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
).