## 2 Full-Duplex Transceiver with Passive/Active Eavesdrop Transmission System  
### General System Model  
We consider a short-packet FD transmission wiretap channel between three users, such as user B (transmitter), user A (legitimate receiver), and user E (eavesdrop), as shown in Figure 1, where the transmitter is equipped with only one antenna for transmission while the receiver and the eavesdropper are attached with one transmitter and one receiver antenna each to simultaneously receive the intended information message and transmit self-jamming or jamming signals. The 5G QC-LDPC codes, which are considered fundamental codes for short-packet uplink and downlink transmissions [29; 30; 31], are used in all transceivers.  
At the transmitter, the \((N,K)\) 5G QC-LDPC encoding process between the exponent parity check matrix \(\mathbf{H}\) and the information bit sequence is based on the Gauss-Jordan elimination algorithm [32], where \(K\) and \(N\) denote the lengths of the information message and the code word message, respectively. Let us denote the channel gain between two users and the SI channel gain of itself as \(\mathbf{h}_{XY}\) and \(\mathbf{h}_{YY}\), respectively, in which \(X\in\{A,B,E\}\) and \(Y\in\{A,E\}\), where \(A,B,E\) represent user A, user B, and user E, respectively. In this paper, the SI channel is modeled as quasi-static Rayleigh fading in the digital domain due to the assumption that the Line-of-Sight (LoS) component is fully suppressed by antenna and analog cancellation techniques, whereas the residual SI is the Non-Line-of-Sight (NLoS) component [8; 33]. Note that \(\mathbf{h}_{XY}\) and \(\mathbf{h}_{YY}\) are i.i.d complex Gaussian random variables with \(\mathcal{CN}(0,1)\)[34; 35]. Moreover, the transmitted power of each user is denoted as \(p_{X}\), where \(X\in\{A,B,E\}\), and we further denote \(w_{Y}\) as the complex background noise at user \(Y\) with \(\mathcal{CN}(0,\sigma_{Y}^{2})\), where \(Y\in\{A,E\}\). Based on the background noise as reference and without loss in generality, we further denote \(\rho_{XY}=p_{X}/\sigma_{Y}^{2}\) and \(\rho_{YY}=p_{Y}/\sigma_{Y}^{2}\) as the power-to-noise ratio provided by the self-jamming or jamming channel from user X to user Y and the SI channel at user Y, respectively. We also denote \(SNR_{A}=p_{B}/\sigma_{A}^{2}\) and \(SNR_{E}=p_{B}/\sigma_{E}^{2}\) as  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notations** & **Meaning** \\ \hline \(p_{Y}\) & Transmitting power of user Y \\ \(\sigma_{Y}^{2}\) & Noise power at user Y \\ \(\mathbf{w}_{Y}\) & Background noise at user Y \\ \(\rho_{XY}\) & Self-jamming power-to-noise ratio from user X to user Y \\ \(\rho_{YY}\) & SI power-to-noise ratio at user Y \\ \(\lambda\) & Forget factor of the RLS algorithm \\ \(i\) & Index of joint iterative iterations \\ \(j\) & Index of 5G QC-LDPC decoding iterations \\ \(k\) & Index of signal in the binary domain \\ \(n\) & Index of signal in the discrete time domain \\ \hline \hline \end{tabular}
\end{table}
Table 1: \(Cont.\)  
Figure 1: General system model.  
the SNR at user A and user E, where \(\sigma_{A}^{2}\) and \(\sigma_{E}^{2}\) are the noise powers at user A and user E, respectively.