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In this paper, we consider an asymmetric time-division multiple access relay system consisting of two sources, one relay and one destination, where the channel conditions and message lengths of the two sources are allowed to be different. To enhance the link robustness and the system throughput, joint network-channel coding (JNCC) is employed with a specially designed rateless code which conducts both the channel coding and network coding simultaneously. In particular, at the sources, messages are rateless coded and then broadcasted to the relay and destination. While at the relay, a novel two-dimensional (2-D) LT code is proposed, which jointly encodes the precoded message bits of the two sources using a 2-D degree profile and at the meantime completes the network coding inherently. Interestingly, the proposed scheme can be degraded to several conventional JNCC schemes based on rateless coding. To further approach the theoretical limit, the corresponding degree profiles implemented at both sources and the relay are jointly designed based on the extrinsic information transfer (EXIT) function analysis. Simulations show that our proposed JNCC scheme with the optimized degree profiles outperforms other JNCC schemes with the conventional profiles both on the BER and throughput performances.