The paper proposes a joint blind iterative Self-Interference (SI) cancellation, propagation channel estimation and decoding algorithm in Full-Duplex (FD) transmissions via feedback of channel estimates and decoded messages combined with the process of Digital Self-Interference Cancellation (DSIC). Different from the conventional algorithm, the proposed blind algorithm simultaneously estimates the self-interference and propagation channels and decodes messages in each decoding iteration of 5G Quasi-Cyclic Low Density Parity Check (QC-LDPC) codes. The temporary propagation channel estimate and decoded message are fed back to improve the self-interference cancellation and also the channel estimation as well as decoding in the next iteration. The results show that the proposed algorithm outperforms the conventional algorithm, especially at high signal to noise ratio (SNR) and small number of symbols, and requires much less processing time and computational complexity while achieving the convergence performance. The results also show that the proposed algorithm is less sensitive to SI level than the conventional algorithm. The paper further proposes a partial feedback scheme, which only use few feedback symbols for channel estimation, to significantly reduce the processing time and computational complexity while maintaining the performance. These good properties seem quite suitable for a use of this proposed blind iterative algorithm for short-length packet FD transmissions in Internet-of-Things (IoT) applications and green communications.