# Linear feedback coding scheme for multiple-access fading channels with degraded message sets

## TL;DR

This paper introduces a new channel coding method for wireless communication that improves performance and security in fading multiple-access channels.

## Contribution

A novel linear feedback coding scheme is proposed for fading multiple-access channels with degraded message sets.

## Key findings

- The proposed scheme transforms complex signals into scalar sub-channels using beamforming and channel splitting.
- The scheme achieves finite blocklength sum-rate and secrecy sum-rate in SISO and MISO cases.
- Numerical results confirm the effectiveness and security of the proposed coding solution.

## Abstract

Channel coding technology plays an important role in wireless communication systems, and it serves as a crucial mechanism to reduce interference during the transmission process. As the fifth-generation (5G) and sixth-generation (6G) wireless communication systems rapidly advance, requirements of the users on the quality and security of wireless service are increasing. To solve these problems, it calls for us to explore the new channel coding technologies. In this paper, a linear feedback coding scheme for fading multiple-access channels with degraded message sets (FMAC-DMS) is proposed. In this scheme, the transmitting beamforming and channel splitting are used to transform the channel with complex signals into scalar equivalent sub-channels. Then, the extended Schalkwijk-Kailath coding scheme (SK) is further applied to each sub-channel. The channel capacity, finite blocklength (FBL) sum-rate and FBL secrecy achievable sum-rate of the FMAC-DMS in single-input single-output (SISO) and multi-input single-output (MISO) cases are derived. Finally, we show that the proposed scheme not only provides a FBL coding solution but also guarantees physical layer security(PLS). The numerical and simulation results show the effectiveness of the proposed scheme as a channel coding solution. The study of this paper provides a new method to construct a practical FBL scheme for the FMAC-DMS.