Cognitive radio (CR) is an emerging and powerful solution that can significantly improve the utilization of limited radio spectrum resources by allowing secondary users to borrow unused spectrum from primary licensed networks. In conventional CR protocols, a secondary user (SU) is allowed to transmit only when the primary users (PU) are not active. However, waiting for idle timeslots may induce large packet delay and loss and result in poor quality of service (QoS) for the secondary user. To overcome this, a joint coding and scheduling method for cognitive multiple access is proposed in this paper. In the physical layer, a successive interference decoder is utilized to thoroughly mitigate the SU's interference to PU. A joint channel-aware and queue-aware scheduling protocol is then proposed, at the MAC layer, to minimize the average packet delay of SU given an average transmit power constraint. We shall formulate Markov models to derive the analytical results of delay, packet-loss rate, and power consumption of the proposed scheme. The optimal scheduling parameter and the minimal average delay are also obtained by solving a cross-layer optimization problem.