Yuan Haoheng, Xie Guangfen, Dai Bin
School of Information Science and Technology, Southwest Jiaotong University, Chengdu 611756, China.
Peng Cheng Laboratory, Shenzhen 518055, China.
Entropy (Basel). 2023 Sep 15;25(9):1339. doi: 10.3390/e25091339.
For the point-to-point additive white Gaussian noise (AWGN) channel with an eavesdropper and feedback, it has already been shown that the secrecy capacity can be achieved by a secret key-based feedback scheme, where the channel feedback is used for secret sharing, and then encrypting the transmitted message by the shared key. By secret sharing, any capacity-achieving coding scheme for the AWGN channel without feedback can be secure by itself, which indicates that the capacity of the same model without the secrecy constraint also affords an achievable secrecy rate to the AWGN channel with an eavesdropper and feedback. Then it is natural to ask: is the secret key-based feedback scheme still the optimal scheme for the AWGN multiple-access channel (MAC) with an external eavesdropper and channel feedback (AWGN-MAC-E-CF), namely, achieving the secrecy capacity region of the AWGN-MAC-E-CF? In this paper, we show that the answer to the aforementioned question is no, and propose the optimal feedback coding scheme for the AWGN-MAC-E-CF, which combines an existing linear feedback scheme for the AWGN MAC with feedback and the secret key scheme in the literature. This paper provides a way to find optimal coding schemes for AWGN multi-user channels in the presence of an external eavesdropper and channel feedback.
对于具有窃听者和反馈的点对点加性高斯白噪声（AWGN）信道，已经表明，通过基于密钥的反馈方案可以实现保密容量，其中信道反馈用于秘密共享，然后通过共享密钥对传输的消息进行加密。通过秘密共享，任何用于无反馈AWGN信道的达到容量的编码方案本身都可以是安全的，这表明没有保密约束的相同模型的容量也为具有窃听者和反馈的AWGN信道提供了一个可实现的保密速率。然后自然会问：基于密钥的反馈方案对于具有外部窃听者和信道反馈的AWGN多址接入信道（MAC）（AWGN-MAC-E-CF）仍然是最优方案吗，即实现AWGN-MAC-E-CF的保密容量区域？在本文中，我们表明上述问题的答案是否定的，并提出了AWGN-MAC-E-CF的最优反馈编码方案，该方案将现有的用于具有反馈的AWGN MAC的线性反馈方案与文献中的密钥方案相结合。本文提供了一种在存在外部窃听者和信道反馈的情况下为AWGN多用户信道找到最优编码方案的方法。
