On three-receiver more capable channels

In this paper we show that superposition coding is not optimal for three-receiver more capable channels. The optimality of superposition coding region has been open for k-receiver (k ≥ 3) more capable broadcast channel. The main contribution is in identifying a counterexample to demonstrate that superposition coding is sub-optimal. We also compute the capacity region for the counter example. On the other hand, we show that the sum-capacity for a k-receiver more capable broadcast channel is obtained by transmitting all the information to the most capable receiver.