In the literature, it has been shown that feedback does not increase the optimal rate-distortion region of the dirty paper channel with state estimation at the receiver (SE-R). On the other hand, it is well-known that feedback helps to construct low-complexity coding schemes in Gaussian channels, such as the elegant Schalkwijk-Kailath (SK) feedback scheme. This motivates us to explore capacity-achieving SK-type schemes in dirty paper channels with SE-R and feedback. In this paper, we first propose a capacity-achieving feedback scheme for the dirty paper channel with SE-R (DPC-SE-R), which combines the superposition coding and the classical SK-type scheme. Then, we extend this scheme to the dirty paper multiple-access channel with SE-R and feedback, and also show the extended scheme is capacity-achieving. Finally, we discuss how to extend our scheme to a noisy state observation case of the DPC-SE-R. However, the capacity-achieving SK-type scheme for such a case remains unknown.

Linear feedback coding scheme, such as the elegant Schalkwijk-Kailath (SK) scheme, receives much attention in the literature since its decoding error probability decreases as a second-order exponential in the coding blocklength. In recent years, a linear feedback scheme has been proposed for the Gaussian relay channel (GRC) with destination-source feedback, which combines the SK scheme and the amplify-and-forward (AF) relay strategy. Since there exists three possible feedback links in the GRC, then one question beckons: is there any rate gain if there exist multiple feedback links in the GRC, and can any other relay strategy outperform the AF strategy? In this paper, we answer this question by investigating four feedback models of the GRC, namely, the GRC with destination-source and destination-relay feedback, the GRC with destination-relay and relay-source feedback, the GRC with destination-source and relay-source feedback, and the GRC with all feedback links, respectively. We propose SK-type schemes for these feedback models, and numerical examples show that when the coding blocklength is not long, the rates of our proposed schemes almost approach their asymptotic values, and these rates may be larger than those of existing schemes in the literature. The study of this paper shows that different number/location of feedback links may bring additional rate gain in finite blocklength regime.

The problem of reliably reconstructing a function of sources over a multiple-access channel (MAC) is revisited by considering channel feedback. First, a linear feedback scheme is proposed to compute the average of the Gaussian sources transmitted over the Gaussian MAC. Next, numerical results show that in some cases, our proposed scheme performs better than the existing ones without using channel feedback. Finally, we show that with a slight modification, our scheme can be directly extended to compute any linear function of the Gaussian sources transmitted over the Gaussian MAC.

Linear feedback coding scheme, such as the elegant Schalkwijk-Kailath (SK) scheme, receives much attention in the literature since its decoding error probability decreases as a second-order exponential in the coding blocklength. In recent years, a linear feedback scheme has been proposed for the Gaussian relay channel (GRC) with destination-source feedback, which combines the SK scheme and the amplify-and-forward (AF) relay strategy. Since there exists three possible feedback links in the GRC, then one question beckons: is there any rate gain if there exist two feedback links in the GRC, and can any other relay strategy outperform the AF strategy? In this paper, we answer this question by investigating two feedback models of the GRC, namely, the GRC with destination-source and destination-relay feedback, and the GRC with destination-relay and relay-source feedback. We propose two SK-type schemes which are respectively based on the decode-and-forward (DF) relay strategy and the compress-and-forward (CF) relay strategy. Numerical examples show that the achievable rates of our proposed schemes may be larger than that of the AF relay strategy based SK-type scheme in the literature.

In this paper, the sum-capacity of the symmetric finite-state Gaussian multiple access channel (FS-GMAC) with delayed feedback is determined, where the channel state is perfectly obtained by the receiver, and the receiver sends the state and channel output back to the two transmitters through two noiseless feedback channel after same time delay. We first propose a linear-feedback coding scheme for this model, which is based on multiplexing coding and a variant of Schalkwijk- Kailath scheme, and derive the corresponding achievable sum-rate. Then, by establishing an upper bound on the sum-capacity of the same model, we further show that the proposed scheme is capacity-achieving.

In the literature, channel feedback has already been shown to be an effective way to realize ultra-reliable and low-latency communication (URLLC). In this paper, we aim to extend the point-to-point Schalkwijk-Kailath (SK)-type noisy feedback scheme to Vehicle-to-Everything (V2X) communication scenario. Although enhanced mobile broadband (eMBB) and URLLC services are considered as key enablers for V2X communication, here we mainly focus on URLLC service due to the urgency nature of the practical transportation systems. To be specific, based on the SK-type noisy feedback scheme, we propose a finite blocklength feedback coding scheme for URLLC message by mitigating the interference of eMBB message through dirty paper coding. Then, we explore security performance of the proposed scheme by calculating the information leakage to the eavesdropper. Numerical results show that the blocklength of the proposed scheme is significantly short for the desired decoding error probability, and the proposed scheme almost meets the physical layer security requirement for some cases. The study in this paper provides a new method for the secure URLLC in V2X communication.

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 dirty-tape channel (the white Gaussian channel with causal state interference at the trans-mitter) is revisited by considering a noisy feedback link between the transmitter and receiver. A finite blocklength (FBL) coding scheme is proposed for this model, which is based on the classical Schalkwijk-Kailath (SK) scheme and an existing lattice-based interference canceling scheme. Based on the proposed scheme, an achievable rate for given blocklength and decoding error probability is obtained, and the results of this paper are further illustrated via numerical examples.

In this paper, the two-way full-duplex Gaussian channel (TW-FD-GC) is revisited by considering Gaussian state interference non-causally known by the corresponding transmitter, which is also called the two-way full-duplex dirty paper channel (TW-FD-DPC). We propose a novel coding scheme for the TW-FD-DPC, which perfectly eliminates the effect of the state interference. Numerical result shows that for a fixed decoding error probability, the encoding-decoding complexity of this scheme is extremely low.

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.