We design rateless codes for correlated multi-source relay networks over packet erasure channels. In particular, we optimize relay combining process of distributed Luby transform (DLT) codes for a multi-source single-relay network where information data is correlated among the sources. Density evolution is used to characterize the asymptotic performance in terms of unrecovered information symbols termed as erasure rate. By exploiting the decoding graph, we derive the closed form expressions for asymptotic performance of DLT codes in a network where correlated sources transmit to a single destination via a relay. Consequently, a design framework is developed to optimize the degree distributions in terms of overhead. It is shown that the proposed DLT codes significantly outperform existing DLT coding schemes in terms of erasure and success rates. Numerical examples are provided to verify the asymptotic analysis. Numerical results also confirm the performance gain of the proposed DLT code as compared to its uncorrelated counterparts in the finite-length regime.
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