The feedback-assisted PD-type quantized iterative learning control problem is studied for discrete linear systems with iteration-varying trial lengths. Considering that the system signal is transmitted to the controller or actuator after being quantized. Two quantization schemes are given, including tracking error signal quantization and control input signal quantization. In the case of iteration-varying trial lengths and iteration-varying initial state conditions, a feedback-assisted PD-type update law is developed based on the quantized signal. The learning convergence condition under mathematical expectations derived with the sector bound method and the lifting representation:tracking error signal quantization can obtain zero tracking error, and control input signal quantization only guarantee that the tracking error converges to a bound. Simulation examples are provided to demonstrate the effectiveness and superiority of the proposed scheme under the two quantization schemes.