We present an alternative design for the physical and medium access control (MAC) layers of a wireless ad hoc network formed by half-duplex radios.  A node equipped with a half-duplex radio cannot simultaneously transmit and receive useful signals at the same frequency.  The key to the design is a signaling scheme, called rapid on-off-division duplex.  Unlike in conventional designs, where a node's transmission frames are scheduled away from its reception, RODD lets each node transmit its signal through a unique on-off duplex mask (or signature) over every frame interval, and receive a signal through each off-slot.  Over the period of a single frame, every node can transmit a message to its peers, and simultaneously receive a message from each peer.  Thus RODD allows virtual full-duplex communication using half-duplex radios without complicated scheduling at the frame level.  The throughput of RODD is determined under some simple settings, which is significantly larger than that of certain random access schemes.  RODD is especially efficient in case the dominant traffic is simultaneous broadcast from nodes to their one-hop peers.  Design issues such as peer discovery, synchronization and coding schemes will also be addressed.