Aligned Interference Neutralization and the Degrees of Freedom of the 2 User Interference Channel with Instantaneous Relay

It is well known that the classical 2 user Gaussian interference channel has only 1 degree of freedom (DoF), which can be achieved by orthogonal time division among the 2 users. It is also known that the use of conventional relays, which introduce a processing delay of at least one symbol duration relative to the direct paths between sources and destinations, does not increase the DoF of the 2 user interference channel. The use of instantaneous relays (relayswithout-delay) has been explored for the single user point-to-point setting and it is known that such a relay, even with memoryless forwarding at the relay, can achieve a higher capacity than conventional relays. In this work, we show that the 2 user interference channel with an instantaneous relay, achieves 32 DoF. Thus, an instantaneous relay increases not only the capacity but also the DoF of the 2 user interference channel. The achievable scheme is inspired by the aligned interference neutralization scheme recently proposed for the 2×2×2 interference channel. Remarkably the DoF gain is achieved with memoryless relays, i.e., with relays that have no memory of past received symbols. 1 ar X iv :1 10 2. 38 33 v1 [ cs .I T ] 1 8 Fe b 20 11