For fading broadcast channels, different capacity regions such as the ergodic, outage, minimum rate, or limited-jitter capacity region can be represented by a triplet of rate constraint parameters from each user: a maximum rate, a minimum rate, and a shortage probability over which the minimum rate needs not be guaranteed. For each fading state, the capacity region is obtained by evaluating a finite set of possible extreme points. The optimal power allocation strategy across fading states is determined by the power requirements associated with the maximum and minimum rates, combined with water-filling for the excess power when the maximum and minimum rate constraints are not tight. Shortage capacity can be obtained by optimizing the power allocation over the shortage fading states, when the minimum rate constraints are removed, and the non-shortage fading states.
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