A symmetric butterfly network (BFN) with a full-duplex relay operating in a bi-directional fashion for feedback is considered. This network is relevant for a variety of wireless networks, including cellular systems dealing with cell-edge users. Upper bounds on the capacity region of the general memoryless BFN with feedback are derived based on cut-set and cooperation arguments and then specialized to the linear deterministic BFN with really-source feedback. It is shown that the upper bounds are achievable using combinations of the compute-forward strategy and the classical decode-and-forward strategy, thus fully characterizing the capacity region. It is shown that net rate gains are possible in certain parameter regimes.
@article{arxiv.1207.6540,
title = {Achieving Net Feedback Gain in the Butterfly Network with a Full-Duplex Bidirectional Relay},
author = {Anas Chaaban and Aydin Sezgin and Daniela Tuninetti},
journal= {arXiv preprint arXiv:1207.6540},
year = {2012}
}