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In this paper, we design capacity approaching low-density parity-check (LDPC) codes in the low signal-to-noise ratio (SNR) regime for flat Rayleigh fading channels with channel side information at transmitter and receiver. We use the structure advocated by Caire et al, which uses a single codebook with dynamic power allocation. The extrinsic information transfer (EXIT) function method is used to design the LDPC codes which approach the channel capacities. We also study the EXIT functiondoi:10.1109/tcomm.2008.041040 fatcat:haa6focuhje6zebkarm5rpvvua