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For non-contiguous OFDM (NC-OFDM) based communication systems, especially NC-OFDM-based cognitive ratio (CR) systems, one of critical challenges is to establish spectrum synchronization between the transmitter and receiver before data transmission. In , an a posterior probability (APP) detection algorithm has been proposed for the receiver to detect the subchannels occupied by the transmitter (active subchannels). However, the encoding scheme adopted in  is a concatenation of a convolutional coder and a low rate repetition coder so that the system code rate is only 1/4 when half of the subcarriers are active. In this paper, we consider using low density parity-check (LDPC) codes to improve the system data transmission rate. Furthermore, with the channel model a of NC-OFDM-based communication system, we employ density evolution algorithm to obtain good degree distribution pairs and adopt a modified progressive edge-growth (PEG) algorithm to construct the parity-check matrix for the LDPC code. Simulation results show that our optimized LDPC code for NC-OFDM-based communication systems could obtain satisfactory error performance at a high data transmission rate (system code rate of 1/2).