## 1 Introduction
DSIC is usually based on adaptive filtering with the knowledge of the SI signal provided by the transmitter, and the intended channel can be estimated by using an equaliser with blind or semi-blind estimations [23; 24; 25]. In recent years, the authors in [26; 27] proposed joint algorithm channel estimation for SI cancellation and signal detection in FD transmission. However, the results were not satisfactory in short-packet transmissions because the systems require many data symbols to obtain a good second-order statistics of the received signal. Therefore, the constraints of time-, bandwidth-, and power-efficient approaches for short-packet transmission in FD transmission have to be considered carefully. Indeed, a potential technique for channel estimation and data detection in short-packet FD transmission is to consider semi-blind channel estimation, which is the concatenation between the known pilot symbols and the information symbols in order to form a transmitted sequence [28; 29; 30; 31]. For instance, the authors in [29] proposed an iterative semi-blind receiver with Carrier Frequency Offset (CFO) for uRLLC in short-packet FD transmission systems. Moreover, a semi-blind FD Amplify-and-Forward (AF) relay system with adaptive SI processing assisted by Independent Component Analysis (ICA) was proposed in order to improve the low latency and high reliability in IoT communications [30]. Furthermore, a new Semi-blind Minimum Mean-Squared Error (S-MMSE) technique was also proposed to further suppress the residual SI power in FD mmWave massive MIMO systems [31]. Their proposed algorithm was used to overcome the problem of ergodic capacity and outage capacity, as well as the length of pilot symbols, which are the biggest challenges in short-packet transmissions. Moreover, there still exist some limitations in FD short-packet transmissions such as the high error in the SI channel estimation [29] and the high latency of the decoding process, i.e., in the 5G Quasi-Cyclic Low-Density Parity Check (QC-LDPC) decoder [32; 33], because the system needs to use many decoding iterations to reach the convergence or saturation level. Therefore, many concerns of researchers focus on these challenges of the FD short-frame transmission. In this paper, a semi-blind algorithm is proposed for joint iterative SI cancellation and intended channel estimation in 5G QC-LDPC-encoded FD short-packet transmissions in the digital domain, by taking into account only a small number (four at least) of pilot symbols and the feedback of the estimate of the channel to achieve a nearly optimal performance and efficient use in practical scenarios. Throughout the paper, the performance evaluation of the proposed algorithm is based on four metrics: Mean-Squared Error (MSE), Bit-Error-Rate (BER), processing time, and computational complexity. The contributions of this paper can be summarised as follows:  
* We propose a joint iterative _semi-blind_ SI cancellation and channel estimation in 5G QC-LDPC-encoded short-packet FD transmissions;
* We characterise the out-performance of the system with the proposed algorithm compared to the conventional algorithm. In particular, this _semi-blind_ technique can significantly improve the performances of the MSE and BER, while requiring only the addition of a few pilot symbols for the channel estimation feedback processes;
* We point out that the time consumption and computational complexity of the proposed algorithm are lower than the conventional algorithm, which is suitable for IoT applications and green communications. The remainder of this paper is organised as follows. Section 2 describes briefly the system model of FD transmissions with the conventional DSIC algorithm and the 5G QC-LDPC channel coding scheme. Section 3 proposes the joint iterative _semi-blind_ channel estimation and decoding algorithm. Then, the numerical results and comparisons with the conventional algorithm and the comparison of the processing time and computational complexity of all schemes are presented in Section 4.