Super-activated channels

Wei Liang Zeng

Rafael F. Schaefer, Holger Boche, H. Vincent Poor

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.

James M. McCracken

David F. P. Pile

Rafael F. Schaefer, Holger Boche, H. Vincent Poor

The wiretap channel models secure communication between two users in the presence of an eavesdropper who must be kept ignorant of transmitted messages. This communication scenario is studied for arbitrarily varying channels (AVCs), in which the legitimate users know only that the true channel realization comes from a pre-specified uncertainty set and that it varies from channel use to channel use in an arbitrary and unknown manner. This concept not only captures the case of channel uncertainty, but also models scenarios in which malevolent adversaries influence or jam the transmission of the legitimate users. For secure communication over orthogonal arbitrarily varying wiretap channels (AVWCs) it has been shown that the phenomenon of super-activation occurs; that is, there are orthogonal AVWCs, each having zero secrecy capacity, which allow for transmission with positive 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. As a consequence, a super-activated AVWC is robust and continuous in the uncertainty set, although a single AVWC might not be. Moreover, it is shown that the question of super-activation and the continuity of the secrecy capacity solely depends on the legitimate link. Accordingly, the single-user AVC is subsequently 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. Such knowledge is important for medium access control and in particular resource allocation as it determines the overall performance of a system.

Yu Luo, Yongming Li, Zhengjun Xi