  In our previous work we considered the uplink of a hexagonal cellular network
topology and showed that linear "one-shot" interference alignment (IA) schemes
are able to achieve the optimal degrees of freedom (DoFs) per user, under a
decoded-message passing framework that allows base-stations to exchange their
own decoded messages over local backhaul links. In this work, we provide the
dual framework for the downlink of cellular networks with the same backhaul
architecture, and show that for every "one-shot" IA scheme that can achieve $d$
DoFs per user in the uplink, there exists a dual "one-shot" IA scheme that can
achieve the same DoFs in the downlink. To enable "Cellular IA" for the
downlink, base-stations will now use the same local backhaul links to exchange
quantized versions of the dirty-paper precoded signals instead of user
messages.
