Low-density multiple-input multiple-output code (LDMC) can reduce the complexity of tree-search detection in MIMO systems. In this paper, we present a new modified progressive edge-growth (PEG) algorithm to construct large girth LDMCs, which are referred to as PEG-LDMCs. We analyze the complexity of the LDMC constrained sphere decoding (SD) and show that the LDMC constrained SD detection can be used for high reliability of the data transmission in MIMO systems. Furthermore, we propose two new efficient iterative decoding algorithms for LDMCs, which are high speed serial decoding and fast convergence shuffled decoding. Finally, we compare the bit error rate (BER) performance of PEG-LDMCs to that of the existing LDMCs. The simulation results show that the PEG-LDMCs can achieve better BER performance than that of the existing LDMCs. © 2018, The Author(s).