. Traditionally, the wiretapper is passive in the sense that he only tries to eavesdrop the communication using his received channel output. In this paper, more powerful active wiretappers are studied. In addition to eavesdropping, these wiretappers are able to influence the communication conditions of all users by controlling the corresponding channel states. Since legitimate transmitters and receivers do not know the actual channel realization or the wiretapper's strategy of influencing the channel states, they are confronted with arbitrarily varying channel (AVC) conditions. The corresponding secure communication scenario is, therefore, given by the arbitrarily varying wiretap channel (AVWC). In the context of AVCs, common randomness (CR) has been shown to be an important resource for establishing reliable communication, in particular, if the AVC is symmetrizable. But availability of CR also affects the strategy space of an active wiretapper as he may or may not exploit the common randomness for selecting the channel states. Several secrecy capacity results are derived for the AVWC. In particular, the CR-assisted secrecy capacity of the AVWC with an active wiretapper exploiting CR is established and analyzed in detail. Finally, it is demonstrated for active wiretappers how two orthogonal AVWCs, each useless for transmission of secure messages, can be super-activated to a useful channel allowing for secure communication at nonzero secrecy rates. To the best of our knowledge, this is not possible for passive wiretappers and, further, provides the first example of such super-activation, which has been expected to appear only in the area of quantum communication. Such knowledge is particularly important as it provides valuable insights for the design and the medium access control of future wireless communication systems.
In this thesis, we consider a class of information protection problems requiring confidentiality (secrecy) from eavesdropping and integrity (reliability) from jamming in an information-theoretic context. For this purpose, we introduce the arbitrarily varying wire-tap channel (AVWTC) model consisting of a family of wiretap channels indexed by some state that is selected by the jammer in an arbitrary and time-varying manner. We study this model for traditional wiretap codes and randomized wiretap codes, and develop insights about the corresponding secrecy capacity and randomized-code secrecy capacity, respectively. We characterize a lower bound on the randomized-code secrecy capacity of the AVWTC that suggests the secrecy is mainly dictated by a worst-case scenario. Additionally, we establish two upper bounds on the randomized-code secrecy capacity that suggest a single bad ``averaged' state can preclude secure communication, while certain superiorities of the legitimate receiver over the eavesdropper in all ``averaged' states result in a positive secrecy capacity. Finally, we prove that the secrecy capacity of the AVWTC is either zero or equal to its randomized-code secrecy capacity. We show that a ``two-layer' wiretap code is appropriate for combatting the two non-colluding jamming and eavesdropping adversaries.
We analyze arbitrarily varying classical-quantum wiretap channels. These channels are subject to two attacks at the same time: one passive (eavesdropping), and one active (jamming). We progress on previous works [5] and [6] by introducing a reduced class of allowed codes that fulfills a more stringent secrecy requirement than earlier definitions. In addition, we prove that non-symmetrizability of the legal link is sufficient for equality of the deterministic and the common randomness assisted secrecy capacities. At last, we focus on analytic properties of both secrecy capacities: We completely characterize their discontinuity points, and their super-activation properties.
The question of additivity of the capacity of a channel goes back to Shannon who asked this for the zero error capacity function. Despite the common sense that the capacity is usually additive, there is surprisingly little known for non-trivial channels. This paper addresses this question for the arbitrarily varying wiretap channel (AVWC) which models secure communication in the presence of arbitrarily varying channel (AVC) conditions. For orthogonal AVWCs it has been shown that the non-additivity phenomenon of super-activation occurs; that is, there are orthogonal AVWCs, each having zero secrecy capacity, which allow for transmission with positive secrecy rate if they are used together. It is shown that for such orthogonal AVWCs super-activation is generic in the sense that whenever super-activation is possible, it is possible for all AVWCs in a certain neighborhood as well. Moreover, it is shown that the issue of super-activation and the continuity of the secrecy capacity solely depend on the legitimate link. Accordingly, the single-user AVC is studied and it is shown that in this case, super-activation for non-secure message transmission is not possible, making it a unique feature of secure communication over AVWCs. However, the capacity for message transmission of the single-user AVC is shown to be super-additive including a complete characterization.