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IEEE Transactions on Information Forensics and Security

Feedback Enhances the Security of State-Dependent Degraded Broadcast Channels With Confidential Messages

Bin Dai, Zheng Ma, Xuming Fang

Published Apr 3, 2015• 16 citations
Publisher

Abstract

In this paper, we investigate the state-dependent degraded broadcast channels with confidential messages (SD-DBC-CM), and with or without noiseless feedback. In this new model, the channel state is available at the transmitter in a noncausal or causal manner, and there may exist a noiseless feedback link from the nondegraded receiver to the transmitter. For the discrete memoryless SD-DBC-CM, inner and outer bounds on the capacity-equivocation regions are provided for both the noncausal and causal cases. For the discrete memoryless SD-DBC-CM with feedback, inner and outer bounds on the capacity-equivocation region are provided for the noncausal case, and the capacity-equivocation region is determined for the causal case. The results of this paper are further explained via Gaussian and binary examples.

DOI
10.1109/tifs.2015.2419182

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In this paper, we investigate the state-dependent degraded broadcast channels with confidential messages (SD-DBC-CM), and with or without noiseless feedback. In this new model, the channel state is available at the transmitter in a noncausal or causal manner, and there may exist a noiseless feedback link from the nondegraded receiver to the transmitter. For the discrete memoryless SD-DBC-CM, inner and outer bounds on the capacity-equivocation regions are provided for both the noncausal and causal cases. For the discrete memoryless SD-DBC-CM with feedback, inner and outer bounds on the capacity-equivocation region are provided for the noncausal case, and the capacity-equivocation region is determined for the causal case. The results of this paper are further explained via Gaussian and binary examples.
In this paper, we investigate the degraded broadcast channels with confidential messages (DBC-CM), causal channel state information (CSI), and with or without noiseless feedback. The inner and outer bounds on the capacity-equivocation region are given for the non-feedback mode, and the capacity-equivocation region is determined for the feedback model. We find that by using this noiseless feedback, the achievable rate-equivocation region (inner bound on the capacity-equivocation region) of the DBC-CM with causal CSI is enhanced.
In this paper, we investigate the model of degraded broadcast channel with noncausal side information, confidential messages and noiseless feedback. This work is from Steinberg's work on the degraded broadcast channel with noncausal side information, and Csiszár and Körner's work on broadcast channel with confidential messages. In this new model, the transmitter sends a confidential message to the non-degraded receiver, and meanwhile sends a common message to both the degraded and non-degraded receivers. Moreover, the channel for the non-degraded receiver is controlled by channel state information (side information), and it is available to the transmitter in a noncausal manner (termed here noncausal side information). In addition, we assume that there is a noiseless feedback from the output of the channel for the non-degraded receiver to the transmitter, and it helps them share a secret key, which enlarges the degraded receiver's uncertainty about the confidential message. Measuring the uncertainty by equivocation (conditional entropy), the capacity-equivocation region composed of all achievable rates-equivocation triples is determined for this new model. Furthermore, the secrecy capacity is formulated, which provides the best transmission rate with perfect secrecy.
From the perspective of secure communication, we study transmitting confidential messages in broadcast channel with action-dependent states. Transmitter aims to convey a common message to both receiver 1 and 2, and a confidential message only to receiver 1. It can take actions to affect the generation of channel states which are causally known to the encoder. The inner and outer bounds on the capacity-equivocation region of such a channel are characterized. The corresponding bounds on the secrecy capacity are also obtained. To achieve the rate-equivocation triples, we construct coding schemes using superposition coding and Wyner's random binning. For the special case where no common message is sent, the inner and outer bounds coincide with each other. A binary example is given to illustrate the results.
The noiseless feedback is introduced in channels with information embedding on actions. Two channel models are considered. One is wiretap channel with information embedding on actions and noiseless feedback (WT-IEANF), the other is degraded broadcast channel with noncausal action-dependent states and noiseless feedback (DBC-NADSNF). For the WT-IEANF, we characterize both inner and outer bounds on the capacity-equivocation region. For the DBC-NADSNF, an inner bound on the capacity-equivocation region is obtained, and a proper coding scheme is constructed, in which the noiseless feedback plays the role of a shared secret key between the transmitter and legal receiver. We find that the feedback does help increase the secure information transmission rates of the two models, but, at the same time, it enables the illegal receiver to get another chance to eavesdrop the private message. Besides, when secrecy constraint condition is removed, it is found that feedback is not useful for enhancing the capacity of the channel with information embedding on actions.
The discrete memoryless broadcast channels (DMBCs) with noiseless feedback are studied. The entire capacity-equivocation regions of two models of the DMBCs with noiseless feedback are obtained. One is the degraded DMBCs with rate-limited feedback; the other is the less and reversely less noisy DMBCs with causal feedback. In both models, two kinds of messages are transmitted. The common message is to be decoded by both the legitimate receiver and the eavesdropper, while the confidential message is only for the legitimate receiver. Our results generalize the secrecy capacity of the degraded wiretap channel with rate-limited feedback (Ardestanizadeh et al., 2009) and the restricted wiretap channel with noiseless feedback (Dai et al., 2012). Furthermore, we use a simpler and more intuitive deduction to get the single-letter characterization of the capacity-equivocation region, instead of relying on the recursive argument which is complex and not intuitive.
In this paper, the general wiretap channel with channel state information (CSI) at the transmitter and noiseless feedback is investigated, where the feedback is from the legitimate receiver to the transmitter, and the CSI is available at the transmitter in a causal or noncausal manner. The capacity-equivocation regions are determined for this model in both causal and noncausal cases, and the results are further explained via Gaussian and binary examples. For the Gaussian model, we find that in some particular cases, the noiseless feedback performs better than Chia and El Gamal’s CSI sharing scheme, i.e., the secrecy capacity of this feedback scheme is larger than that of the CSI sharing scheme. For the degraded binary model, we find that the noiseless feedback performs no better than Chia and El Gamal’s CSI sharing scheme. However, if the cross-over probability of the wiretap channel is large enough, we show that the two schemes perform the same.