  In this paper, we characterize the capacity region for the two-user linear
Gaussian compound Multiple Access Channel with common message (MACC) and with
intersymbol interference (ISI) under an input power constraint. The region is
obtained by converting the channel to its equivalent memoryless one by defining
an n-block memoryless circular Gaussian compound MACC model and applying the
discrete Fourier transform (DFT) to decompose the n-block channel into a set of
independent parallel channels whose capacities can be found easily. Indeed, the
capacity region of the original Gaussian compound MACC equals that of the
n-block circular Gaussian compound MACC in the limit of infinite block length.
Then by using the obtained capacity region, we derive the capacity region of
the strong interference channel with common message and ISI.
