Abstract: This paper introduces a single-carrier system with hybrid time-frequency domain Decision Feedback Equalization (DFE), in which the short pn (Pseudo-Noise) sequence with fixed waveform replaces the cyclic prefix (CP) in the conventional Single Carrier systems with Frequency Domain Equalization (SC-FDE), and the long PN sequences composed of several short pn sequences are employed as the channel training sequences to complete the initial estimation and tracking for fast-varying channel. In this system, the received training sequences are averaged in time domain and then the channel is estimated in frequency domain. In comparison with traditional SC-FDE systems, its complexity is lower. Furthermore, an approach of adding sum-check blocks to original Low-Density Parity-Check (LDPC) blocks is presented, and the effective improvements of this system performance can be achieved. Finally, the simulation results show that this system works well over the fading channel.