We present a structured Quantize-Map-and- Forward (QMF) scheme for cooperative communication over wireless networks, that employs LDPC ensembles for the node operations and message-passing algorithms for decoding. We demonstrate through extensive simulation results over the full- duplex parallel relay network, that our scheme, with no transmit channel state information, offers a robust performance over fading channels and achieves the full diversity order of our network at moderate SNRs.