Scalable Feedback Protocol Asymptotically Achieving Broadcast Channel Sum-capacity

Distributed feedback-protocols are developed for multi-user diversity to (a) keep the feedback amount fixed regardless of the number of users (denoted as U); (b) maintain identical protocols; (c) asymptotically achieve sum-capacity; and (d) minimize power consumption. With proposed methods, the users with signal-to-noise ratio (SNR) larger than a threshold
T

_k
send feedback messages at slot
k
.
Tk
is designed for the probability of feedback transmission at any slot to be
p
. With proper
p
, the probability of feedback from the user with the largest SNR is prescribed probability s regardless of
U
. Then, all four objectives are achieved with the proposed feedback methods.