In order to improve the performances of a communication system, new coded cooperative communication schemes employing regular LDPC (low-density parity-check code) and irregular systematic LDPC codes respectively were proposed, and the methods of constructing the double LDPC codes used by source and relay nodes were given. The overall parity-check matrix corresponding to the double LDPC codes was deduced, then the bilayer Tanner graph of the deduced parity-check matrix was given. A new joint iterative decoding algorithm based on the bilayer Tanner graph was used for decoding of the destination node. Theoretical analysis and simulation results show that the proposed ideal LDPC-coded cooperative schemes offer a significant performance gain over the coded non-cooperative scheme under the same conditions. Under the conditions of a BER (bit error rate) of 10-5 and 10 decoding iterations, the ideal regular LDPC and irregular systematic LDPC-coded cooperative schemes achieve respectively 1.0 and 0.6 dB gains over the coded non-cooperative scheme.