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arXiv:2107.14163 · IEEE Journal on Selected Areas in Communications

Achievable Regions and Precoder Designs for the Multiple Access Wiretap Channels With Confidential and Open Messages

Hao Xu, Tianyu Yang, Kai‐Kit Wong, Giuseppe Caire

Published Jan 27, 2022• 14 citations
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Abstract

This paper investigates the secrecy achievable region of multiple access wiretap (MAC-WT) channels where, besides confidential messages, the users have also open messages to transmit. All these messages are intended for the legitimate receiver (or Bob for brevity) but only the confidential messages need to be protected from the eavesdropper (Eve). We first consider a discrete memoryless (DM) MAC-WT channel where both Bob and Eve jointly decode their interested messages. By using random coding, we find an achievable rate region, within which perfect secrecy can be realized, i.e., all users can communicate with Bob with arbitrarily small probability of error, while the confidential information leaked to Eve tends to zero. Due to the high implementation complexity of joint decoding, we also consider the DM MAC-WT channel where Bob simply decodes messages independently while Eve still applies joint decoding. We then extend the results in the DM case to a Gaussian vector (GV) MAC-WT channel. Based on the information theoretic results, we further maximize the sum secrecy rate of the GV MAC-WT system by designing precoders for all users. Since the problems are non-convex, we provide iterative algorithms to obtain suboptimal solutions. Simulation results show that compared with existing schemes, secure communication can be greatly enhanced by the proposed algorithms, and in contrast to the works which only focus on the network secrecy performance, the system spectrum efficiency can be effectively improved since open messages can be simultaneously transmitted.

DOI
10.1109/jsac.2022.3145916

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This paper investigates the secrecy achievable region of multiple access wiretap (MAC-WT) channels where, besides confidential messages, the users have also open messages to transmit. All these messages are intended for the legitimate receiver (or Bob for brevity) but only the confidential messages need to be protected from the eavesdropper (Eve). We first consider a discrete memoryless (DM) MAC-WT channel where both Bob and Eve jointly decode their interested messages. By using random coding, we find an achievable rate region, within which perfect secrecy can be realized, i.e., all users can communicate with Bob with arbitrarily small probability of error, while the confidential information leaked to Eve tends to zero. Due to the high implementation complexity of joint decoding, we also consider the DM MAC-WT channel where Bob simply decodes messages independently while Eve still applies joint decoding. We then extend the results in the DM case to a Gaussian vector (GV) MAC-WT channel. Based on the information theoretic results, we further maximize the sum secrecy rate of the GV MAC-WT system by designing precoders for all users. Since the problems are non-convex, we provide iterative algorithms to obtain suboptimal solutions. Simulation results show that compared with existing schemes, secure communication can be greatly enhanced by the proposed algorithms, and in contrast to the works which only focus on the network secrecy performance, the system spectrum efficiency can be effectively improved since open messages can be simultaneously transmitted.
This paper investigates the capacity region of a discrete memoryless (DM) multiple access wiretap (MAC-WT) channel where, besides confidential messages, the users have also open messages to transmit. All these messages are intended for the legitimate receiver but only the confidential messages need to be protected from the eavesdropper. By using random coding, we find an achievable secrecy rate region, within which perfect secrecy can be realized, i.e., all users can communicate with the legitimate receiver with arbitrarily small probability of error, while the confidential information leaked to the eavesdropper tends to zero.
This paper investigates the achievable region and precoder design for multiple access wiretap (MAC-WT) channels, where each user transmits both secret and open (i.e., non-confidential) messages. All these messages are intended for the legitimate receiver (or Bob for brevity) and the eavesdropper (Eve) is interested only in the secret messages of all users. By allowing users with zero secret message rate to act as conventional MAC channel users with no wiretapping, we show that the achievable region of the discrete memoryless (DM) MAC-WT channel given in [1] can be enlarged. In [1], the achievability was proven by considering the two-user case, making it possible to prove a key auxiliary lemma by directly using the Fourier-Motzkin elimination procedure. However, this approach does not generalize to the case with any number of users. In this paper, we provide a new region that generally enlarges that in [1] and provide general achievability proof.
This paper investigates the achievable region of a K-user discrete memoryless (DM) multiple access wiretap (MAC-WT) channel, where each user transmits both secret and open (i.e., non-confidential) messages. All these messages are intended for the legitimate receiver (Bob), while the eavesdropper (Eve) is only interested in the secret messages. In the achievable coding strategy, the confidential information is protected by open messages and also by the introduction of auxiliary messages. When introducing an auxiliary message, one has to ensure that, on one hand, its rate is large enough for protecting the secret message from Eve and, on the other hand, the resulting sum rate (together with the secret and open message rate) does not exceed Bob’s decoding capability. This yields an inequality structure involving the rates of all users’ secret, open, and auxiliary messages. To obtain the rate region, the auxiliary message rates must be eliminated from the system of inequalities. A direct application of the Fourier-Motzkin elimination procedure is elusive since a) it requires that the number of users K is explicitly given, and b) even for small$K = 3, 4, \ldots $, the number of inequalities becomes extremely large. We prove the result for general K through the combined use of Fourier-Motzkin elimination procedure and mathematical induction. This paper adopts the strong secrecy metric, characterized by information leakage. To prove the achievability under this criterion, we analyze the resolvability region of a K-user DM-MAC channel (not necessarily a wiretap channel). In addition, we show that users with zero secrecy rate can play different roles and use different strategies in encoding their messages. These strategies yield non-redundant (i.e., not mutually dominating) rate inequalities. By considering all possible coding strategies, we provide a new achievable region for the considered channel, and show that it strictly improves those already known in the existing literature by considering a specific example.
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).
This paper investigates the information-theoretic secrecy problem for a K-user discrete memoryless (DM) multiple-access wiretap (MAC-WT) channel. Instead of using the weak secrecy criterion characterized by information leakage rate, we adopt the strong secrecy metric defined by information leakage to better protect the confidential information. We provide an achievable rate region and prove its achievability by providing a coding scheme and analyzing the output statistics in terms of (average) variational distance. We show that the rate region obtained in previous works on the subject is a special case of ours. We also show that the achievability proof in such works is incomplete, because it is assumed that certain inequalities hold while they may not in some cases. We solve this problem by constructing an inequality structure for the rates of all users’ secret and redundant messages, and analyzing the conditions required to maintain this structure.
This paper considers a Gaussian multi-input multi-output (MIMO) multiple access wiretap (MAC-WT) channel, where an eavesdropper (Eve) wants to extract the confidential information of all users. Assuming that both the legitimate receiver and Eve jointly decode their interested messages, we aim to maximize the sum secrecy rate of the system by precoder design. Although this problem could be solved by first using the iterative majorization minimization (MM) based algorithm to get a sequence of convex log-determinant optimization subproblems and then using some general tools, e.g., the interior point method, to deal with each subproblem, this strategy involves quite high computational complexity. Therefore, we propose a simultaneous diagonalization based low-complexity (SDLC) method to maximize the secrecy rate of a simple one-user wiretap channel, and then use this method to iteratively optimize the covariance matrix of each user. Simulation results show that in contrast to the existing approaches, the SDLC scheme achieves similar secrecy performance but requires much lower complexity.