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Information Theory and Applications Workshop (ITA)

Resource allocation in fading multiple access wiretap channel via game theoretic learning

Shahid Mehraj Shah, Atmakuri Krishna Chaitanya, Vinod Sharma

Published Jan 1, 2016• 4 citations
Publisher

Abstract

In this paper we consider a K-user fading multiple access wiretap channel, where each user wants to transmit a message confidentially. There is a passive eavesdropper (Eve) at the receiving end. We are interested in allocating rates and powers to the users fairly and reliably without the eavesdropper being able to decode the message. Initially we assume that each user knows only its own channel gain to the receiver and to the eavesdropper. When any user transmits a message, the receiver send an ACK if the message is decoded correctly and confidentially, else it sends a NACK. We use Multiplicative Weight no-regret algorithm to obtain a coarse correlated equilibrium. Next we maximize the weighted sum of utility of all the users and obtain Pareto optimal points. Since not all Pareto points are fair, we also obtain Nash Bargaining (NB) solutions which ensure certain fairness to all the users. In the next part of the paper we make more realistic assumption that each user knows only its own channel gain, and is ignorant of the channel gain to Eve (only its distribution is known). We use secrecy outage as the metric at the receiver to decide weather the message is correctly decoded or not. We obtain a coarse correlated equilibrium, a Pareto point and a Nash bargaining solution.

DOI
10.1109/ita.2016.7888137

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In this paper we consider a K-user fading multiple access wiretap channel, where each user wants to transmit a message confidentially. There is a passive eavesdropper (Eve) at the receiving end. We are interested in allocating rates and powers to the users fairly and reliably without the eavesdropper being able to decode the message. Initially we assume that each user knows only its own channel gain to the receiver and to the eavesdropper. When any user transmits a message, the receiver send an ACK if the message is decoded correctly and confidentially, else it sends a NACK. We use Multiplicative Weight no-regret algorithm to obtain a coarse correlated equilibrium. Next we maximize the weighted sum of utility of all the users and obtain Pareto optimal points. Since not all Pareto points are fair, we also obtain Nash Bargaining (NB) solutions which ensure certain fairness to all the users. In the next part of the paper we make more realistic assumption that each user knows only its own channel gain, and is ignorant of the channel gain to Eve (only its distribution is known). We use secrecy outage as the metric at the receiver to decide weather the message is correctly decoded or not. We obtain a coarse correlated equilibrium, a Pareto point and a Nash bargaining solution.
A Gaussian multiple access wire-tap channel with confidential messages is studied, where multiple users attempt to transmit private messages to a legitimate receiver in the presence of an eavesdropper. While prior work focused on the case where the users were cooperative, we assume that each user is selfish and and so are modeled as playing a non-cooperative game. We assume all users send a superposition of two Gaussian codebooks: one for their confidential messages and one for “filling” the evesdropper's channel. For such a scheme, we give a characterization of the achievable rate region defined by Tekin and Yener using polymatroid properties. We then use this to find the Nash equilibrium region for this non-cooperative game. Furthermore, we give algorithms for finding the best and worst Nash equilibria for a given channel.
The fading cognitive multiple-access channel with confidential messages (CMAC-CM) is investigated, in which two users (users 1 and 2) wish to transmit a common message to a destination and user 1 also has a confidential message intended for the destination. The two users transmit to the destination via a multiple access channel, and user 2 also receives noisy channel outputs. Such channel outputs potentially help user 2 to learn user 1's confidential information (although they are not exploited by user 2 for channel transmission). Hence, user 1 views user 2 as an eavesdropper and wishes to keep its confidential message as secret as possible from user 2. A parallel CMAC-CM with independent subchannels is first studied. The secrecy capacity region of the parallel CMAC-CM is established, which yields the secrecy capacity regions of the parallel CMAC-CM with degraded subchannels and the parallel Gaussian CMAC-CM. These results are then applied to study the fading CMAC-CM, in which both the user-to-user channel and the user-to-destination channel are corrupted by multiplicative fading gain coefficients in addition to additive white Gaussian noise. The channel state information (CSI) is assumed to be known at both the users and the destination. With the CSI, users can dynamically change their transmission powers with the channel realization to achieve the optimal performance. The closed-form power allocation function that achieves every boundary point of the secrecy capacity region is derived.
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.
The fading cognitive multiple-access channel with confidential messages (CMAC-CM) is investigated, in which two users attempt to transmit common information to a destination and user 1 also has confidential information intended for the destination. User 1 views user 2 as an eavesdropper and wishes to keep its confidential information as secret as possible from user 2. The multiple-access channel (both the user-to-user channel and the user-to-destination channel) is corrupted by multiplicative fading gain coefficients in addition to additive white Gaussian noise. The channel state information (CSI) is assumed to be known at both the users and the destination. A parallel CMAC-CM with independent subchannels is first studied. The secrecy capacity region of the parallel CMAC-CM is established, which yields the secrecy capacity region of the parallel CMAC-CM with degraded subchannels. Next, the secrecy capacity region is established for the parallel Gaussian CMAC-CM, which is used to study the fading CMAC-CM. When both users know the CSI, they can dynamically change their transmission powers with the channel realization to achieve the optimal performance. The closed-form power allocation function that achieves every boundary point of the secrecy capacity region is derived.
Security constraint results in rate-loss in wiretap channels. In this paper we propose a coding scheme for two user Multiple Access Channel with Wiretap (MAC-WT), where previous messages are used as a key to enhance the secrecy rates of both the users until we achieve the usual capacity region of a Multiple Access Channel (MAC) without the wiretapper (Shannon capacity region). With this scheme only the message that is being transmitted is proved to be secure with respect to all the information that the adversary (eavesdropper) possesses. In the second part of the paper we improve the security constraint such that not only the message being transmitted is secure but all the messages transmitted in the immediate past are secure w.r.t. all the information o f the eavesdropper. To achieve this goal we introduce secret key buffers at both the users, as well as at the legitimate receiver (Bob). 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 (in ergodic sense).
For a communication where agent Alice aims at transmitting to agent Bob a message which must be kept secret to a third agent Eve, we consider terminals equipped with multiple antennas, obtaining the multiple-input multiple-output multiple-output-eavesdropper (MIMOME) channel. In this scenario, we assume that Alice knows the instantaneous channel conditions of the Alice-Bob channel before transmission, while knowing only the statistics of the Alice-Eve channel. For Rayleigh fading channels there is a non-zero probability that Eve gets a better channel than Bob, thus obtaining some information on the secret message (secrecy outage probability). We derive a closed form expression of the secrecy outage probability and then we consider the problem of allocating the power among the space streams, in order to maximize the total rate of the secret message under a constraint on the secrecy outage probability.