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IEEE Information Theory Workshop (ITW)

A multiple access approach for the compound wiretap channel

Etienne Perron, Suhas N. Diggavi, Emre Telatar

Published Jan 1, 2009• 3 citations
Publisher

Abstract

The compound wiretap channel generalizes the classical problem in broadcast information-theoretic secrecy by allowing a class of potential eavesdroppers. This represents uncertainty in the eavesdropper channel and the characterization of its secrecy capacity is an open question. In this paper we present a new coding scheme that generalizes known approaches to this problem. The scheme prefixes an artificial multiple access channel to the transmission scheme in order to design a structured transmit codebook. The idea is that such a structure can potentially increase the perfect secrecy rate for the legitimate users in the presence of the class of eavesdroppers. We develop the achievable secrecy rate of this scheme and provide examples where this scheme is optimal.

DOI
10.1109/itw.2009.5351484

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The compound wiretap channel generalizes the classical problem in broadcast information-theoretic secrecy by allowing a class of potential eavesdroppers. This represents uncertainty in the eavesdropper channel and the characterization of its secrecy capacity is an open question. In this paper we present a new coding scheme that generalizes known approaches to this problem. The scheme prefixes an artificial multiple access channel to the transmission scheme in order to design a structured transmit codebook. The idea is that such a structure can potentially increase the perfect secrecy rate for the legitimate users in the presence of the class of eavesdroppers. We develop the achievable secrecy rate of this scheme and provide examples where this scheme is optimal.
The compound wiretap channel provides a general framework for studying secrecy communication under channel uncertainty. Characterizing the secrecy capacity of nondegraded compound wiretap channels is a challenging problem in information theory. This paper considers the class of parallel Gaussian compound wiretap channels with only one possible channel realization for the legitimate receiver and characterizes the secrecy capacity. (Such parallel Gaussian compound wiretap channels are generally nondegraded.) Moreover, it is shown that the proposed coding scheme strictly outperforms the best known single-letter scheme with Gaussian codebooks.
This paper investigates the secure transmission in multiple access wiretap channels, where multiple legitimate users transmit private information to an intended receiver in the presence of multiple eavesdroppers. In order to improve security, we propose a novel cooperative jamming scheme, in which users do not share channel state information (CSI) but the legitimate channels will not be degraded by the artificial noise. The basic idea is to make each user exploit its own CSI in two slots to design artificial noise, so that the intended receiver can eliminate all the artificial noise but the eavesdroppers cannot. In this process, the interference between users plays a key role to achieve security, because it guarantees that the artificial noise from different users helps each other. We consider the non-collusion and collusion of eavesdroppers and analyze the secrecy performance for both scenarios. We adopt the secrecy sum-rate as the main metric, and show that positive secrecy sum-rate can be achieved by using the proposed scheme. Especially, we observe that when eavesdroppers collude and their additive white Gaussian noise (AWGN) close to zero, the number of users must not be less than twice the number of eavesdroppers to ensure positive secrecy sum-rate. Finally, simulation results are provided to corroborate our theoretical findings.
This paper considers the compound wiretap channel, which generalizes Wyner's wiretap model to allow the channels to the (legitimate) receiver and to the eavesdropper to take a number of possible states. No matter which states occur, the transmitter guarantees that the receiver decodes its message and that the eavesdropper is kept in full ignorance about the message. The compound wiretap channel can also be viewed as a multicast channel with multiple eavesdroppers, in which the transmitter sends information to all receivers and keeps the information secret from all eavesdroppers. For the discrete memoryless channel, lower and upper bounds on the secrecy capacity are derived. The secrecy capacity is established for the degraded channel and the semideterministic channel with one receiver. The parallel Gaussian channel is further studied. The secrecy capacity and the secrecy degree of freedom ( ) are derived for the degraded case with one receiver. Schemes to achieve the for the case with two receivers and two eavesdroppers are constructed to demonstrate the necessity of a prefix channel in encoder design. Finally, the multi-antenna (i.e., MIMO) compound wiretap channel is studied. The secrecy capacity is established for the degraded case and an achievable is given for the general case.
In this paper, we study the secure transmission in multiple access wiretap channels when the instantaneous channel state information (CSI) of the wiretap channels is unknown by the legitimate users. We propose a two-phase jamming-assisted secure transmission scheme based on the randomness and independence of wireless channels. In this scheme, we appropriately design artificial noise in two transmission phases and make sure that the eavesdropper's channel is degraded by the artificial noise but the legitimate user's channel is free of the artificial noise. We analyze the capacity of the legitimate channel after using successive interference cancellation (SIC), and demonstrate that the eavesdropping capacity has an upper bound. Furthermore, we prove that a positive secrecy rate can be achieved and the achievable secrecy rate can be maximized by allocating appropriate power to the private information and the artificial noise.
The problem of secure communication over a multiple access wiretap channel (MAWC) is studied. Here, two transmitters send confidential messages to a legitimate receiver while keeping a non-legitimate eavesdropper ignorant of them. In this paper, this communication scenario is studied for compound channels, for which it is only known to the users that the actual channel realization is fixed and belongs to a known set of possible channels. The criterion of strong secrecy is analyzed and its impact on the decoding performance of the eavesdropper is specified. It is shown that the average decoding error at the eavesdropper approaches one exponentially fast regardless of the applied decoding strategy. Furthermore, an achievable strong secrecy rate region is presented and a multi-letter outer bound is derived. Both together establish a multi-letter description of the strong secrecy capacity region.
It is commonly known that physical layer security is achieved with a trade-off in terms of the achievable rate. Hence, security constraints generate rate losses in wiretap channels. To mitigate such rate losses in multi-user channels, we propose a coding/decoding scheme for multi-user multiple access wiretap channel (MAC-WT), where previously transmitted messages are used as a secret key to enhance the secrecy rates of the transmitting users, until the usual Shannon capacity region of a multiple access channel (MAC) is achieved without the secrecy constraint. With this coding scheme, all messages transmitted in the recent past are secure with respect to all the information of the eavesdropper till now. To achieve this goal, we introduce secret key buffers at both the users and the legitimate receiver. Finally, we consider a fading MAC-WT and show that with this coding/decoding scheme, we can achieve the capacity region of a fading MAC channel (in the ergodic sense).