Outage Performance of Fountain‐Coded NOMA‐Based Hybrid Satellite‐Terrestrial Relay Networks

This paper investigates the outage performance of a Fountain‐coded non‐orthogonal multiple access (NOMA) hybrid satellite–terrestrial relay (HSTR) network serving two multicast user clusters. The satellite independently generates Fountain‐coded packets for the two clusters and superimposes them using power‐domain NOMA. A half‐duplex decode‐and‐forward (HD‐DF) terrestrial relay is employed as a low‐complexity regenerative forwarding node when reliable direct satellite‐to‐user links are unavailable. The relay adopts a state‐dependent forwarding rule: it jointly forwards both decoded packets using NOMA when both streams are recovered, whereas it assigns its full transmit power to the far‐cluster packet when only that packet is successfully decoded. Fountain‐code recovery is modeled through a finite‐window packet‐accumulation abstraction in which the required number of received encoded packets is related to the source‐block size and coding overhead. Considering Shadowed‐Rician fading for the satellite‐to‐relay link and Rayleigh fading for the terrestrial links, analytical expressions are derived for the relay decoding states, packet‐success probabilities, and multicast cluster outage probabilities. Because both clusters experience the same sequence of relay decoding states, their finite‐window recovery events are statistically coupled even though their terrestrial fading channels are independent. We therefore derive the joint system outage probability by conditioning on the common relay‐state counts rather than multiplying the marginal cluster‐success probabilities. Monte Carlo simulations validate the analytical results and quantify the effects of transmit SNR, NOMA power allocation, Fountain‐code recovery overhead, transmission‐window length, and cluster size. Resource‐matched OMA‐Fountain and non‐accumulating NOMA benchmarks are further introduced to distinguish the gains associated with non‐orthogonal transmission and finite‐window Fountain‐packet accumulation. The results identify the reliability tradeoffs among power allocation, coding overhead, transmission delay, and multicast group size.