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An achievable rate region is obtained for a primary multiple access networkcoexisting with a secondary link of one transmitter and a correspondingreceiver. The rate region depicts the sum primary rate versus the secondaryrate and is established assuming that the secondary link performsrate-splitting. The achievable rate region is the union of two types ofachievable rate regions. The first type is a rate region established assumingthat the secondary receiver cannot decode any primary signal, whereas thesecond is established assuming that the secondary receiver can decode thesignal of one primary receiver. The achievable rate region is determined firstassuming discrete memoryless channel (DMC) then the results are applied to aGaussian channel. In the Gaussian channel, the performance of rate-splitting ischaracterized for the two types of rate regions. Moreover, a necessary andsufficient condition to determine which primary signal that the secondaryreceiver can decode without degrading the range of primary achievable sum ratesis provided. When this condition is satisfied by a certain primary user, thesecondary receiver can decode its signal and achieve larger rates withoutreducing the primary achievable sum rates from the case in which it does notdecode any primary signal. It is also shown that, the probability of having atleast one primary user satisfying this condition grows with the primary signalto noise ratio.

On Rate-Splitting by a Secondary Link in Multiple Access Primary Network