Rafael F. Schaefer

Physical Layer Service Integration in Wireless Networks : Signal processing challenges

It is becoming more important that next-generation wireless networks wisely integrate multiple services at the physical layer to increase spectral efficiency. In this article, physical layer service integration in wireless networks is considered, where senders not only transmit individual data to certain receivers but also integrate additional multicast or confidential services that have to be kept secret from nonlegitimate receivers. In this context, physical layer security techniques are becoming a promising complement to cryptographic techniques since they establish security using only the physical properties of the wireless channel. State-of-the-art solutions for certain important communication scenarios are discussed, and signal processing challenges and promising research directions are identified.

Capacity results and super-activation for wiretap channels with active wiretappers

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 wiretappers 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.

On the Continuity of the Secrecy Capacity of Compound and Arbitrarily Varying Wiretap Channels

The wiretap channel models secure communication between two users in the presence of an eavesdropper who must be kept ignorant of transmitted messages. The performance of such a system is usually characterized by its secrecy capacity which determines the maximum transmission rate of secure communication. In this paper, the issue of whether or not the secrecy capacity is a continuous function of the system parameters is examined. In particular, this is done for channel uncertainty modeled via compound channels and arbitrarily varying channels, in which the legitimate users know only that the true channel realization is from a prespecified uncertainty set. In the former model, this realization remains constant for the entire duration of transmission, while in the latter the realization varies from channel use to channel use in an unknown and arbitrary manner. These models not only capture the case of channel uncertainty, but are also suitable for modeling scenarios in which a malicious adversary jams or otherwise influences the legitimate transmission. The secrecy capacity of the compound wiretap channel is shown to be robust in the sense that it is a continuous function of the uncertainty set. Thus, small variations in the uncertainty set lead to small variations in secrecy capacity. On the other hand, the deterministic secrecy capacity of the arbitrarily varying wiretap channel is shown to be discontinuous in the uncertainty set meaning that small variations can lead to dramatic losses in capacity.

The secrecy capacity of a compound MIMO Gaussian channel

The compound MIMO Gaussian wiretap channel is studied, where the channel to the legitimate receiver is known and the eavesdropper channel is not known to the transmitter but is known to have a bounded spectral norm (channel gain). The compound secrecy capacity is established without the de-gradedness assumption and the optimal signaling is identified: the compound capacity equals the worst-case channel capacity thus establishing the saddle-point property, the optimal signaling is Gaussian and on the eigenvectors of the legitimate channel and the worst-case eavesdropper is isotropic. The eigenmode power allocation somewhat resembles the standard water-filling but is not identical to it.

Secure Communication Under Channel Uncertainty and Adversarial Attacks

Information theoretic approaches to security have been examined as a promising complement to current cryptographic techniques. Such information theoretic approaches establish reliable communication and data confidentiality directly at the physical layer of a communication network by taking the properties of the noisy channel into account leading to unconditional security regardless of the computational capabilities of eavesdroppers. The provision of accurate channel state information is a major challenge particularly in wireless communication systems, especially information about the channels to eavesdroppers. In addition, there might be malevolent adversaries who jam or influence the channel of the legitimate users. This paper surveys different models for secure communication under channel uncertainty and adversarial attacks and reviews the corresponding secrecy capacity results, which characterize the maximum rate at which information can be sent to legitimate receivers while being kept perfectly security from eavesdroppers.

Wireless physical layer security

Significance Security is a very important issue in the design and use of wireless networks. Traditional methods of providing security in such networks are impractical for some emerging types of wireless networks due to the light computational abilities of some wireless devices [such as radio-frequency identification (RFID) tags, certain sensors, etc.] or to the very large scale or loose organizational structure of some networks. Physical layer security has the potential to address these concerns by taking advantage of the fundamental ability of the physics of radio propagation to provide certain types of security. This paper provides a review of recent research in this field. Security in wireless networks has traditionally been considered to be an issue to be addressed separately from the physical radio transmission aspects of wireless systems. However, with the emergence of new networking architectures that are not amenable to traditional methods of secure communication such as data encryption, there has been an increase in interest in the potential of the physical properties of the radio channel itself to provide communications security. Information theory provides a natural framework for the study of this issue, and there has been considerable recent research devoted to using this framework to develop a greater understanding of the fundamental ability of the so-called physical layer to provide security in wireless networks. Moreover, this approach is also suggestive in many cases of coding techniques that can approach fundamental limits in practice and of techniques for other security tasks such as authentication. This paper provides an overview of these developments.

Wiretap Channels With Side Information—Strong Secrecy Capacity and Optimal Transceiver Design

The wiretap channel models the communication scenario where two legitimate users want to communicate in such a way that a wiretapper is kept ignorant. In this paper, the wiretap channel with side information is studied, where the wiretapper has additional side information available. This side information allows the wiretapper to restrict the transmitted message to a certain subset of messages before further postprocessing. Two different criteria are employed to model the secrecy of the confidential message: the information theoretic criterion of strong secrecy and a signal-processing-inspired criterion based on the decoding performance of the wiretapper. For the latter, the wiretapper is required to have the worst decoding performance regardless of the specific decoding strategy that is used. It is shown that both criteria are equivalent in terms of secrecy capacity. Furthermore, the secrecy capacity equals the one of the classical wiretap channel without side information available at the wiretapper. In addition, the corresponding capacity-achieving code structure and optimal transceiver design are characterized and properties are identified. Finally, extensions to channel uncertainty and multiple wiretappers are discussed.

The Secrecy Capacity of Compound Gaussian MIMO Wiretap Channels

Strong secrecy capacity of compound wiretap channels is studied. The known lower bounds for the secrecy capacity of compound finite-state memoryless channels under discrete alphabets are extended to arbitrary uncertainty sets and continuous alphabets under the strong secrecy criterion. The conditions under which these bounds are tight are given. Under the saddle-point condition, the compound secrecy capacity is shown to be equal to that of the worst-case channel. Based on this, the compound Gaussian multiple-input multiple-output wiretap channel is studied under the spectral norm constraint and without the degradedness assumption. First, it is assumed that only the eavesdropper channel is unknown, but is known to have a bounded spectral norm (maximum channel gain). The compound secrecy capacity is established in a closed form and the optimal signaling is identified. The compound capacity equals the worst-case channel capacity and thus establishing the saddlepoint property; the optimal signaling is Gaussian and on the eigenvectors of the legitimate channel and the worst-case eavesdropper is isotropic. The eigenmode power allocation somewhat resembles the standard water-filling but is not identical to it. More general uncertainty sets are considered and the existence of a maximum element is shown to be sufficient for a saddle-point to exist, so that signaling on the worst-case channel achieves the compound capacity of the whole class of channels. The case of rank-constrained eavesdropper is considered and the respective compound secrecy capacity is established. Subsequently, the case of additive uncertainty in the legitimate channel, in addition to the unknown eavesdropper channel, is studied. Its compound secrecy capacity and the optimal signaling are established in a closed form as well, revealing the same saddle-point property. When a saddle-point exists under strong secrecy, strong and weak secrecy compound capacities are equal.

Robust Broadcasting of Common and Confidential Messages Over Compound Channels: Strong Secrecy and Decoding Performance

The broadcast channel with confidential messages (BCC) consists of one transmitter and two receivers, where the transmitter sends a common message to both receivers and, at the same time, a confidential message to one receiver which has to be kept secret from the other one. In this paper, this communication scenario is studied for compound channels, where it is only known to the transmitter and receivers that the actual channel realization is fixed and from a prespecified set of channels. The information theoretic criterion of strong secrecy is analyzed in detail and its impact on the decoding performance of the non-legitimate receiver is characterized. In particular, it is shown that regardless of the computational capabilities and the applied decoding strategy of the non-legitimate receiver, his decoding error always tends to one. This gives a valuable signal processing implication of the strong secrecy criterion and identifies desirable properties of an optimal code design. Further, an achievable strong secrecy rate region is derived and a multiletter outer bound is given. Both together yield a multiletter expression of the strong secrecy capacity region of the compound BCC.

Secrecy Measures for Broadcast Channels With Receiver Side Information: Joint vs Individual

We study the transmission of a common message and three confidential messages over a broadcast channel with two legitimate receivers and an eavesdropper. Each legitimate receiver is interested in decoding two of the three confidential messages, while having the third one as side information. In order to measure the ignorance of the eavesdropper about the confidential messages, we investigate two different secrecy criteria: joint secrecy and individual secrecy. For both criteria, we provide a general achievable rate region. We establish both the joint and individual secrecy capacity if the two legitimate receivers are less noisy than the eavesdropper. We further investigate the scenario where the eavesdropper is less noisy than the two legitimate receivers. It is known that the joint secrecy constraints can not be fulfilled under this scenario, however, we manage to establish a non vanishing capacity region for the individual secrecy case.