  We consider distributed Luby transform (DLT) codes for efficient packet
transmission in a multi-way relay network, where the links are modeled as
erasure channels. Density evolution is applied for asymptotic performance
analysis, and subsequently used in a linear-programming design framework for
optimizing the degree distribution at the relay in terms of overhead. Moreover
a buffer is introduced at the relay to enable efficient downlink transmission
even if packets are lost during uplink transmission. Performance losses in
terms of delay and/or erasure rates caused by link erasures during uplink
transmission are thus alleviated. The proposed DLT codes provide significant
improvements in overhead and decoded erasure rates. Numerical results for
finite-length codes follow closely the asymptotic analysis. Our results
demonstrate that the proposed buffer-based DLT codes outperform its
counterparts for lossy uplink transmission.
