Finite blocklength (FBL) coding is an important way to realize ultra-reliable and low latency communication (URLLC), which is one of the key requirements in future wireless communication systems. In this paper, a FBL approach is proposed for the two-user multi-input single-output (MISO) multiple-access channel (MAC) with noisy feedback channel for the first time, which generalizes the classical Schalkwijk–Kailath (SK) schemes for additive white Gaussian noise (AWGN) channels. In the proposed scheme, by using minimum mean square error estimate and modulo lattice function, the variance of the receiver’s estimation error converges after several iterations, and for a desired demodulation error probability, the required codeword length is significantly short. We further explore security and robustness performances of the proposed scheme, and the numerical examples show that the proposed scheme almost meets the physical layer security requirement in some cases, and when the receiver’s power is sufficiently large, the sum-rate almost approaches the sum-rate capacity.

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.

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.

Ultra-reliable low-latency communication (URLLC) and reconfigurable intelligent surface (RIS) aided communication are two key technologies in future wireless communications. However, secure URLLC over RIS-adied communication channels receives little attention in the literature. In this paper, we propose finite blocklength (FBL) coding schemes for RIS aided SISO/SIMO/MIMO systems in the presence of an eavesdropper (no direct link between the transceiver), which are based on an existing coding scheme for the point-to-point white Gaussian channel with noiseless feedback. Then, we show that the proposed schemes are self-secure when the blocklengths are larger than certain thresholds. Finally, numerical results show that for given decoding error probability and secrecy level, the required coding blocklengths of our proposed schemes are extremely short, and the secrecy capacities of the RIS-aided systems without channel feedback are significantly enhanced by our feedback schemes.