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arXiv:1204.0173

On The Achievable Rate Region of a New Wiretap Channel With Side Information

Hamid G. Bafghi, Babak Seyfe, Mahtab Mirmohseni, Mohammad Reza Aref

Published Apr 1, 2012• 3 citations
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Abstract

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.

DOI
10.48550/arxiv.1204.0173

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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.
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.
We consider the problem of secure communication over a (not necessarily degraded) wiretap channel with two-sided channel state information available at the transmitter and the main receiver, respectively. Using the time sharing argument [1], we establish an achievable rate equivocation region for this channel model. The obtained achievable region generalizes several existing results in the literature. More importantly, through examining various cases with different knowledge of channel state information, we provide a systematic study of the impact of channel state information on secure communication.
In this paper, we investigate the model of wiretap channel with action-dependent channel state information. Given the message to be communicated, the transmitter chooses an action sequence that affects the formation of the channel states, and then generates the channel input sequence based on the state sequence and the message. The main channel and the wiretap channel are two discrete memoryless channels (DMCs), and they are connected with the legitimate receiver and the wiretapper, respectively. Moreover, the transition probability distribution of the main channel depends on the channel state. Measuring wiretapper’s uncertainty about the message by equivocation, inner and outer bounds on the capacity-equivocation region are provided both for the case where the channel inputs are allowed to depend non-causally on the state sequence and the case where they are restricted to causal dependence. Furthermore, the secrecy capacities for both cases are bounded, which provide the best transmission rate with perfect secrecy. The result is further explained via a binary example.
The concept of the wiretap channel was first proposed by Wyner. He considered the case in which data is to be transmitted reliably over a discrete memoryless main channel to a legitimate receiver. The wiretapper views the output of the main channel through another discrete memoryless channel. It is assumed that the wiretapper knows the code being used and his only handicap is the additional noise in his signal. The problem is to maximize the transmission rate R to the legitimate receiver and the equivocation d of the wiretapper. In this dissertation, the additive white Gaussian noise wiretap channel is introduced and the set of all achievable (R,d) pairs is determined explicitly through the use of certain special properties of the Gaussian channel. Some useful characterizations of a special class of wiretap channels are also explored. A model of the wiretap channel with feedback is proposed. It turns out that with the introduction of feedback, even when the main channel is inferior to the wiretapper's channel, it is still possible to reliably communicate with the legitimate receiver in complete secrecy. The binary erasure wiretap channel with feedback is examined and inner and outer bounds on the achievable (R,d) region are given. Finally, a scheme for enlarging the capacity region of multiple-access channels using feedback is analyzed. It is shown that conditions under which an enlargement is possible are fairly weak, indicating that feedback can almost increase the capacity region. (Author)
The problem of secure lossy source-channel wiretapping with arbitrarily correlated side informations at both receivers is investigated. This scenario consists of an encoder (referred to as Alice) that wishes to compress a source and send it through a noisy channel to a legitimate receiver (referred to as Bob). In this context, Alice must simultaneously satisfy the desired requirements on the distortion level at Bob, and the equivocation rate at the eavesdropper (referred to as Eve). This setting can be seen as a generalization of the conventional problems of secure source coding with side information at the decoders, and the wiretap channel. Inner and outer bounds on the rate-distortion-equivocation region for the case of arbitrary channels and side informations are derived. In some special cases of interest, it is shown that separation holds. By means of an appropriate coding, the presence of any statistical difference among the side informations, the channel noises, and the distortion at Bob can be fully exploited in terms of secrecy.
The communication scenario under consideration in this paper corresponds to a multiuser channel with side information and consists of a broadcast channel with two legitimate receivers and an eavesdropper. Mainly, the results obtained are as follows. First, an achievable rate region is provided for the (general) case of discrete-input discrete-output channels, generalizing existing results. Second, the obtained theorem is used to derive achievable transmission rates for two practical cases of Gaussian channels. It is shown that known perturbations can enlarge the rate region of broadcast wiretap channels with side information and having side information at the decoder as well can increase the secrecy rate of channels with side information. Third, we establish for the first time an explicit connection between multiuser channels and observation structures in dynamic games. In this respect, we show how to exploit the proved achievability theorem (discrete case) to derive a communication-compatible upper bound on the minmax level of a player.