  The capacity of the multiple-access channel with any distribution of messages
among the transmitting nodes was determined by Han in 1979 and the expression
of the capacity region contains a number of rate bounds and that grows
exponentially with the number of messages. We derive a more compact expression
for the capacity region of this channel in which the number of rate bounds
depends on the distribution of the messages at the encoders. Using this
expression we prove capacity for a class of general cognitive network that we
denote as "very strong interference" regime. In this regime there is no rate
loss in having all the receivers decode all the messages and the capacity
region reduces to the capacity of the compound multiple-access channel. This
result generalizes the "very strong interference" capacity results for the
interference channel, the cognitive interference channel, the interference
channel with a cognitive relay and many others.
