Distributed Luby transform (DLT) codes achieve significant performance improvement in multi-source relay networks compared to the individual Luby transform (LT) code designed for each source. Since the DLT codes preserve the properties of the LT codes, the error floor is dominated by the low variablenode degrees in the bipartite graph, developed for iterative message passing decoding. Therefore, we analyze the error floor of the DLT codes for a multi-source, single relay, and single destination network over additive white Gaussian noise (AWGN) channels.We modify the encoding process at the sources and propose a new relay combining scheme at the relay. The encoding process at the sources and combining scheme at the relay are coordinated with the aim of improving the error floor performance of the proposed DLT codes. We derive a lower bound of the bit error probability of the DLT codes over AWGN channels. Furthermore, we optimize the relay degree distribution in terms of the overhead by using the framework of extrinsic information transfer (EXIT) chart analysis. Numerical results confirm that the proposed DLT coding scheme significantly outperforms the conventional scheme, especially in the error floor region. identifier:https://dspace.jaist.ac.jp/dspace/handle/10119/15537