Capacity-Equivocation Regions of the DMBCs with Noiseless Feedback

Xinxing Yin,Bin Dai,Zhi Xue

doi:10.1155/2013/102069

Xinxing Yin, Bin Dai + Show 1 more

Open Access

https://doi.org/10.1155/2013/102069

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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 thelessandreversely less noisyDMBCs 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.

Highlights

Secure data transmission is an important requirement in wireless communication
(4) We find that even if the eavesdropper is in a better position than the legitimate receiver, provable secure communication could be implemented in the discrete memoryless broadcast channels (DMBCs) with both common and confidential messages
This paper studies two models of the DMBCs with noiseless feedback

Summary

Introduction

Secure data transmission is an important requirement in wireless communication. Wyner first studied the degraded (the wiretap channel is said to be (physically) degraded if X → Y → Z form a Markov chain, where X is the channel input and Y and Z are the channel outputs of the legitimate receiver and wiretapper, resp.) wiretap channel in [1], where the output ZN of the channel to the wiretapper is degraded to the output YN of the channel to the legitimate receiver. The formal definition of the secrecy capacity is given in Remark 3) and demonstrated that provable secure communication could be implemented by using information theoretic methods This model was extended to a more general case by Csiszar and Korner [2], where broadcast channel with confidential messages was studied; see Figure 1. To further investigate the secure data transmission with both common and confidential messages and noiseless feedback, this paper determines the capacity-equivocation regions of the following two DMBCs with both common and confidential messages. They are unsolved in the previous exploration.

Channel Models and Main Results

Less and Reversely Less Noisy DMBCs with Noiseless

Proof of Theorem 2

Proof of Theorems 4 and 5

Conclusion