Interference channel with delay: Noisy interference

We consider the interference channel with two transmit-receive pairs when there is a delay in receiving the desired message compared to interference. We study this channel in the weak interference regime (noisy interference), and show that delay does not affect the capacity of the interference channel in this region. This also holds for an interference channel with a more general delay, where receiving the desired message is delayed compared to the interference, or vice versa. This result is then applied to a previous results on the interference MIMO relay channel where a scheme is used to transform it to an interference channel with delay. We show that using a relay can be helpful when interference is treated as noise in the interference relay channel.