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arXiv:1807.06448 · EURASIP Journal on Wireless Communications and Networking

Resource allocation for secure Gaussian parallel relay channels with finite-length coding and discrete constellations

Linda Senigagliesi, Marco Baldi, Stefano Tomasin

Published Dec 1, 2019• 4 citations
arXivHTMLPDF

Abstract

Abstract We investigate the transmission of a secret message from Alice to Bob in the presence of an eavesdropper (Eve) and many of decode-and-forward relay nodes. Each link comprises a set of parallel channels, modeling for example an orthogonal frequency division multiplexing transmission. We consider the impact of efficient implementations, including discrete constellations and finite-length coding, defining an achievable secrecy rate under a constraint on the equivocation rate at Eve. Then, we propose a power and channel allocation algorithm that maximizes the achievable secrecy rate by resorting to two coupled Gale-Shapley algorithms for stable matching problem. We consider the scenarios of both full and partial channel state information at Alice. In the latter case, we only guarantee anoutagesecrecy rate, i.e., the rate of a message that remains secret with a given probability. Numerical results are provided for Rayleigh fading channels in terms of average outage secrecy rate, showing that practical schemes achieve a performance quite close to that of ideal ones.

DOI
10.1186/s13638-019-1603-1

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arXiv:1011.2115•IEEE Transactions on Information Forensics and Security•Jan 31, 2012•33 citations
Abstract We investigate the transmission of a secret message from Alice to Bob in the presence of an eavesdropper (Eve) and many of decode-and-forward relay nodes. Each link comprises a set of parallel channels, modeling for example an orthogonal frequency division multiplexing transmission. We consider the impact of efficient implementations, including discrete constellations and finite-length coding, defining an achievable secrecy rate under a constraint on the equivocation rate at Eve. Then, we propose a power and channel allocation algorithm that maximizes the achievable secrecy rate by resorting to two coupled Gale-Shapley algorithms for stable matching problem. We consider the scenarios of both full and partial channel state information at Alice. In the latter case, we only guarantee anoutagesecrecy rate, i.e., the rate of a message that remains secret with a given probability. Numerical results are provided for Rayleigh fading channels in terms of average outage secrecy rate, showing that practical schemes achieve a performance quite close to that of ideal ones.
Alice aims at transmitting Bob a message to be kept secret from Eve, with the assistance of relays operating in a decode-and-forward fashion. Each link between node couples comprises a set of parallel channels. Both Alice and relays knows all legitimate channel gains, while they only have a statistical knowledge of the channels to Eve. By fixing a secrecy outage probability per channel, we optimize power and rate of the messages sent by Alice to the relays (phase one) and from the relays to Bob (phase two), in order to maximize the achievable end-to-end outage secrecy rate. Since the phase-one rate cannot exceed the phase-two rate for each relay, the allocations in the two phases are tightly coupled, making the optimization quite challenging. Therefore we propose a solution based on the Gale-Shapley approach to the stable matching problem. The algorithm iterates between two stages, one in which each relay proposes Bob a secret rate on a specific channel, and another in which Bob discards the offer providing the lowest rate. The process is repeated until a single offer is available on each channel. Offers by the relays are based on (and in turns influence) the resource allocation by Alice with respect to her transmission to the relays. Numerical results are provided, showing the merit of the proposed solution with respect to existing approaches.
A transmission between two agents, Alice and Bob, over a set of parallel sub-channels is overheard by a third agent Eve, through a second set of parallel sub-channels. All subchannels are flat with random and independent gains and additive white Gaussian noise (AWGN). Alice splits the total amount of available power among the sub-channels, with the purpose of maximizing the communication rate to Bob, under reliability and secrecy constraints. To this end, two schemes are considered. In one case the secret message is encoded with a single wiretap code and then split among the sub-channels. In the latter case the secret message is first split into a number of sub-messages, each separately encoded and transmitted on a different sub-channel. The achievable secrecy rates under a constraint on the secrecy outage probability (SOP) are derived and closed form expressions for Rayleigh fading sub-channels are obtained. In order to limit the complexity of resources optimization (power and rates) we also consider suboptimal solutions based on the selection of active sub-channels over which power is split either equally or according to a waterfilling algorithm with respect to the Alice-Bob channel.
We consider a four terminal parallel relay-eavesdropper channel which consists of multiple independent relay-eavesdropper channels as subchannels. For the discrete memoryless case, we establish inner and outer bounds on the rate equivocation region. For each subchannel, secure transmission is obtained through one of two coding schemes at the relay: decoding-and-forwarding the source message or confusing the eavesdropper through noise injection. The inner bound allows relay mode selection. We then apply our results to study the fading Gaussian relay-eavesdropper channel. In this case, we focus on perfectly secure transmission. We establish a lower bound on the perfect secrecy rate. Furthermore, considering individual sum power constraints at source and relay, we study power adjustment among the independent subchannels. We illustrate the results through some numerical examples.
We consider a system where an agent (Alice) aims at transmitting a message to a second agent (Bob) over a set of parallel channels, while keeping it secret from a third agent (Eve) by using physical layer security techniques. We assume that Alice perfectly knows the set of channels with respect to Bob, but she has only a statistical knowledge of the channels with respect to Eve. We derive bounds on the achievable outage secrecy rates, by considering coding either within each channel or across all parallel channels. Transmit power is adapted to the channel conditions, with a constraint on the average power over the whole transmission. We also focus on the maximum cumulative outage secrecy rate that can be achieved. Moreover, in order to assess the performance in a real life scenario, we consider the use of practical error correcting codes. We extend the definitions of security gap and equivocation rate, previously applied to the single additive white Gaussian noise channel, to Rayleigh distributed parallel channels, on the basis of the error rate targets and the outage probability. Bounds on these metrics are also derived, considering the statistics of the parallel channels. Numerical results are provided, that confirm the feasibility of the considered physical layer security techniques.
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.
We investigate the problem of secure communication over parallel relay channel in the presence of a passive eavesdropper. We consider a four-terminal relay-eavesdropper channel which consists of multiple relay-eavesdropper channels as subchannels. For the discrete memoryless model, we establish outer and inner bounds on the rate-equivocation region. The inner bound allows mode selection at the relay. For each subchannel, secure transmission is obtained through one of two coding schemes at the relay: decoding-and-forwarding the source message or confusing the eavesdropper through noise injection. For the Gaussian memoryless channel, we establish lower and upper bounds on the perfect secrecy rate. Furthermore, we study a special case in which the relay does not hear the source and show that under certain conditions the lower and upper bounds coincide. The results established for the parallel Gaussian relay-eavesdropper channel are then applied to study the fading relay-eavesdropper channel. Analytical results are illustrated through some numerical examples.