Rateless Codes for the Multi-Way Relay Channel

Abstract: 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.