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On the rate-equivocation region of parallel relay eavesdropper channels

Zohaib Hassan Awan, Abdellatif Zaidi, Luc Vandendorpe, Future Network and Mobile Summit

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

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.

Related papers

On secure transmission over parallel relay eavesdropper channel

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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.

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2 Secure Communication over Parallel Relay Channel

Zohaib Hassan Awan, Abdellatif Zaidi, Luc Vandendorpe

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.

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A new achievable rate-equivocation region for the relay-eavesdropper channel

Amir Sonee, Somayeh Salimi

In this paper, we propose an information-theoretic scheme which achieves a new rate-equivocation region for the four-terminal relay-eavesdropper channel. The coding scheme used to achieve this region is a combination of the partial decode and forward, compress and forward and noise forwarding strategies. In this strategy the relay cooperates with the source to have both a reliable and secure communication by decoding some part of the source message, compressing the received signal and also sending the codewords independent of the transmitted message. Using this scheme we can obtain the perfect secrecy capacity of the semi- deterministic and deterministic relay channels.

Iranian Conference on Electrical Engineering•May 1, 2010•3 citations

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

Linda Senigagliesi, Marco Baldi, Stefano Tomasin

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.

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Relay Broadcast Channels with Confidential Messages.

Bin Dai, Zheng Ma

We investigate the effects of an additional relay node on the secrecy of broadcast channels by considering the model of relay broadcast channels with confidential messages. We show that this additional relay node can increase the achievable secrecy rate region of the broadcast channels with confidential messages. More specifically, first, we investigate the discrete memoryless relay broadcast channels with two confidential messages and one common message. Three inner bounds (with respect to decode-forward, generalized noise-forward and compress-forward strategies) and an outer bound on the capacity-equivocation region are provided. Removing the secrecy constraint, this outer bound can also be served as a new outer bound for the relay broadcast channel. Second, we investigate the discrete memoryless relay broadcast channels with two confidential messages (no common message). Inner and outer bounds on the capacity-equivocation region are provided. Then, we study the Gaussian case, and find that with the help of the relay node, the achievable secrecy rate region of the Gaussian broadcast channels with two confidential messages is enhanced. Finally, we investigate the discrete memoryless relay broadcast channels with one confidential message and one common message. This work generalizes Lai-Gamals work on the relay-eavesdropper channel by considering an additional common message for both the legitimate receiver and the eavesdropper. Inner and outer bounds on the capacity-equivocation region are provided, and the results are further explained via a Gaussian example. Compared with Csiszár-Körner’s work on broadcast channels with confidential messages (BCC), we find that with the help of the relay node, the secrecy capacity region of the Gaussian BCC is enhanced.

•Dec 24, 2013•0 citations
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 study 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 the 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. For the Gaussian model we establish lower and upper bounds on the perfect secrecy rate. We show that the bounds meet in some special cases, including when the relay does not hear the source. We illustrate the analytical results through some numerical examples.
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.
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.
In this paper, we propose an information-theoretic scheme which achieves a new rate-equivocation region for the four-terminal relay-eavesdropper channel. The coding scheme used to achieve this region is a combination of the partial decode and forward, compress and forward and noise forwarding strategies. In this strategy the relay cooperates with the source to have both a reliable and secure communication by decoding some part of the source message, compressing the received signal and also sending the codewords independent of the transmitted message. Using this scheme we can obtain the perfect secrecy capacity of the semi- deterministic and deterministic relay channels.
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.
We investigate the effects of an additional relay node on the secrecy of broadcast channels by considering the model of relay broadcast channels with confidential messages. We show that this additional relay node can increase the achievable secrecy rate region of the broadcast channels with confidential messages. More specifically, first, we investigate the discrete memoryless relay broadcast channels with two confidential messages and one common message. Three inner bounds (with respect to decode-forward, generalized noise-forward and compress-forward strategies) and an outer bound on the capacity-equivocation region are provided. Removing the secrecy constraint, this outer bound can also be served as a new outer bound for the relay broadcast channel. Second, we investigate the discrete memoryless relay broadcast channels with two confidential messages (no common message). Inner and outer bounds on the capacity-equivocation region are provided. Then, we study the Gaussian case, and find that with the help of the relay node, the achievable secrecy rate region of the Gaussian broadcast channels with two confidential messages is enhanced. Finally, we investigate the discrete memoryless relay broadcast channels with one confidential message and one common message. This work generalizes Lai-Gamals work on the relay-eavesdropper channel by considering an additional common message for both the legitimate receiver and the eavesdropper. Inner and outer bounds on the capacity-equivocation region are provided, and the results are further explained via a Gaussian example. Compared with Csiszár-Körner’s work on broadcast channels with confidential messages (BCC), we find that with the help of the relay node, the secrecy capacity region of the Gaussian BCC is enhanced.