The capacity region of a class of broadcast channels with a sequence of less noisy receivers

Determining the capacity region of a broadcast channel consisting of k-receivers that lie in a less noisy sequence has been open, when k ≥ 3. We solve this problem for the case k = 3. Generalizing this result, we prove that superposition coding is optimal for a class of broadcast channels with a sequence of less noisy receivers. The main contribution of this work is a new information inequality, for less noisy receivers, used in the converse.