  An achievable rate region is obtained for a primary multiple access network
coexisting with a secondary link of one transmitter and a corresponding
receiver. The rate region depicts the sum primary rate versus the secondary
rate and is established assuming that the secondary link performs
rate-splitting. The achievable rate region is the union of two types of
achievable rate regions. The first type is a rate region established assuming
that the secondary receiver cannot decode any primary signal, whereas the
second is established assuming that the secondary receiver can decode the
signal of one primary receiver. The achievable rate region is determined first
assuming discrete memoryless channel (DMC) then the results are applied to a
Gaussian channel. In the Gaussian channel, the performance of rate-splitting is
characterized for the two types of rate regions. Moreover, a necessary and
sufficient condition to determine which primary signal that the secondary
receiver can decode without degrading the range of primary achievable sum rates
is provided. When this condition is satisfied by a certain primary user, the
secondary receiver can decode its signal and achieve larger rates without
reducing the primary achievable sum rates from the case in which it does not
decode any primary signal. It is also shown that, the probability of having at
least one primary user satisfying this condition grows with the primary signal
to noise ratio.
