Soliton-like network coding for a single relay

For the binary erasure channel, Luby Transform (LT) and Raptors codes have been shown to achieve capacity by carefully designed degree distributions for multicasting scenarios. Generalizing fountain codes to multihop networks requires transport nodes to perform network coding (NC). However, if intermediate nodes perform decentralized NC blindly, the statistical properties imposed by the fountain code are lost, and thus, a Gaussian elimination decoder must be used at the sink at the cost of significant increase in complexity compared to a belief propagation (BP) decoder. Addressing this problem, in this paper, we propose a new protocol, namely Soliton-like rateless coding (SLRC), by exploiting the benefits of fountain coding and NC coding over a Y-network. Ensuring key properties of the fountain code are preserved, BP can be effectively applied when transport nodes perform NC. The SLRC scheme is evaluated against buffer-and-forwarding, and other state of the art schemes; SLRC exhibits a 5% reduction in overhead at high decoding success rates. Simulations show that the proposed scheme preserves the benefits of NC and fountain coding.