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IEEE Transactions on Information Theory

Wiretap Channel With Side Information

Yanling Chen, A. J. Han Vinck

Published Jan 1, 2008• 142 citations
Publisher

Abstract

This correspondence gives an achievable rate equivocation region for the discrete memoryless wiretap channel with side information. We extend our results to the Gaussian case. The main contribution of this correspondence is that, for the Gaussian wiretap channel, the side information helps to get a largersecrecy capacityand a largerrate equivocationregion.

DOI
10.1109/tit.2007.911157

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Wiretap channel with side information

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This paper gives a rate equivocation achievable region for the discrete memoryless wiretap channel with side information. The secrecy capacities in some special cases are also determined. We extend our result to the Gaussian case. It is very interesting to find that, for the wiretap channel, unlike the dirty paper channel, the side information helps to get larger secrecy capacity. Moreover, the rate equivocation region is also larger than that of the Gaussian wiretap channel where the side information is absent

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We have proved a coding theorem for the discrete memoryless wiretap channel with side information. Extending the result to the Gaussian case, an achievable rate equivocation region is given by using a strategy similar to Costa's method on dirty paper channel. In this paper, we propose an extended region for the Gaussian wiretap channel with side information. On the other hand, it is well known that, to yield the optimal rate, Costa only considers the situation when the codeword sent by the encoder is independent of side information. Here we will show that, for the wiretap channel, to yield higher rate with the same equivocation, it might be a better choice to send a codeword dependent of side information in some cases.

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This paper introduces a new applicable Gaussian wiretap channel with side information. In this channel, the state of the channel to the wiretapper is separated from the main channel's one. It means that the legitimate receiver and the wiretapper are listening to the transmitted signal through the different channels with different channel states which may have some correlation to each other. The state of the main channel, is assumed to be known at the transmitter, helps the sender to encrypt its messages. The achievable equivocation-rate region for this model is drived in the Gaussian case and the results are reduced to the previous works as special cases.

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In this correspondence, we extend the Gaussian wiretap channel model introduced by Leung-Yan-Cheong and Hellman to the Gaussian wiretap channel with side information by introducing additive white Gaussian interference in the main channel, which is available to the encoder in advance. This model is also an extension of the dirty-paper channel introduced by Costa since its main channel is the dirty-paper channel. A perfect-secrecy-achieving coding strategy for the model is proposed. It is used to derive achievable rates with asymptotic perfect secrecy and an achievable rate-equivocation region. The achievable rates with asymptotic perfect-secrecy are then compared to upper and lower bounds. The comparison indicates that the proposed coding strategy is optimal in some cases.

IEEE Transactions on Information Theory•Apr 28, 2006•123 citations
This correspondence gives an achievable rate equivocation region for the discrete memoryless wiretap channel with side information. We extend our results to the Gaussian case. The main contribution of this correspondence is that, for the Gaussian wiretap channel, the side information helps to get a largersecrecy capacityand a largerrate equivocationregion.
This paper gives a rate equivocation achievable region for the discrete memoryless wiretap channel with side information. The secrecy capacities in some special cases are also determined. We extend our result to the Gaussian case. It is very interesting to find that, for the wiretap channel, unlike the dirty paper channel, the side information helps to get larger secrecy capacity. Moreover, the rate equivocation region is also larger than that of the Gaussian wiretap channel where the side information is absent
We have proved a coding theorem for the discrete memoryless wiretap channel with side information. Extending the result to the Gaussian case, an achievable rate equivocation region is given by using a strategy similar to Costa's method on dirty paper channel. In this paper, we propose an extended region for the Gaussian wiretap channel with side information. On the other hand, it is well known that, to yield the optimal rate, Costa only considers the situation when the codeword sent by the encoder is independent of side information. Here we will show that, for the wiretap channel, to yield higher rate with the same equivocation, it might be a better choice to send a codeword dependent of side information in some cases.
In this paper, the model of wiretap channel has been reconsidered for the case that the main channel is controlled by channel state information (side information), and it is available at the transmitter in a noncausal manner (termed here noncausal side information) or causal manner (termed here causal side information). Inner and outer bounds are derived on the capacity-equivocation regions for the noncausal and causal manners, and the secrecy capacities for both manners are described and bounded, which provide the best transmission rate with perfect secrecy. Moreover, for the case that the side information is available at the transmitter in a memoryless manner (termed here memoryless side information), both the capacity-equivocation region and the secrecy capacity are determined. The results of this paper extend the previous work on wiretap channel with noncausal side information by providing an outer bound on the capacity-equivocation region. In addition, we find that the memoryless side information can not help to obtain the same secrecy capacity as that of the causal case, and this is different from the well known fact that the memoryless manner can achieve the capacity of the channel with causal side information.
This paper introduces a new applicable Gaussian wiretap channel with side information. In this channel, the state of the channel to the wiretapper is separated from the main channel's one. It means that the legitimate receiver and the wiretapper are listening to the transmitted signal through the different channels with different channel states which may have some correlation to each other. The state of the main channel, is assumed to be known at the transmitter, helps the sender to encrypt its messages. The achievable equivocation-rate region for this model is drived in the Gaussian case and the results are reduced to the previous works as special cases.
A new applicable wiretap channel with separated side information is considered here which consist of a sender, a legitimate receiver and a wiretapper. In the considered scenario, the links from the transmitter to the legitimate receiver and the eavesdropper experience different conditions or channel states. So, the legitimate receiver and the wiretapper listen to the transmitted signal through the channels with different channel states which may have some correlation to each other. It is assumed that the transmitter knows the state of the main channel non-causally and uses this knowledge to encode its message. The state of the wiretap channel is not known anywhere. An achievable equivocation rate region is derived for this model and is compared to the existing works. In some special cases, the results are extended to the Gaussian wiretap channel.
In this correspondence, we extend the Gaussian wiretap channel model introduced by Leung-Yan-Cheong and Hellman to the Gaussian wiretap channel with side information by introducing additive white Gaussian interference in the main channel, which is available to the encoder in advance. This model is also an extension of the dirty-paper channel introduced by Costa since its main channel is the dirty-paper channel. A perfect-secrecy-achieving coding strategy for the model is proposed. It is used to derive achievable rates with asymptotic perfect secrecy and an achievable rate-equivocation region. The achievable rates with asymptotic perfect-secrecy are then compared to upper and lower bounds. The comparison indicates that the proposed coding strategy is optimal in some cases.