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IEEE Transactions on Communications

Two-Way Full-Duplex Gaussian Channels With or Without Eavesdropper: Revisit

Dengfeng Xia, Chuanchuan Yang, Bin Dai

Published Jun 27, 2022• 5 citations
Publisher

Abstract

In this paper, the role of feedback in two-way full-duplex Gaussian channel (TW-FD-GC) is revisited. First, we propose a practical coding scheme for the TW-FD-GC, which is based on the noisy type of the well-known Schalkwijk-Kailath (SK) feedback scheme. We show that though this scheme cannot achieve the capacity of the TW-FD-GC, the codeword length that achieves desired decoding error probability is extremely short. Then, we further prove that the proposed scheme is secure by itself, i.e., the achievable rate region of the proposed scheme is also an achievablesecrecyrate region of the two-way full-duplex Gaussian wiretap channel (TW-FD-GWTC). In addition, for the TW-FD-GWTC, numerical result shows that thesecrecysum rate of our proposed scheme can be as large as those achieved by existing schemes in the literature for some cases. Next, we extend the proposed scheme to the TW-FD-GC with Gaussian state interference non-causally known by the corresponding transmitter. We show that the interference can be perfectly canceled by this extended scheme. Finally, we prove that this extended scheme is also secure by itself, and numerical result shows that this extended scheme may perform better than the existing ones in the literature.

DOI
10.1109/tcomm.2022.3186720

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In this paper, the role of feedback in two-way full-duplex Gaussian channel (TW-FD-GC) is revisited. First, we propose a practical coding scheme for the TW-FD-GC, which is based on the noisy type of the well-known Schalkwijk-Kailath (SK) feedback scheme. We show that though this scheme cannot achieve the capacity of the TW-FD-GC, the codeword length that achieves desired decoding error probability is extremely short. Then, we further prove that the proposed scheme is secure by itself, i.e., the achievable rate region of the proposed scheme is also an achievablesecrecyrate region of the two-way full-duplex Gaussian wiretap channel (TW-FD-GWTC). In addition, for the TW-FD-GWTC, numerical result shows that thesecrecysum rate of our proposed scheme can be as large as those achieved by existing schemes in the literature for some cases. Next, we extend the proposed scheme to the TW-FD-GC with Gaussian state interference non-causally known by the corresponding transmitter. We show that the interference can be perfectly canceled by this extended scheme. Finally, we prove that this extended scheme is also secure by itself, and numerical result shows that this extended scheme may perform better than the existing ones in the literature.
In this paper, the role of feedback in two-way full-duplex Gaussian wiretap channel (TW-FD-GWTC) is revisited. Traditionally, in the TW-FD-GWTC, one direction channel (feedback channel) is used to transmit a secret key which ensures the secure communication over the other direction channel (feedforward channel), i.e., the transmission rate of the feedback channel is sacrificed to ensure the physical layer security (PLS) in the feedforward channel. Can both directions achieve positive secrecy rates? We answer this question by proposing a noisy feedback scheme for the TW-FD-GWTC. In this proposed new scheme, both directions achieve positive secrecy rates, and the maximum secrecy sum rate approaches that in the literature. The study of this paper offers a new option for the enhancement of the physical layer security in two-way full-duplex wiretap channel.
The two-user Gaussian broadcast wiretap channel with common message and feedback (GBC-WTC-CM-F) is revisited. Traditionally, achievable secrecy rate of this model is achieved by combining Marton’s coding scheme for the two-user broadcast channel (BC) and the secret-key based feedback scheme, where both of the two feedback links are used to transmit secret keys shared between the transceivers. Recently, it has been shown that for the Gaussian wiretap channel with feedback, the Schalkwijk-Kailath (SK) feedback scheme achieves its secrecy capacity. Then it is natural to ask: can we do better when applying the SK-type scheme to the GBC-WTC-CM-F? In this paper, we answer this question by proposing two kinds of SK-type schemes. Specifically, first, we propose a hybrid scheme where one feedback link is used to transmit a secret key, and the other one is used for SK-type coding. We show that this hybrid scheme may perform better than the existing one in some cases. Next, we show that Ozarow’s extended SK scheme for the two-user Gaussian BC with feedback, where both feedback links are used for SK-type coding, is self-secure (satisfying perfect weak secrecy constraint by itself) and may perform the best. We further show that Ozarow’s scheme is in fact a secure finite blocklength coding scheme, and extend it to the static fading SISO and SIMO cases. Finally, the results of this paper are further explained by numerical examples.
In the literature, it has already been shown that a feedback control based coding scheme enhances the secrecy capacity of the Gaussian broadcast wiretap channel (GBC-WTC) with common message, and it performs better than the conventional random key based feedback scheme. However, note that the previously proposed scheme is based on the assumption that both the two receivers can send their received signals back to the transmitter via two feedback channels, which may not be available when a certain feedback channel fails to work. In this paper, we study the GBC-WTC with common message and partial feedback, where only one legitimate receiver can send his received signal back to the sender via a perfect feedback channel. A hybrid scheme, which combines the classical Schalkwijk-Kailath (SK) feedback control scheme, a dirty paper pre-coding scheme and the conventional random binning scheme is proposed for this model. Numerical results show that even in such a partial feedback case, our proposed scheme still works well and outperforms the existing secret-key based scheme in the literature.
The classical Schalkwijk-Kailath (SK) scheme, which achieves the capacity of the additive white Gaussian noise (AWGN) channel with noiseless feedback, is also shown to be an excellent secure finite blocklength (FBL) coding scheme for the AWGN wiretap channel with noiseless feedback. In this paper, the dirty tape channel (AWGN channel with Gaussian state interference causally known by the transmitter) with noiseless/noisy feedback is investigated. First, SK-type feedback schemes are proposed for this model by introducing a lattice-based strategy into the classical SK scheme, and it is shown that this strategy helps to eliminate the impact of the state interference and the feedback channel noise on the performance of the SK scheme. Then, we analyze the security performance of the proposed schemes, in particular, for the dirty tape channel with noisy feedback and eavesdropper, we give a lower bound on the normalized eavesdropper’s equivocation by establishing a novel inequality about the differential entropy of the Gaussian modulo-lattice function. Finally, performances of our proposed schemes are further explained by 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.
In this paper, the Gaussian wiretap feedback channel is revisited, and some new results on its secrecy capacity are obtained. To be specific, first, we show that the Schalkwijk–Kailath (SK) feedback scheme, which achieves the secrecy capacity of the degraded Gaussian wiretap feedback channel, also achieves the secrecy capacity of the non-degraded Gaussian wiretap feedback channel. Second, applying the existing secret key-based feedback schemes to Gaussian wiretap feedback channels, we derive some new lower bounds on the secrecy capacities of these models. Finally, we compare the performances of the above feedback schemes in the degraded and non-degraded Gaussian wiretap feedback channels and show which feedback scheme performs better for these channel models.