Design of adaptive constellations and error protection coding for wireless network coding in 5-node butterfly networks

In this paper, we focus on the design of a reliable communication scheme for generic 5-node wireless butterfly networks (WBN). Since the WBN represents a natural extension of the basic two-way relay communication channel, we follow the paradigm ofWireless Physical Layer Network Coding and we show that the design of novel adaptive constellations is desirable to exploit the promising performance of wireless network coding in WBN. We introduce a systematic constellation design algorithm, and we show that the proposed constellations are capable of outperforming conventional point-to-point modulations in WBN over the whole range of channel signal to noise ratios. To further support the applicability of the proposed constellations in a practical system, we integrate a simple binary channel coding scheme, providing a robust adaptive modulation and coding scheme for relaying in symmetric WBNs with arbitrary channel conditions.