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Mathematical Problems in Engineering

Capacity-Equivocation Regions of the DMBCs with Noiseless Feedback

Xinxing Yin, Zhi Xue, Bin Dai

Published Jan 1, 2013• 2 citations
Publisher

Abstract

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.

DOI
10.1155/2013/102069

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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.
This paper studies the degraded broadcast channel with rate-limited feedback. The transmitter aims to convey a common message to receiver 1 and 2 in addition to a confidential message intended only for receiver 1. The feedback symbol, independent of the channel outputs, is introduced to serve as a secret key between the transmitter and receiver 1. The capacity-equivocation region of this channel model is obtained. A simpler and more intuitive derivation instead of the recursive argument is used to get the single-letter characterization of the upper bound. Furthermore, a novel coding scheme is presented to achieve the upper bound. This paper also derives the secrecy capacity of this channel which subsumes the secrecy capacity of the degraded wiretap channel with rate-limited feedback.
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.
This paper studies capacity bounds for discrete memoryless broadcast channels with confidential messages. Two private messages as well as a common message are transmitted; the common message is to be decoded by both receivers, while each private message is only for its intended receiver. In addition, each private message is to be kept secret from the unintended receiver where secrecy is measured by equivocation. Both inner and outer bounds are proposed to the rate equivocation region for broadcast channels with confidential messages. The proposed inner bound generalizes Csiszar and Korner's rate equivocation region for broadcast channels with a single confidential message, Liu 's achievable rate region for broadcast channels with perfect secrecy, Marton's and Gel'fand-Pinsker's achievable rate region for general broadcast channels. The proposed outer bounds, together with the inner bound, help establish the rate equivocation region of several classes of discrete memoryless broadcast channels with confidential messages, including the less noisy, deterministic, and semideterministic broadcast channels. Furthermore, specializing to the general broadcast channel by removing the confidentiality constraint, the proposed outer bounds reduce to new capacity outer bounds for the discrete memory broadcast channel.
In this paper, we consider non-degraded discrete memoryless broadcast channels where two private messages as well as a common message are transmitted at rate R1, R2and Rorespectively. The common message is for both receivers to decode; the private message is only for its intended receiver of which the other receiver shall be kept as ignorant as possible. Measuring ignorance by equivocation, we propose an achievable rate region (R1, R2, Ro, Re1, Re2) for this channel where Re1and Re2are the equivocation rates for the two receivers respectively. This result generalizes Csiszar and Kornerpsilas capacity region for broadcast channels with single private message, Liu et alpsilas result for broadcast channels with perfect secrecy, Gelpsilafand and Pinskerpsilas achievable rate region for broadcast channels with common message, and Martonpsilas achievable rate region for general broadcast channels.
This paper investigates the secure data transmission in the broadcast channel with noiseless feedback by using the information-theoretic method. We consider transmitting a private message and a common message to two receivers, of which the common message is to be decoded by both receivers while the private message is only for the intended receiver. The channel to the intended receiver is assumed to be independent of that to the other receiver. Feedback from the output of the intended receiver is used as a shared secret key to enhance the secrecy in the transmission. The capacity-equivocation region and the secrecy capacity of this new model are obtained. We find the secrecy capacity is enhanced by using feedback, even in the case that the other receiver is in a better position than the intended receiver. In addition, our results generalize the secrecy capacity of the degraded wiretap channel with secure feedback, and the capacity region of the degraded broadcast channel.
We investigate the wiretap channel in the presence of action-dependent states and noiseless feedback. 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, the message, and the noiseless feedback, where the noiseless feedback is from the output of the main channel to the channel encoder. 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. The transition probability distribution of the main channel depends on the channel state. Measuring wiretapper’s uncertainty about the message by equivocation, the capacity equivocation regions are provided both for the case where the channel inputs are allowed to depend noncausally on the state sequence and the case where they are restricted to causal dependence. Furthermore, the secrecy capacities for both cases are formulated, which provide the best transmission rate with perfect secrecy. The result is further explained via a binary example.