  We consider communication over heterogeneous parallel channels, where a
transmitter is connected to two users via two parallel channels: a MIMO
broadcast channel (BC) and a noiseless rate-limited multicast channel. We
characterize the optimal degrees of freedom (DoF) region of this setting when
the transmitter has delayed channel state information (CSIT) regarding the MIMO
BC. Our results show that jointly coding over the two channels strictly
outperforms simple channel aggregation and can even achieve the instantaneous
CSIT performance with completely outdated CSIT on the MIMO BC in the sum DoF
sense; this happens when the multicast rate of the second channel is larger
than a certain threshold. The main idea is to send information over the MIMO BC
at a rate above its capacity and then use the second channel to send additional
side information to allow for reliable decoding at both receivers. We call this
scheme a two-phase overload-multicast strategy. We show that such a strategy is
also sum DoF optimal for the K-user MIMO BC with a parallel multicast channel
when the rate of the multicast channel is high enough and can again achieve the
instantaneous CSIT performance (optimal sum DoF) with completely outdated CSIT.
For the regime where the capacity of the multicast channel is small, we propose
another joint coding strategy which is sum DoF optimal.
