We consider a cognitive radio network scenario where a primary transmitter and a secondary transmitter, respectively, communicate a message to their respective primary receiver and secondary receiver over a packet-based wireless link, using a joint automatic-repeat-request (ARQ) error control scheme. The secondary transmitter assists in the retransmission of the primary message, which improves the primary performance, and is granted limited access to the transmission resources. Conventional ARQ, as well as two network-coding schemes are investigated for application in the retransmission phase; namely the static network-coding (SNC) scheme and the adaptive network-coding (ANC) scheme. For each scheme we analyze the transmission process by investigating the distribution of the number of transmission attempts and approximate it by normal distributions. Considering both the cases of an adaptive frame size and a truncated frame size, we derive analytical results on packet throughput and infer that the ANC scheme outperforms the SNC scheme.