In this thesis, we study the use of low-density parity check (LDPC) codes for the compress-and-forward systems. Cooperative communication has been shown effective in building a virtual multiple-antenna system which exploits the spatial diversity. Unlike the conventional amplify-and-forward (AF) and decode-and-forward (DF), thecompress-and-forward (CF) uses the relay to perform soft decoding of the received source signals , and then forwards the quantized/estimated soft information to the destination. In this thesis, we exploit the good error-correcting capability of low-density parity check codes for the compress-and-forward scheme in conjunction with the relaying based on hard bits or soft bits. Simulations show that the proposed soft information relaying scheme can outperform traditional CF scheme.