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arXiv:1605.05693

Capacity of the State-Dependent Wiretap Channel: Secure Writing on Dirty Paper

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

Published May 18, 2016• 2 citations
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Abstract

In this paper we consider the State-Dependent Wiretap Channel (SD-WC). As the main idea, we model the SD-WC as a Cognitive Interference Channel (CIC), in which the primary receiver acts as an eavesdropper for the cognitive transmitter's message. By this point of view, the Channel State Information (CSI) in SD-WC plays the role of the primary user's message in CIC which can be decoded at the eavesdropper. This idea enables us to use the main achievability approaches of CIC, i.~e., Gel'fand-Pinsker Coding (GPC) and Superposition Coding (SPC), to find new achievable equivocation-rates for the SD-WC. We show that these approaches meet the capacity under some constraints on the rate of the channel state. Similar to the dirty paper channel, extending the results to the Gaussian case shows that the GPC lead to the capacity of the Gaussian SD-WC which is equal to the capacity of the wiretap channel without channel state. Hence, we achieve the capacity of the Gaussian SD-WC using the dirty paper technique. Moreover, our proposed approaches provide the capacity of the Binary SD-WC. It is shown that the capacity of the Binary SD-WC is equal to the capacity of the Binary wiretap channel without channel state.

DOI
10.48550/arxiv.1605.05693

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In this paper we consider the State-Dependent Wiretap Channel (SD-WC). As the main idea, we model the SD-WC as a Cognitive Interference Channel (CIC), in which the primary receiver acts as an eavesdropper for the cognitive transmitter's message. By this point of view, the Channel State Information (CSI) in SD-WC plays the role of the primary user's message in CIC which can be decoded at the eavesdropper. This idea enables us to use the main achievability approaches of CIC, i.~e., Gel'fand-Pinsker Coding (GPC) and Superposition Coding (SPC), to find new achievable equivocation-rates for the SD-WC. We show that these approaches meet the capacity under some constraints on the rate of the channel state. Similar to the dirty paper channel, extending the results to the Gaussian case shows that the GPC lead to the capacity of the Gaussian SD-WC which is equal to the capacity of the wiretap channel without channel state. Hence, we achieve the capacity of the Gaussian SD-WC using the dirty paper technique. Moreover, our proposed approaches provide the capacity of the Binary SD-WC. It is shown that the capacity of the Binary SD-WC is equal to the capacity of the Binary wiretap channel without channel state.
We study the state-dependent (SD) wiretap channel (WTC) with non-causal channel state information (CSI) at the encoder. This model subsumes all other instances of CSI availability as special cases, and calls for an efficient utilization of the state sequence both for reliability and security purposes. A lower bound on the secrecy-capacity, that improves upon the previously best known result by Chen and Han Vinck, is derived based on a novel superposition coding scheme. The improvement over the Chen and Han Vinck result is strict for some SD-WTCs. Specializing the lower bound to the case where CSI is also available to the decoder reveals that it is at least as good as the achievable formula by Chia and El-Gamal, which is already known to outperform the adaptation of the Chen and Han Vinck code to the encoder and decoder CSI scenario. The results are derived under the strict semantic-security metric that requires negligible information leakage for all message distributions. The proof of achievability relies on a stronger version of the soft-covering lemma for superposition codes.
The dirty paper wiretap channel, also referred to as the Gaussian wiretap channel with noncausal channel state at the transmitter, plays an important role in wireless physical layer security. In this paper, the dirty paper wiretap channel is revisited by considering actions on the channel state, i.e., the transmitter generates an action sequence that affects the formation of the channel state. Lower and upper bounds on the secrecy capacity of this model are proposed, and numerical results indicate that the actions on the state help to increase the achievable secrecy rate of the dirty paper wiretap channel. The study of this paper offers a new option for enhancing the secrecy rates of the state-dependent wiretap channel models.
Like the conventional two-user interference channel, the cognitive interference channel consists of two transmitters whose signals interfere at two receivers. It is assumed that there is a common message (message 1) known to both transmitters, and an additional independent message (message 2) known only to the cognitive transmitter (transmitter 2). The cognitive receiver (receiver 2) needs to decode messages 1 and 2, while the non cognitive receiver (receiver 1) should decode only message 1. Furthermore, message 2 is assumed to be a confidential message which needs to be kept as secret as possible from receiver 1, which is viewed as an eavesdropper with regard to message 2. The level of secrecy is measured by the equivocation rate. In this paper, a single-letter expression for the capacity-equivocation region of the discrete memoryless cognitive interference channel is obtained. The capacity-equivocation region for the Gaussian cognitive interference channel is also obtained explicitly. Moreover, particularizing the capacity-equivocation region to the case without a secrecy constraint, the capacity region for the two-user cognitive interference channel is obtained, by providing a converse theorem.
We investigate the (forward) key capacity of a Gaussian state-dependent wiretap channel (G-SWC) paralleled with a public channel having capacity Cpϵ [0, ∞). This model consists of a sender, a main receiver, and a wiretapper. The channel state information (CSI) is an additive white Gaussian interference (AWGI) which is non-causally known at the sender. A lower bound (LB) on the key capacity is achieved by using a generalized version of the dirty paper coding (DPC) in which the transmitted signal is correlated with the interference. The correlation coefficient is to be determined by Cp. The achievable scheme is asymptotically optimum as Cp→ ∞. This optimum key capacity is also asymptotically achievable for any Cp≥ 0 in high signal to interference ratio (SIR) regime. In this regime, the public channel has negligible contribution in key generation. Generally, the CSI enhances the key capacity such that it exceeds the main channel capacity of the G-SWC in low SIR regime.
In this paper, the secrecy problem in the state dependent causal cognitive interference channel is studied. The channel state is non-causally known at the cognitive encoder. The message of the cognitive encoder must be kept secret from the primary receiver. We use a coding scheme which is a combination of compress-and-forward strategy with Marton coding, Gel’fand-Pinsker coding and Wyner’s wiretap coding at the cognitive encoder. We use rate splitting for messages at both transmitters. Furthermore, the cognitive user compresses its channel observation using Wyner-Ziv coding and splits the index of its compressed signal. By using this scheme we derive an achievable secrecy rate region for this channel and extend the results to the Gaussian case and provide some numerical results.
We revisit a channel coding problem where the channel state information (CSI) is rate-limited (or coded) and available to the channel encoder. A wiretapper is added into this model, and the confidential message is intended only for the legal receiver and should be kept from being eavesdropped by the wiretapper. Equivocation analysis is provided to evaluate the level of information leakage to the wiretapper. We characterize an achievable rate-equivocation region as well as an outer bound for this security model. To achieve the rate-equivocation triples, we propose an efficient coding scheme, in which the coded CSI serves as the CSI for the channel encoder, based on Gel’fand and Pinsker’s coding and Wyner’s random coding . Furthermore, an example of Gaussian wiretap channel with rate-limited CSI is presented, of which a lower bound on the secrecy capacity is obtained. By simulation, we find there exists an optimal rate of the coded CSI at which the biggest secrecy transmission rate of the Gaussian case is achieved.