Low density parity check code (LDPC) has constructed a flexible, low decoding complexity and performance close to Shannon limit benefits. This paper introduces the LDPC codes and bit-interleaved coded modulation with iterative decoding (BICM-ID) scheme, given its log-likelihood ratio belief propagation (LLR-BP) decoding algorithm. Achieved with LDPC codes as component codes in BICM-ID scheme is applied to Multi-Level Quadrature Amplitude Modulation (MQAM) in the OFDM communication system, then the performance of OFDM communication system is explored on LF, MF and HF channels based on LDPC-BICM-ID scheme and rate compatible punctured convolutional (RCPC)/Multi-level code(MLC) scheme. Simulation results show that the proposed scheme is better than RCPC / MLC scheme.