In this paper, we apply q-ary LDPC codes to differential modulation systems, and study the design and performance of the resultant coded modulation systems. Two low-complexity joint detection-decoding methods for noncoherent demodulation are proposed, in which the hard-message-passing strategy is used for a joint factor graph. The first method is based on the joint detection-decoding algorithm introduced in [1]; and the second one is developed by combining trellis-based differential detection and the hard-decision-based decoding of nonbinary LDPC codes. The Max-Log-MAP algorithm with soft-in hard-out is used for the differential detection. Simulation results show that both methods offer acceptable performances with greatly reduced complexities.