Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Entropy

Secrecy Capacity Region of the AWGN MAC with External Eavesdropper and Feedback

Haoheng Yuan, Guangfen Xie, Bin Dai

Published Sep 15, 2023• 1 citation
Publisher

Abstract

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.

DOI
10.3390/e25091339

Related papers

Secrecy Capacity Region of the AWGN MAC with External Eavesdropper and Feedback

Haoheng Yuan, Han Deng, Guangfen Xie +2 more

For the point-to-point additive white Gaussian noise (AWGN) channel with 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, any capacity-achieving coding scheme for the AWGN channel without feedback is secure by itself, which indicates that the capacity of the same model without secrecy constraint is also an achievable secrecy rate of the AWGN channel with eavesdropper and feedback. Then it is natural to ask: is the secret key based feedback scheme still an optimal scheme for the AWGN multiple-access channel (MAC) with 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 an 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. The study of this paper provides a way to find optimal coding schemes for AWGN multi-user channels in the presence of external eavesdronner and channel feedback.

Globecom•Dec 4, 2023•2 citations

Secrecy Capacity of Colored Gaussian Noise Channels With Feedback

Chong Li, Yingbin Liang, H. Vincent Poor +1 more

In this paper, the finite-order autoregressive moving average (ARMA) Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of signals in both forward and feedback channels. It is shown that the generalized Schalkwijk-Kailath scheme, a capacity-achieving coding scheme for the Gaussian feedback channel, achieves the same maximum rate for the same channel even with the presence of an eavesdropper. Therefore, the secrecy capacity is equal to the feedback capacity without the presence of an eavesdropper for the Gaussian feedback channel. Furthermore, the results are extended to the additive white Gaussian noise (AWGN) channel with quantized feedback. It is shown that the proposed coding scheme achieves a positive secrecy rate. Our result implies that as the amplitude of the quantization noise decreases to zero, the secrecy rate converges to the capacity of the AWGN channel.

IEEE Transactions on Information Theory•Mar 13, 2019•26 citations

Secrecy Capacity of Colored Gaussian Noise Channels with Feedback

Chong Li, Yingbin Liang, H. Vincent Poor +1 more

In this paper, the k-th order autoregressive moving average (ARMA(k)) Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of the signals in both forward and feedback channels. It is shown that a variant of the generalized Schalkwijk-Kailath scheme, a capacity-achieving coding scheme for the feedback Gaussian channel, achieves the same maximum rate for the same channel with the presence of an eavesdropper. Therefore, the secrecy capacity is equal to the feedback capacity without the presence of an eavesdropper for the feedback channel. Furthermore, the results are extended to the additive white Gaussian noise (AWGN) channel with quantized feedback. It is shown that the proposed coding scheme achieves a positive secrecy rate. As the amplitude of the quantization noise decreases to zero, the secrecy rate converges to the capacity of the AWGN channel.

arXiv:1801.06702•Jan 20, 2018•0 citations

Secure Joint Source-Channel Coding for the AWGN Channel with Feedback: A Finite Blocklength Analysis

Sheng Su, Yuhan Yang, Chao Qi +3 more

In the literature, it has been shown that the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel with noise-free feedback equals the capacity of the same model without secrecy constraint, and the classical Schalkwijk-Kailath (SK) scheme achieves the secrecy capacity. In this paper, we show that in finite blocklength regime, the SK scheme is not optimal, and propose a modified SK scheme which may perform better than the classical one. Besides this, this paper establishes a finite blocklength converse for the AWGN wiretap channel with feedback, which can also be viewed as a converse for the same model without secrecy constraint. To the best of the authors' knowledge, this is the first paper to address such a problem, and the results of this paper are further explained via numerical examples.

arXiv:2601.07472•IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2026•1 citation

A Coding Scheme for Colored Gaussian Wiretap Channels with Feedback

Chong Li, Yingbin Liang, H. Vincent Poor +1 more

In this paper, the finite-order autoregressive moving average (ARMA) Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of the signals in both forward and feedback channels. It is shown that the generalized Schalkwijk-Kailath scheme, a capacity-achieving coding scheme for the feedback Gaussian channel, achieves the same maximum rate for the same channel with the presence of an eavesdropper. Therefore, the secrecy capacity is equal to the feedback capacity without the presence of an eavesdropper for the feedback channel. Furthermore, the results are extended to the additive white Gaussian noise (AWGN) channel with quantized feedback. It is shown that the proposed coding scheme achieves a positive secrecy rate. As the amplitude of the quantization noise decreases to zero, the secrecy rate converges to the capacity of the AWGN channel.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2018•7 citations

Feedback Capacity of Gaussian Multiple-Access Wiretap Channel with Degraded Message Sets

Bin Dai, Chong Li, Yingbin Liang +2 more

The Schalkwijk-Kailath (SK) feedback scheme is a capacity-achieving coding scheme for the point-to-point white Gaussian channel with feedback. Recently, it has been shown that the SK scheme, which is not designed with consideration of secrecy, already achieves perfect weak secrecy by itself, i.e., the secrecy capacity of the Gaussian wiretap channel with feedback equals the capacity of the same model without secrecy constraint. In this paper, we propose a capacity-achieving SK type feedback scheme for the two-user Gaussian multiple-access channel with degraded message sets (GMAC-DMS). Similarly to the inherent secrecy nature of the classical SK scheme, we show that the proposed scheme is also secure by itself, which indicates that the feedback secrecy capacity of the two-user Gaussian multiple-access wiretap channel with degraded message sets (GMAC-WT-DMS) equals the capacity of the same model without secrecy constraint.

IEEE Information Theory Workshop (ITW)•Apr 11, 2021•1 citation
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.
For the point-to-point additive white Gaussian noise (AWGN) channel with 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, any capacity-achieving coding scheme for the AWGN channel without feedback is secure by itself, which indicates that the capacity of the same model without secrecy constraint is also an achievable secrecy rate of the AWGN channel with eavesdropper and feedback. Then it is natural to ask: is the secret key based feedback scheme still an optimal scheme for the AWGN multiple-access channel (MAC) with 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 an 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. The study of this paper provides a way to find optimal coding schemes for AWGN multi-user channels in the presence of external eavesdronner and channel feedback.
In this paper, the finite-order autoregressive moving average (ARMA) Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of signals in both forward and feedback channels. It is shown that the generalized Schalkwijk-Kailath scheme, a capacity-achieving coding scheme for the Gaussian feedback channel, achieves the same maximum rate for the same channel even with the presence of an eavesdropper. Therefore, the secrecy capacity is equal to the feedback capacity without the presence of an eavesdropper for the Gaussian feedback channel. Furthermore, the results are extended to the additive white Gaussian noise (AWGN) channel with quantized feedback. It is shown that the proposed coding scheme achieves a positive secrecy rate. Our result implies that as the amplitude of the quantization noise decreases to zero, the secrecy rate converges to the capacity of the AWGN channel.
In this paper, the k-th order autoregressive moving average (ARMA(k)) Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of the signals in both forward and feedback channels. It is shown that a variant of the generalized Schalkwijk-Kailath scheme, a capacity-achieving coding scheme for the feedback Gaussian channel, achieves the same maximum rate for the same channel with the presence of an eavesdropper. Therefore, the secrecy capacity is equal to the feedback capacity without the presence of an eavesdropper for the feedback channel. Furthermore, the results are extended to the additive white Gaussian noise (AWGN) channel with quantized feedback. It is shown that the proposed coding scheme achieves a positive secrecy rate. As the amplitude of the quantization noise decreases to zero, the secrecy rate converges to the capacity of the AWGN channel.
In the literature, it has been shown that the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel with noise-free feedback equals the capacity of the same model without secrecy constraint, and the classical Schalkwijk-Kailath (SK) scheme achieves the secrecy capacity. In this paper, we show that in finite blocklength regime, the SK scheme is not optimal, and propose a modified SK scheme which may perform better than the classical one. Besides this, this paper establishes a finite blocklength converse for the AWGN wiretap channel with feedback, which can also be viewed as a converse for the same model without secrecy constraint. To the best of the authors' knowledge, this is the first paper to address such a problem, and the results of this paper are further explained via numerical examples.
In this paper, the finite-order autoregressive moving average (ARMA) Gaussian wiretap channel with noiseless causal feedback is considered, in which an eavesdropper receives noisy observations of the signals in both forward and feedback channels. It is shown that the generalized Schalkwijk-Kailath scheme, a capacity-achieving coding scheme for the feedback Gaussian channel, achieves the same maximum rate for the same channel with the presence of an eavesdropper. Therefore, the secrecy capacity is equal to the feedback capacity without the presence of an eavesdropper for the feedback channel. Furthermore, the results are extended to the additive white Gaussian noise (AWGN) channel with quantized feedback. It is shown that the proposed coding scheme achieves a positive secrecy rate. As the amplitude of the quantization noise decreases to zero, the secrecy rate converges to the capacity of the AWGN channel.
The Schalkwijk-Kailath (SK) feedback scheme is a capacity-achieving coding scheme for the point-to-point white Gaussian channel with feedback. Recently, it has been shown that the SK scheme, which is not designed with consideration of secrecy, already achieves perfect weak secrecy by itself, i.e., the secrecy capacity of the Gaussian wiretap channel with feedback equals the capacity of the same model without secrecy constraint. In this paper, we propose a capacity-achieving SK type feedback scheme for the two-user Gaussian multiple-access channel with degraded message sets (GMAC-DMS). Similarly to the inherent secrecy nature of the classical SK scheme, we show that the proposed scheme is also secure by itself, which indicates that the feedback secrecy capacity of the two-user Gaussian multiple-access wiretap channel with degraded message sets (GMAC-WT-DMS) equals the capacity of the same model without secrecy constraint.