  It is known that the capacity of parallel (multi-carrier) Gaussian
point-to-point, multiple access and broadcast channels can be achieved by
separate encoding for each subchannel (carrier) subject to a power allocation
across carriers. In this paper we show that such a separation does not apply to
parallel Gaussian interference channels in general. A counter-example is
provided in the form of a 3 user interference channel where separate encoding
can only achieve a sum capacity of $\log({SNR})+o(\log({SNR}))$ per carrier
while the actual capacity, achieved only by joint-encoding across carriers, is
$3/2\log({SNR}))+o(\log({SNR}))$ per carrier. As a byproduct of our analysis,
we propose a class of multiple-access-outerbounds on the capacity of the 3 user
interference channel.
