Erasure Floor Analysis of Distributed LT Codes

We investigate the erasure floor performance of distributed Luby transform (DLT) codes for transmission within a multi-source, single-relay, and single-destination erasure-link network. In general, Luby transform (LT) codes exhibit a high erasure floor due to poor minimum-distance properties, which can be improved by maximizing the minimum variable-node degree. The same behavior is observed for DLT codes, and therefore a new combining scheme at the relay is proposed to maximize the minimum variable-node degree in the decoding graph. Furthermore, the encoding process at the sources and the combining scheme at the relay are coordinated to improve the transmission overhead. To characterize the asymptotic performance of the proposed DLT codes, we derive closed-form density-evolution expressions, considering both lossless and lossy source-relay channels, respectively. To support the asymptotic analysis, we evaluate the performance of the proposed DLT codes by numerical examples and demonstrate that the numerical results correspond closely to the analysis. Significant improvements in both the erasure floor and transmission overhead are obtained for the proposed DLT codes, as compared to conventional DLT codes.