Wireless (Physical Layer) Network Coding With Limited Hierarchical Side Information: Maximal Sum-Rates in 5-Node Butterfly Network

Favorable characteristics of wireless channels (including the inherent broadcast and superposition nature) provide a fertile ground for the extension of conventional network coding (NC) principles to wireless communication networks. However, the research of emerging wireless (physical layer) network coding (WNC) techniques have already revealed several non-trivial research problems that do not appear in the conventional (wireline) NC systems, including the sensitivity to channel parametrization and challenging multi-source transmission synchronization. In this paper, we uncover another significant research challenge typical for multi-node WNC systems. We show that the performance of contemporary WNC bi-directional relaying strategies is dominated by the availability of a specific hierarchical side information (HSI), required for the successful decoding of desired information from hierarchical (WNC-coded) data streams. We analyze the impact of unreliable transmission of HSI on the performance of a wireless butterfly network (WBN), and we show that all state-of-the-art relaying strategies must be appropriately modified to avoid the deterioration of WBN performance in the limited HSI regime.