A butterfly network (BFN) consisting of 2 source
nodes, 2 destination nodes, and a relay, with relay-source
feedback is considered. Transmission schemes are proposed for
this setup, which exploit feedback based on compute-forward
using nested-lattice codes. A novel nested-lattice interference
neutralization strategy is also proposed. The performance of these
schemes is compared and discussed, and it is shown that these
schemes can provide net-gain, i.e., the gain in the sum-capacity
gain is larger than the number of feedback bits invested.