Interference cancellation in groups

Consider a multiuser white noise channel of bandwidth W Hz, white noise spectral density η/2, with M users all received at power P, all requiring the same rate R bits/sec. It is known that that there is a Shannon capacity for the channel and that it is achievable by FDMA. This capacity can also be achieved by an interference cancellation procedure that involves M² cancellations, and Rimoldi and Urbanke (see IEEE Trans. Inform. Theory, 1994) have shown that it is achievable with at most 2M cancellation steps. We show that we can achieve rates arbitrarily close to capacity with O(1) cancellation steps in the particular case of equal powers and equal rates