Comparison of the blocklength and decoding error probability of the LDPC code, Turbo code, LDGM code and the proposed linear feedback coding scheme for the FMAC-DMS.

Comparison of the blocklength and decoding error probability of the LDPC code, Turbo code, LDGM code and the proposed linear feedback coding scheme for the FMAC-DMS.</p

The model of SISO-FMAC-DMS.

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.</div

The relationship between the FBL sum rate, decoding error probability and blocklength for the MISO-FMAC-DMS.

The relationship between the FBL sum rate, decoding error probability and blocklength for the MISO-FMAC-DMS.</p

The relationship between the sum rate, number of transmitting antenna <i>A</i> = <i>B</i> and power constraint <i>P</i>_<i>A</i> = <i>P</i>_<i>B</i> = <i>P</i> for the MISO-FMAC-DMS.

The relationship between the sum rate, number of transmitting antenna A = B and power constraint PA = PB = P for the MISO-FMAC-DMS.</p

Key notations.

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.</div

The sum rate and secrecy sum rate when the blocklength is larger than a threshold for the MISO-FMAC-DMS and external eavesdropper.

The sum rate and secrecy sum rate when the blocklength is larger than a threshold for the MISO-FMAC-DMS and external eavesdropper.</p

The relationship between the sum rate, decoding error probability and power constraint for the MISO-FMAC-DMS.

The relationship between the sum rate, decoding error probability and power constraint for the MISO-FMAC-DMS.</p

Parameters in simulation.

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.</div

S1 Appendix -

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.</div

Comparison of the SNR and decoding error probability of the LDPC code, Turbo code, LDGM code and the proposed linear feedback coding scheme for the FMAC-DMS.

Comparison of the SNR and decoding error probability of the LDPC code, Turbo code, LDGM code and the proposed linear feedback coding scheme for the FMAC-DMS.</p