An Improved Algorithm for Testing the Membership of Gaussian Multiple-Access Channel Capacity Region

In this letter, we investigate the problem of testing the membership of Gaussian multiple-access channel capacity region (GMACR), which involves $2^{N}-1$ inequalities, where $N$ is the number of senders. Given a fixed rate tuple and positive power constraint, we propose a simple but efficient algorithm to test the membership of the GMACR. It is unveiled that the algorithm can be accomplished in $O(N\log _{2}N)$ operations, which is much more efficient than the approach by Zhang et al. , whose complexity bound is larger than $O(N^{5})$ .