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In this paper, we consider the half-duplex cooperative multiple-access channel (CMAC). We seek to design multiple turbo codes to minimize the information outage in the block fading channel. Since we consider an outage to occur even if the message of one of the sources fails to be decoded successfully, we employ a joint network-channel coding approach in our design. The codes are optimized using the extrinsic information transfer (EXIT) chart analysis, based on the convergence thresholds of the iterative decoding tailored for CMAC. Numerical examples shows that with our design technique, the achieved frame error rate is within 0.5 dB of the information outage, while a naive code optimized for each user separately performs 2 dB away from the information outage.