In this paper, we examine the marriage of Fountain coding and network coding (NC). Fountain codes are capacity achieving erasure codes designed for point-to-point transmissions. NC is a throughput-optimal data dissemination technique, but its high-complexity decoding makes it unattractive for applications where limited resources are available. In this paper, we consider Fountain network coding to take advantage of efficient fountain decoders. Protocols such as Soliton-like rateless coding (SLRC) have previously addressed this issue, yet the re-encoding at the relay is expensive while there is still room for improving the performance. Extending SLRC, we propose the Improved Soliton-like Rateless Coding (ISLRC) protocol, where the relay is designed to perform distribution shaping given limited resources. ISLRC preserves the same properties as SLRC, but also makes the aggregate degree distribution more efficient for Fountain decoding. We analyze ISLRC's degree distribution and perform an asymptotic error analysis for the case where resources are most scarce. The ISLRC scheme is compared against other existing schemes. Simulation results show that even under the worst-case scenario of ISLRC, better performance can be achieved compared to SLRC and other existing schemes.

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. Additionally, the proposed coding protocol is resilient to nodes churn rates. The SLRC scheme is evaluated against buffer-and-forwarding, and the distributed LT (DLT) codes; SLRC exhibits a 5% reduction in overhead compared to the state of the art DLT code at high decoding success rates. Simulations show that the proposed scheme preserves the benefits of NC and fountain coding.