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.
Index Terms-Multi-source networks, distributed LT codes, buffer, relay combining, erasure floor.
I. INTRODUCTIONR ELIABLE transmission over time-varying channels is a challenging task. For example, traditional fixed-rate channel error-control coding is inefficient, at best, subject to channel variations. A similar problem arises in broadcast and multicast transmissions where the channel links from the source to the receivers are time-invariant but different from each other. A promising approach is to employ a class of graph-based codes, termed fountain codes, first introduced in [1] as an efficient approach for reliable information delivery in broadcast and multicast transmission. These codes are rateless as the rate of the code can be adjusted on-the-fly.The first practical rateless coding scheme was the Luby transform (LT) code introduced in [2], exhibiting excellent overhead performance for transmission over a binary erasure channel Manuscript