The main reference for this lecture is Chapter 6 in Tse and Viswanath.
The optimal power allocation for the symmetric sum capacity is
R. Knopp and P. Humblet, "Information capacity and power control
in single-cell mulituser communications,"
Proc. of ICC '95, June 1995.
The optimal power allocation for other points in the capacity
region is discussed in
D. Tse and S. Hanly, "Multi-access Fading Channels: Part I:
Polymatroid Structure, Optimal Resource Allocation
and Throughput Capacities," IEEE trans. on
Informaiton Theory, Nov. 1998.
(In this work, the polymatroid structure of the capacity region
discussed in Lecture 18 is exploited to
find the optimal power allocation.)