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The capacity of the multiple-access channel with any distribution of messagesamong the transmitting nodes was determined by Han in 1979 and the expressionof the capacity region contains a number of rate bounds and that growsexponentially with the number of messages. We derive a more compact expressionfor the capacity region of this channel in which the number of rate boundsdepends on the distribution of the messages at the encoders. Using thisexpression we prove capacity for a class of general cognitive network that wedenote as "very strong interference" regime. In this regime there is no rateloss in having all the receivers decode all the messages and the capacityregion reduces to the capacity of the compound multiple-access channel. Thisresult generalizes the "very strong interference" capacity results for theinterference channel, the cognitive interference channel, the interferencechannel with a cognitive relay and many others.

On the Capacity of a General Multiple-Access Channel and of a Cognitive Network in the Very Strong Interference Regime