Aligned Interference Neutralization and the Degrees of Freedom of the Two-User Wireless Networks with an Instantaneous Relay

A conventional relay causes a processing delay of at least one symbol duration relative to the direct paths between a source and a destination. This delay caused by using the conventional relay limits the degrees of freedom (DoF) gain in a wireless interference network. In this paper, it is shown that the exploitation of an instantaneous relay (relay-without-delay) improves DoF gain significantly for a two-user wireless network. Specifically, for two different message settings: the interference channel and the X channel, it is shown that a total of 3/2 and 5/3 DoF are achievable almost surely, respectively. The achievable schemes are inspired by the notion of aligned interference neutralization recently proposed for the layered two-user two-hop interference channel.