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IEEE Transactions on Communications

Feedback Coding Schemes for the Broadcast Channel With Mutual Secrecy Requirement at the Receivers

Bin Dai, Linman Yu, Xuxun Liu, Zheng Ma

Published Jun 20, 2019• 4 citations
Publisher

Abstract

The broadcast channel with mutual secrecy requirement at the receivers (BC-MSR-R) is a basic model characterizing the physical layer security (PLS) in the down-link of the wireless communication systems, where one transmitter sends two independent messages to two receivers via a broadcast channel, and each receiver can successfully decode his/her intended message and wishes to overhear the other one's message. This paper studies how to enhance the already existing secrecy rate region of the BC-MSR-R via receivers' feedback. Specifically, we propose two feedback strategies for the BC-MSR-R, where one uses the feedback to generate pure secret keys protecting the transmitted messages, and the other uses the feedback to generate not only keys but also cooperative messages helping the receivers to improve their decoding performance. Different inner bounds on the secrecy capacity region of the BC-MSR-R with noiseless feedback are constructed according to different feedback strategies, and these bounds are further illustrated by a Dueck-type example.

DOI
10.1109/tcomm.2019.2924206

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The broadcast channel with mutual secrecy requirement at the receivers (BC-MSR-R) is a basic model characterizing the physical layer security (PLS) in the down-link of the wireless communication systems, where one transmitter sends two independent messages to two receivers via a broadcast channel, and each receiver can successfully decode his/her intended message and wishes to overhear the other one's message. This paper studies how to enhance the already existing secrecy rate region of the BC-MSR-R via receivers' feedback. Specifically, we propose two feedback strategies for the BC-MSR-R, where one uses the feedback to generate pure secret keys protecting the transmitted messages, and the other uses the feedback to generate not only keys but also cooperative messages helping the receivers to improve their decoding performance. Different inner bounds on the secrecy capacity region of the BC-MSR-R with noiseless feedback are constructed according to different feedback strategies, and these bounds are further illustrated by a Dueck-type example.
Recently, the physical layer security (PLS) of the communication systems has been shown to be enhanced by using legal receiver's feedback. The present secret key based feedback scheme mainly focuses on producing key from the feedback and using this key to protect part of the transmitted message. However, this feedback scheme has been proved only optimal for several degraded cases. The broadcast channel with mutual secrecy requirement (BC-MSR) is important as it constitutes the essence of physical layer security (PLS) in the down-link of the wireless communication systems. In this paper, we investigate the feedback effects on the BC-MSR, and propose two inner bounds and one outer bound on the secrecy capacity region of the BC-MSR with noiseless feedback. One inner bound is constructed according to the already existing secret key based feedback coding scheme for the wiretap channel, and the other is constructed by a hybrid coding scheme using feedback to generate not only keys protecting the transmitted messages but also cooperative messages helping the receivers to improve their decoding performance. The performance of the proposed feedback schemes and the gap between the inner and outer bounds are further explained via two examples.
The current feedback coding strategy for the physical layer security (PLS) mainly focuses on generating secret key used for protecting the transmitted message, and this strategy has been proved only optimal for several degraded cases. Our previous work has proposed a new hybrid feedback strategy for the classical PLS model-the wiretap channel (WTC), where the feedback is not only used to generate key, but also used to produce cooperative information helping the legitimate parties to improve the communication between them. It has been shown that for the general WTC, this hybrid feedback strategy performs better than the already existing secret key based feedback scheme. In this paper, we extend the previous proposed feedback strategy for the WTC to a multi-terminal case, and apply this generalized feedback strategy to the broadcast channel with mutual secrecy requirement (BC-MSR), which constitutes the essence of physical layer security (PLS) in the down-link of the wireless communication systems. From a non-degraded example (Dueck-type broadcast channel), we show that for the BC-MSR, this generalized feedback strategy may perform better than the already existing one.
The model for a broadcast channel with confidential messages (BC-CM) plays an important role in the physical layer security of modern communication systems. In recent years, it has been shown that a noiseless feedback channel from the legitimate receiver to the transmitter increases the secrecy capacity region of the BC-CM. However, at present, the feedback coding scheme for the BC-CM only focuses on producing secret keys via noiseless feedback, and other usages of the feedback need to be further explored. In this paper, we propose a new feedback coding scheme for the BC-CM. The noiseless feedback in this new scheme is not only used to produce secret keys for the legitimate receiver and the transmitter but is also used to generate update information that allows both receivers (the legitimate receiver and the wiretapper) to improve their channel outputs. From a binary example, we show that this full utilization of noiseless feedback helps to increase the secrecy level of the previous feedback scheme for the BC-CM.
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.
A broadcast channel (BC) where the decoders cooperate via a one-sided link is considered. One common and two private messages are transmitted and the private message to the cooperative user should be kept secret from the cooperation-aided user. The secrecy level is measured in terms of strong secrecy, i.e., a vanishing information leakage. An inner bound on the capacity region is derived by using a channel-resolvability-based code that double-bins the codebook of the secret message, and by using a likelihood encoder to choose the transmitted codeword. The inner bound is shown to be tight for semideterministic and physically degraded BCs, and the results are compared with those of the corresponding BCs without a secrecy constraint. Black well and Gaussian BC examples illustrate the impact of secrecy on the rate regions. Unlike the case without secrecy, where sharing information about both private messages via the cooperative link is optimal, our protocol conveys parts of the common and non-confidential messages only. This restriction reduces the transmission rates more than the usual rate loss due to secrecy requirements. An example that illustrates this loss is provided.
The physical layer security in the up-link of the wireless communication systems is often modeled as the multiple access wiretap channel (MAC-WT), and recently it has received a lot attention. In this paper, the MAC-WT has been re-visited by considering the situation that the legitimate receiver feeds his received channel output back to the transmitters via two noiseless channels, respectively. This model is called the MAC-WT with noiseless feedback. We present a new hybrid inner bound on the secrecy capacity region of this feedback model, and it is constructed by using the feedback as a tool not only to allow the independent transmitters to co-operate with each other (decode each other's transmitted message from the feedback), but also to generate two secret keys respectively shared between the legitimate receiver and the two transmitters. We show that this hybrid inner bound is strictly larger than the already existing decode-and-forward (DF) inner bound. Moreover, we provide a sato-type outer bound on the secrecy capacity region of the MAC-WT with noiseless feedback. The results of this paper are further explained via a Gaussian example.