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IEEE International Conference on Information Theory and Information Security

Deterministic multiple access wiretap channel

Vahid Jahandideh, Somayeh Salimi, Mahmoud Salmasizadeh

Published Dec 1, 2010• 2 citations
Publisher

Abstract

Two-user Multiple Access Channel with a Wire-Tapper (MAC-WT) is considered. A general outer bound for the secrecy capacity region is given. Also, we have defined the Deterministic MAC-WT, where the channel input of each user is a deterministic function of the channel output and the channel input of the other user. For this network single-letter inner and outer bounds for the secrecy capacity region are given. Furthermore, it is shown that in the Deterministic MAC-WT, if the wiretapper channel is a degraded version of the main channel, inner and outer bounds meet and the secrecy capacity region is characterized.

DOI
10.1109/icitis.2010.5689656

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Two-user Multiple Access Channel with a Wire-Tapper (MAC-WT) is considered. A general outer bound for the secrecy capacity region is given. Also, we have defined the Deterministic MAC-WT, where the channel input of each user is a deterministic function of the channel output and the channel input of the other user. For this network single-letter inner and outer bounds for the secrecy capacity region are given. Furthermore, it is shown that in the Deterministic MAC-WT, if the wiretapper channel is a degraded version of the main channel, inner and outer bounds meet and the secrecy capacity region is characterized.
We develop an outer bound for the secrecy capacity region of a class of multiple access wiretap channels (MAC-WT). In this class, which we call the weak eavesdropper class, each user's link to the legitimate receiver is stronger than its link to the eavesdropper. Our outer bound partially matches the achievable region in an n-letter form. In addition, a looser version of our outer bound provides close approximations to the capacity region of the Gaussian MAC-WT channel. In particular, we prove that our outer bound is within 0.5 bits/channel use of the achievable rates along the individual rates for all weak eavesdropper Gaussian MAC-WT, and within 0.5 bits/channel use in all directions for certain weak eavesdropper Gaussian MAC-WT channels.
Several security models of multiple-access channel (MAC) are investigated. First, we study the degraded MAC with confidential messages, where two users transmit their confidential messages (no common message) to a destination, and each user obtains a degraded version of the output of the MAC. Each user views the other user as a eavesdropper, and wishes to keep its confidential message as secret as possible from the other user. Measuring each user's uncertainty about the other user's confidential message by equivocation, the inner and outer bounds on the capacity-equivocation region for this model have been provided. The result is further explained via the binary and Gaussian examples. Second, the discrete memoryless multiple-access wiretap channel (MAC-WT) is studied, where two users transmit their corresponding confidential messages (no common message) to a legitimate receiver, while an additional wiretapper wishes to obtain the messages via a wiretap channel. This new model is considered into two cases: the general MAC-WT with cooperative encoders, and the degraded MAC-WT with non-cooperative encoders. The capacity-equivocation region is totally determined for the cooperative case, and inner and outer bounds on the capacity-equivocation region are provided for the non-cooperative case. For both cases, the results are further explained via the binary examples.
In this paper, some new results on the multiple-access wiretap channel (MAC-WT) are provided. Specifically, first, we investigate the degraded MAC-WT, where two users transmit their corresponding confidential messages (no common message) to a legitimate receiver via a multiple-access channel (MAC), while a wiretapper wishes to obtain the messages via a physically degraded wiretap channel. The secrecy capacity region of this model is determined for both the discrete memoryless and Gaussian cases. For the Gaussian case, we find that this secrecy capacity region is exactly the same as the achievable secrecy rate region provided by Tekin and Yener, i.e., Tekin–Yener’s achievable region is exactly the secrecy capacity region of the degraded Gaussian MAC-WT. Second, we study a special Gaussian MAC-WT, and find the power control for two kinds of optimal points (max-min point and single user point) on the secrecy rate region of this special Gaussian model.
In this paper, the discrete memoryless multiple-access wiretap channel (MAC-WT) with non-cooperative encoders is studied, where two users (cooperation between the users is not allowed) transmit their corresponding confidential messages (no common message) to a legitimate receiver, while an additional wiretapper wishes to obtain the messages via a wiretap channel. The inner and outer bounds on the capacity-equivocation region are provided forthis new model, and the result is further explained via a binary example.
In this paper, we study the problem of secret communication over a multiple-access channel with a common message. Here, we assume that two transmitters have confidential messages, which must be kept secret from the wiretapper (the second receiver), and both of them have access to a common message which can be decoded by the two receivers. We call this setting as Multiple-Access Wiretap Channel with Common message (MAWC-CM). For this setting, we derive general inner and outer bounds on the secrecy capacity region for the discrete memoryless case and show that these bounds meet each other for a special case called the switch channel. As well, for a Gaussian version of MAWC-CM, we derive inner and outer bounds on the secrecy capacity region. Providing numerical results for the Gaussian case, we illustrate the comparison between the derived achievable rate region and the outer bound for the considered model and the capacity region of compound multiple access channel.
We consider the Gaussian multiple access wire-tap channel (GMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed wire-tapper who receives a degraded version of the signal at the receiver. We define a suitable security measure for this multi-access environment. We derive an outer bound for the rate region such that secrecy to some pre-determined degree can be maintained. We also find, using Gaussian codebooks, an achievable such secrecy region. Gaussian codewords are shown to achieve the sum capacity outer bound, and the achievable region coincides with the outer bound for Gaussian codewords, giving the capacity region when inputs are constrained to be Gaussian. We present numerical results showing the new rate region and compare it with that of the Gaussian multiple-access channel (GMAC) with no secrecy constraints