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IEEE Transactions on Information Theory

An achievable region for the Gaussian wiretap channel with side information

C. Mitrpant, A. J. Han Vinck, Yuan Luo

Published Apr 28, 2006• 123 citations
Publisher

Abstract

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.

DOI
10.1109/tit.2006.872968

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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.
This paper extends the Gaussian wiretap channel (GWC) model introduced by Leung-Yan-Cheong and Hellman (1978) to the Gaussian wiretap channel with side information (GWCSI) by adding an additive white Gaussian interference in the main channel, which is available to the encoder in advance. It can also be looked at as an extension of the dirty-paper channel (DPC) introduced by Costa (1983). We propose a coding strategy achieving perfect secrecy for the extended channel, called Gaussian wiretap channel with side information. The corresponding achievable rates with asymptotic perfect secrecy are obtained and compared to known upper and lower bounds.
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.
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
Wyner has shown in his seminal paper on (discrete memoryless) wiretap channels that if the channel between the sender and an eavesdropper is a degraded version of the channel between the sender and the legitimate receiver, then the sender can reliably and securely transmit a message to the receiver, while the eavesdropper obtains absolutely no information about the message. Later, Leung-Yan-Cheong and Hellman extended Wyner's result to the case where the noise is white Gaussian. In this paper we extend the white Gaussian wiretap channel to the colored Gaussian case and show the finite block length secrecy capacity of colored Gaussian wiretap channels. We also show the asymptotic secrecy capacity of a specific colored Gaussian wiretap channel for which optimal power allocation can be found by a water-filling procedure.
Wyner has shown in his seminal paper on (discrete memoryless) wiretap channels that if the channel between the sender and an eavesdropper is a degraded version of the channel between the sender and the legitimate receiver, then the sender can reliably and securely transmit a message to the receiver, while the eavesdropper obtains absolutely no information about the message. Later, Leung-Yan-Cheong and Hellman extended Wyner's result to the case where the noise is white Gaussian. In this paper we extend the white Gaussian wiretap channel to the colored Gaussian case and show the finite block length secrecy capacity of colored Gaussian wiretap channels. We also show an asymptotic lower bound on the secrecy capacity of a specific colored Gaussian wiretap channel for which optimum power allocation can be found by water filling.