Linearly-coupled fountain codes for network-coded multiple access

We propose a low-complexity digital fountain approach for network-coded multiple access (NCMA), where each source node encodes its input packets using a fountain code. In NCMA, both physical-layer network coding and multiuser decoding are employed in the physical layer of the sink node, so that the output of the physical layer is the coupling of the fountain codes employed at the source nodes. We demonstrate that a belief propagation (BP) decoding algorithm can effectively decode the coupled fountain codes to recover the input packets of all source nodes. Our approach significantly reduces the decoding complexity compared with the previous NCMA schemes based on Reed-Solomon codes and random linear codes, and hence has the potential to increase throughput and decrease delay in computation-limited NCMA systems.